Econophysicobabble

by Daniel on October 22, 2004

Oh goody, I’ve been waiting for Pile On Stephen Landsburg Week. That column of his in Slate has been winding me up for years.

As my contribution, check out this guest contribution to Marginal Revolution, where half-understood physics meets half-understood economics, with predictable results.

The guts of the post are as follows:

Let’s play a coordination game: You and I are each asked a single question, either “Do you like cats?” or “Do you like dogs?”. Our questions are determined by independent coin flips. We both win if our answers differ, unless we’re both asked about dogs, in which case we both win if our answers match.

Here’s a pretty good strategy we could agree on in advance: We’ll contrive to always differ. Whatever we’re asked, I’ll say yes and you say no. That way we win 3/4 of the time.

Can we do any better? No, if we live in a world governed by classical physics. Yes, if we live in the world we actually inhabit—-the world of quantum mechanics.

I think I know a way to do better, using only classical physics.

If I take in my right hand a notepad and in my left hand a pencil (both objects of classical physics), then I can simply write down the sentence [for example] “They asked me about dogs and I said yes”. Then I take it round to Landsburg’s office and show it to him, then he answers.

I estimate that I could get roughly 90% wins in this method (it would be 100%, but I’m allowing for the fact that 1 time in 10, Landsburg will fuck it up on purpose and write an article about how “counterintuitive” he’s being). This is better than chance, and also better than the 85% win rate that you can apparently get with some sort of funky quantum nonlocality or other.

The point is quite simple. A non-communication game is a non-communication game, and a communication game is a communication game. It doesn’t matter (for the purposes of economics) whether the communication takes the form of face-to-face contact, Bell’s effect or carrier pigeons. What does matter is whether the communication is credible or not; whether it is “cheap talk” whereby it doesn’t cost me anything to give a false signal, or whether there is an incentive condition which means that Landsburg could rely on my not intentionally misrepresenting things to gain some advantage, and whether or not the signal is observed perfectly or with noise. Landsburg is simply wrong to say that “game theory changes dramatically when players have access to quantum technology”, because no important points of economics turn on the precise mechanism of communication.

(In fairness to the authors of the paper Landsburg cites, they aren’t responsible for the use he made of their work; the “games” in their paper have no economic significance and are just being used as convenient ways to describe bounds on the information that can be communicated through a quantum channel. This way of talking about information transfer has been a standard in the engineering literature ever since the original Kelly Betting paper.

Anyone who was thinking for even a minute would have realised that this paper had nothing to do with game theory, and that the “co-ordination game” example was a clear cheat. So why didn’t Landsburg? I can only assume that it’s part of a more general phenomenon; the tendency of economists (and social scientists in general) to drop all their critical phenomena and fall into a swoon when they see the manly form of a physicist. Phil Mirowski makes a decent case that modern economics was conceived in this kind of physics-envy so it’s not exactly surprising, but that doesn’t make it any more correct. Here’s a few things that social scientists should always remember:

1) Despite what they tell you, physicists are human beings. They eat, fart and have sex more or less like the rest of us. There is no secret caste of physicists set apart from humanity; the difference between them and us is that they did a physics degree.

2) There is, to a first approximation, a continuum of physicists on a quality scale going from “genius” to “halfwit”. They come in good and bad varieties, and the bad ones are really quite bad. Furthermore, it is not difficult to tell the difference if you are prepared to learn a little mathematics and apply yourself. Cosma Shalizi tells the tale of statistical physicists who identify power law distributions by considering the R^2 value from a linear regression, and get their papers published. This on its own ought to diminish one’s respect for physicists to healthy levels.

3) That subset of physicists who regularly publish papers on social sciences is unlikely to be a sample from the cream of the profession. To the best of my knowledge, Steven Hawking has kept his opinions on the stock market to himself, and so did Richard Feynman. There are some very good papers in the econophysics literature (if you really want to know about quantum mechanics applied to game theory, here’s an introduction for you, but it doesn’t make the claim to have overturned the fundamentals of the field, or that quantum effects make a difference to classical games. NB also that Landsburg’s paper doesn’t cite Eisert et al’s paper on quantum game theory, illustrating my point that it’s not about economics), but they are massively outnumbered by pieces of work written by second-rate physicists who have decided to set out an ill-informed brain dump on some aspect of the social sciences because they erroneously believe them to be “easier” than doing physics. Have a look on the arxiv if you don’t believe me.

{ 125 comments }

1

dsquared 10.22.04 at 10:01 pm

btw, I personally believe that rigorous quantum game theory is a bit of a cheat too. In the classical sheriff and crooks variety, I’m not allowed to adopt the strategy “I won’t grass, but only if he doesn’t as well”, so it’s unlikely that the sherriff will co-operate in my using some physical device which provides the same sort of effect.

2

Steven E. Landsburg 10.22.04 at 10:18 pm

Oh my Lord, get serious. Did you truly not understand that the implied rules of this game included “no transmission of information”? Or that once you’ve picked up on that implication, your objections vanish completely?

Re citations to Eisert and Wilkens: They weren’t relevant here. I’ve cited them repeatedly in print and in papers soon to be published. I’d prefer to cite what’s relevant where it’s relevant, rather than drop names for the sake of dropping names.

And finally, with regard to this imagined deference toward physicists: I’ve refereed half a dozen jounral articles on quantum game theory in the past few months. I doubt that the recipients of those reports perceived a lot of undue deference.

3

Giles 10.22.04 at 10:25 pm

4. No one in Physics has actually come up with anything innovative and useful in the last 50 years. And quantum theory is the current example.

On the other hand I do think its a bit of a generational thing – economists born in the nuclear age tend to see physists as the highest form of life but now days that perch is occupied by biologists.

4

Joe O 10.22.04 at 10:27 pm

The apparatus described by Landberg is a very complicated communication system indeed.

The thing that I don’t understand is that I thought that communication systems are limited by the speed of light. It seems like the system Landberg describes could be set up to transfer “information” at faster than the speeed of light.

5

dsquared 10.22.04 at 10:42 pm

Hullo, Stephen.

Did you truly not understand that the implied rules of this game included “no transmission of information”? Or that once you’ve picked up on that implication, your objections vanish completely?

I thought I’d made this clear. Once you’ve picked up on that implication, the model vanishes completely. “No transfer of information” means what it says, not “no transfer of information other than through quantum effects”. What the paper you linked to says is, effectively, that if you can communicate, coordination games are a whole lot easier.

“Landsburg’s paper” above refers (slightly unclearly) to the paper you linked to, not your own comment. It doesn’t cite Eisert because it’s very clearly not an economics paper; it’s a paper about quantum communication.

Finally, why am I not surprised by this?

I’ve refereed half a dozen jounral articles on quantum game theory in the past few months.

You should have done a better job; most of the published ones are dreadful.

6

Factory 10.22.04 at 10:56 pm

I suggest we all form a circle around dsquared and steven landsburg and start chanting ‘Fight, fight, fight!’.
One has to do these things according to schoolyard traditions indeed.

7

junius ponds 10.22.04 at 10:58 pm

The article would be much improved if it 1.) gave the state of the entangled particle (presumably |0>|1>-|1>|0>/sqrt(2)) and 2.) actually gave the bases in which measurements are to be made> Instead of having decipher the bit about instrument rotation, all one would have to do is a bit of algebra and application of the rule for collapse.

8

Ted Barlow 10.22.04 at 10:58 pm

Stephen,

For the record, I enjoy your column and quite liked most of your book (Everyday Economics), but it seems that Daniel does have the better argument here. It’s not terribly meaningful to say that you can’t coordinate except for quantum effects. Quantum effects are fascinating, but you might as well make an exception for cell phones, or walkie-talkies, or photons when you give the thumbs-up/thumbs-down signal. Either you’re transmitting information or you’re not.

9

Cosma 10.22.04 at 11:00 pm

This is a tangent, but I’d strongly advised Giles to actually read a modern textbook on condensed matter physics (Chaikin and Lubensky is good, and comparatively cheap in paperback) before offering opinions on whether physicists have done anything innovative and useful in the last fifty years.

10

Lindsay Beyerstein 10.22.04 at 11:01 pm

Steven, why does your solution respect the “no transmission of information” rule?

11

junius ponds 10.22.04 at 11:01 pm

Excuse me, I mean the blog post, not the article. I suppose I should actually look at the latter (RTFA and all.)

12

Steven E. Landsburg 10.22.04 at 11:02 pm

You seem to be asserting that the EPR effect constitutes a transfer of information. I would quite disagree with this, but surely that disagreement would come down to a matter of semantics. The fact remains that if we play this game in separate rooms, and are both required to submit our answers in less time than it would take to send a light signal from one room to the other, then you can do better using the EPR effect than you can in a world ruled by classical physics.

So under rules of the game that I did not make explicit in this informal post, but I’d have thought would be clear to any thoughtful reader, yes, quantum effects really do change the outcome of the game.

And finally:

“I’ve refereed half a dozen jounral articles on quantum game theory in the past few months.”

You should have done a better job; most of the published ones are dreadful.

Did I say I’d accepted any?

13

Ted Barlow 10.22.04 at 11:02 pm

(That’s “Steven”, and that’s “Armchair Economist”. The Onion regrets the error.)

14

Steven E. Landsburg 10.22.04 at 11:03 pm

You seem to be asserting that the EPR effect constitutes a transfer of information. I would quite disagree with this, but surely that disagreement would come down to a matter of semantics. The fact remains that if we play this game in separate rooms, and are both required to submit our answers in less time than it would take to send a light signal from one room to the other, then you can do better using the EPR effect than you can in a world ruled by classical physics.

So under rules of the game that I did not make explicit in this informal post, but I’d have thought would be clear to any thoughtful reader, yes, quantum effects really do change the outcome of the game.

And finally:

“I’ve refereed half a dozen jounral articles on quantum game theory in the past few months.”

You should have done a better job; most of the published ones are dreadful.

Did I say I’d accepted any?

15

Sven 10.22.04 at 11:07 pm

I have to agree with Giles; the intellectual penis envy du jour is biology. Can anyone guess who wrote the following? (hint: he runs a very popular web log)

[A] proper understanding of the role of democracy in our constitutional system suggests that many of the structural reforms being urged by some who complain about special interest dominance are likely to make things worse, rather than better.

To explore this idea, I have chosen as an analogy or metaphor another widely criticized and
misunderstood institution–sex. In short, some discoveries resulting from the application of complexity theory to the question of evolutionary fitness among biological systems have important implications for our discussion of the fitness of the body politic. Both kinds of systems face a similarproblem – maintaining a balance between adaptability and stability on the one hand, while resisting parasitism on the other.

16

John S 10.22.04 at 11:07 pm

In case some readers of this blog have never read Landsburg’s Slate columns and his book ‘The armchair economist’, don’t let this post and John Quiggin’s earlier post put you off. They are well written, even if you don’t agree with them.

File these snipes at Landsburg under “US writers for the masses – must be critised” along with CT’s swipes against Thomas Friedman and Nicholas Kristof and make your own minds up.

17

mg 10.22.04 at 11:08 pm

The fact remains that if we play this game in separate rooms, and are both required to submit our answers in less time than it would take to send a light signal from one room to the other…

…then neither of you would be able to submit an answer on time?

18

junius ponds 10.22.04 at 11:09 pm

>…then neither of you would be able to submit an answer on time?< Or they could be separated by a space-like interval.

19

mg 10.22.04 at 11:16 pm

Um, junius ponds, in case that was directed at me(and even if it wasn’t), I don’t get it. Could you explain?

20

Detached Observer 10.22.04 at 11:22 pm

Steven Landsburg wrote “The fact remains that if we play this game in separate rooms, and are both required to submit our answers in less time than it would take to send a light signal from one room to the other…

This is just patently silly.

21

junius ponds 10.22.04 at 11:24 pm

Eh, I was speculating that the strategy might have relevance if the rooms are separated at such a distance that no signal sent from Room A could reach Room B before an answer is due in B, and vice versa. EPR collapse is instantaneous, naturally.

22

Glenn 10.22.04 at 11:25 pm

Erm, IIRC(and I may not), Landberg is correct here. There is no communication of information here. In no way, shape, or form are you breaking the rules of the game–quantum entanglement is not like a transmitter. THats why the speed of light issue doesn’t wreck causality.

23

Steven E. Landsburg 10.22.04 at 11:29 pm

Steven Landsburg wrote “The fact remains that if we play this game in separate rooms, and are both required to submit our answers in less time than it would take to send a light signal from one room to the other…”

This is just patently silly.

No it’s not. Suppose the rooms have been sealed off from each other in such a way that we couldn’t possibly send a light signal from one to the other without ten minutes of digging. What’s patently silly about being required to submit our answers within ten minutes?

24

dsquared 10.22.04 at 11:35 pm

Hmmm, yes, every time I say “not allowed to communicate” I assume that everyone knows I really mean that we’re travelling on a train at just below the speed of light, with questioner sitting on a chair in St Pancras station.

Whether or not you want to define quantum entanglement as transmission in the physical sense, it’s damn obvious “to any thoughtful observer” that introducing strategies which condition one player’s choice of strategy on the other player’s choice is breaking the non-communication criterion. In the rigorous version Prisoner’s Dilemma, the condition is that the strategies have to be chosen independently of one another. Strategies specified over entangled quanta aren’t independent.

25

Glenn Bridgman 10.22.04 at 11:40 pm

“condition one player’s choice of strategy on the other player’s choice”

You misunderstand quantum entanglement; there is no “condition”/causation involved.

26

dsquared 10.22.04 at 11:41 pm

In no way, shape, or form are you breaking the rules of the game—quantum entanglement is not like a transmitter

However, it does get information from one place to another. By the mechanism described in the linked paper, it would be possible for me, over time and with probability of accurate reception as close to 1 as you like, send the message “Mary Had A Little Lamb” from one room to another, if I had set up the code beforehand. This is communication as far as the Prisoner’s Dilemma is concerned.

27

Steven E. Landsburg 10.22.04 at 11:43 pm

introducing strategies which condition one player’s choice of strategy on the other player’s choice is breaking the non-communication criterion. In the rigorous version Prisoner’s Dilemma, the condition is that the strategies have to be chosen independently of one another. Strategies specified over entangled quanta aren’t independent.

Yes, precisely the point. The referee can separate us by any distance he wants to, and can put up any barriers he wants between us, and yet still can’t force us to play independent strategies. So when we have access to entangled particles, the “rigorous version Prisoner’s Dilemma” becomes a poor model of the game we’re actually playing.

It’s easy to rule out quantum strategies in a purely theoretical context by just issuing a fiat that players aren’t allowed to use them. But if the model is supposed to reflect reality, and if in reality the players can use quantum strategies, then a model without quantum strategies is a poor model.

28

junius ponds 10.22.04 at 11:47 pm

>over time and with probability of accurate reception as close to 1 as you like, send the message “Mary Had A Little Lamb” from one room to another< If that's the case, there's something wrong with the description of the mechanism. The statistics of entangled particles should not be affected by measurement; in the simplest case, measuring (|0>|0> + |1>|1>)/sqrt(2) in the |0>&|1> basis, the probability of Bob measuring 1 is 1/2 regardless of whether Alice has measured or not, because Alice cannot control the fact that the system will collapse to |1>|1> with probability 1/2 upon her own measurement.

29

Glenn Bridgman 10.22.04 at 11:48 pm

“it would be possible for me, over time and with probability of accurate reception as close to 1 as you like, send the message “Mary Had A Little Lamb” from one room to another, if I had set up the code beforehand.”

No you wouldn’t. That would cause all sorts of causality madness. To quote wiki:
“Although no information can be transmitted through entanglement alone, it is possible to transmit information using a set of entangled states used in conjunction with a classical information channel.”
AFAIK, there is no classical information channel during the experiment, thus no information is transmitted.

I admit that this is semantically unsatisfying, but in a purely rigerous sense he’s correct.

30

Lindsay Beyerstein 10.22.04 at 11:53 pm

If Steven’s quantum solution isn’t information transfer, I’d like to know why.

This isn’t just a semantic question. If Steven’s solution is a high tech way of transferring information, then the quantum method is no better than Daniel’s satirical pencil and paper proposal.

The interesting solutions to coordination problems explain what you ought to do when you are completely disconnected from your partner. Any solution that exploits a causal connection between your partner and yourself subverts the puzzle.

Sure it’s interesting that our best physics allows for faster than light transmissions of information through walls. But that doesn’t say anything interesting about coordination problems, per se. All it says is that it’s harder to achieve a true coordination situation than we thought because the participants might exploiting quantum physics as opposed to psychic powers or drugging the sheriff or writing down their answers and showing each other.

31

Steven E. Landsburg 10.22.04 at 11:54 pm

dsquared: it would be possible for me, over time and with probability of accurate reception as close to 1 as you like, send the message “Mary Had A Little Lamb” from one room to another, if I had set up the code beforehand.”

glenn bridgman (and in spirit junius ponds): No you wouldn’t.

Well, sure he would, since he specified “over time”, which means he can use Quiggen’s original mechanism: Write down the words to “Mary had a little lamb” on a piece of paper and walk it over to the other room.

But if he thinks he can actually transmit information via the EPR channel, he is, of course, just confused.

32

junius ponds 10.22.04 at 11:55 pm

Yes, in the example I provided, Alice or Bob 1.) doesn’t know if the other has already measured and 2.) cannot send information by choosing |0>|0> or |1>|1>, because that’s probabilistic. Though there’s an odd correlation, no information is actually transmitted. If both parties follow a prearranged procedure in which they answer in the affirmative or negative to some question depending on the measurement outcomes, both _know_ what the other will be answering, provided no one cheats — hence the (false) intuition that information is actually transmitted.

33

dsquared 10.22.04 at 11:58 pm

The referee can separate us by any distance he wants to, and can put up any barriers he wants between us, and yet still can’t force us to play independent strategies

Don’t be silly. You’re in the sheriff’s office, he’s got the light shining in your eyes, he says “So what’s it gonna be, Stevie-boy? Are you gonna talk or not?”

Then you say “actually, my answer would be a superposition of states to be determined by an observation of this entangled particle”.

What’s wrong with this story?

It’s easy to rule out quantum strategies in a purely theoretical context by just issuing a fiat that players aren’t allowed to use them. But if the model is supposed to reflect reality, and if in reality the players can use quantum strategies, then a model without quantum strategies is a poor model

See, this is why these models are full of it. How many assumptions do you need to be able to assume that the players can use quantum strategies? In the Eisert Prisoner’s Dilemma example, pretend that you’re the chap who’s decided on the superposition of states. You observe the spin and the particle tells you to hang tough and not confess. What do you do? You lie about what the particle said, and confess. The only way that this argument can get off the ground is if a third neutral party makes the observations. You could ask the sheriff to perform this function, but I daresay you’d be out of luck.

34

Steven E. Landsburg 10.23.04 at 12:00 am

Lindsay Beyerstein: If Steven’s quantum solution isn’t information transfer, I’d like to know why.

What is the piece of information that you think is being transferred?

35

Glenn Bridgman 10.23.04 at 12:04 am

Lindsay, relatitivy forbids information being traveled faster than the speed of light. Since the decoherence of the entanglement occurs instantaenously, any information being transfered via that channel is going to be transfered faster than c, thus, no information is transfered.

There is no “causal connection” whatsoever. It is merely a peculiar result of quantum decoherence that doesn’t match up well with our understanding of the classical world.

Steven: Well yeah:p

36

dsquared 10.23.04 at 12:09 am

Glenn:

AFAIK, there is no classical information channel during the experiment, thus no information is transmitted

If there is no classical information channel, then how does Alice know that Bob has an entangled particle in his pocket?

The information is “transmitted” in the same way as it was in Nicholas Gisin’s Geneva experiment; since we have arranged a code ahead of time, we know that if the particle’s spin has one value the other particle must have coded “Mary Had A Little Lamb”, but if it spins the other way it coded “Crooked Timber Is The Greatest”. In the same way, a single lamp in the Old North Church doesn’t itself carry the information “Paul Revere will be coming by land”, but in the right context, it sends that message.

37

Glenn Bridgman 10.23.04 at 12:10 am

D^2, as far as I can see, this method doesn’t puport to solve the prisoners dilemma, mainly because quantum entanglement doesn’t address the conflict of interest at the heart of the PD. In this problem, there is no such conflict, and thus quantum entanglement is useful.

38

Steven E. Landsburg 10.23.04 at 12:11 am

dsquared: You observe the spin and the particle tells you to hang tough and not confess. What do you do? You lie about what the particle said, and confess.

In other words, you either don’t understand what a Nash equilibrium is or don’t understand what the referee observes in the Eisert/Wilkens game.

39

Lindsay Beyerstein 10.23.04 at 12:15 am

Maybe I’m misunderstanding, but it seems to me that exploiting a known correlation is an example of transferring information.

You are not sending a traditional coded signal to your partner, but you are making inferences from facts about entangled particles.

The point is that you can infer what question your partner got from the state of your particle. Once you have evidence of what your partner did, then you’re no longer facing a coordination problem.

40

Steven E. Landsburg 10.23.04 at 12:16 am

dsquared: we know that if the particle’s spin has one value the other particle must have coded “Mary Had A Little Lamb”, but if it spins the other way it coded “Crooked Timber Is The Greatest”.

We know absolutely nothing of the kind, because we know that in equilibrium, the other player will not make a measurement that distinguishes between “Mary” and “Crooked”; he will make some entirely different measurement whose results, as far as we know, are equally likely to be “Jingle Bells” and “Three Blind Mice”.

41

Glenn Bridgman 10.23.04 at 12:17 am

D^2, the Revere analogy and other such arguments aboute “codes” are fallacious. It doeesn’t matter what meaning we assign to each possible outcome, the issue is, given a set of potential communications, which one is the real deal? The lamp communicates precisely one bit of information, whether we identify that information as {1, 0} or {By Land, By Sea}. Meaning is a seperate concept from information.

42

Steven E. Landsburg 10.23.04 at 12:18 am

lindsey beyerstein: The point is that you can infer what question your partner got from the state of your particle.

Absolutely false.

43

Glenn Bridgman 10.23.04 at 12:24 am

Lindsay, let’s say you get the dog question and the particle corresponds to “Yes.” What exactly can you tell about the state of your partners particle?

44

Cosma 10.23.04 at 12:32 am

Having just read the Cleve et al. paper that’s in question, I have to say that there does seem to be a serious difference between the classical and quantum set-ups in terms of the resources available to the players. In the classical case, the players only have access to the questions and independent random bits. In the quantum case, they have those plus access to a pair of entangled qubits. They don’t have to talk with each other, but they do condition their actions on those entangled qubits. This isn’t exactly communication, since no signal goes from one player to another, but it is coordinating on related signals, which isn’t available in the classical case. The appropriate classical analog would be for the players to share access to a set of classical random variables which are independent of the questions but correlated with one another. Without going through the math (it’s Friday night!), I suspect that Bell’s theorem will mean that the quantum players can coordinate better than their counterparts who just share classical signals, but that’s the comparison which needs to be made.

(I can’t wait to tell me experimentalist friends that it’s “easy” for them to create entangled qubits and preserve their entanglement in the face of environmental decoherence.)

45

dsquared 10.23.04 at 12:43 am

Stephen, in re Eisert/Wilkens: Yes I do. I was making the point that this game assumes by fiat the existence of a referee who does a lot of work that would not obviously be done in a variety of real-world situations.

Glenn: When I’m overseas, I have an arrangement with my wife that I’ll call her at 5pm every day to let her know I’m alright. On the day she doesn’t get a call, at 5pm, instantaneously, her information set changes. Obviously no information has been transmitted, because you can’t transmit information by not making a phone call, but there has been a kind of communication. It’s something similar that’s going on in the game-theory example.

46

John Quiggin 10.23.04 at 12:43 am

Glenn, unless I’ve misunderstood this one completely, I would say I can infer with 85 per cent probability that the event {DOG & PP=Yes} OR {CAT & PP=No} has occurred.

Since (before the true answer is known) I could construct and trade in a security with payoff contingent on this event, it certainly seems to me that I’ve acquired some information in the sense in which the term is used by economists.

47

ogged 10.23.04 at 12:46 am

Hey, Cosma actually reads the paper! Which, it should also be noted, contains this sentence:

In a classical strategy, the players can only share classical information; whereas, in a quantum strategy, the players are permitted to share quantum information.

Is the nub of the matter some difference between “communication” and “sharing quantum information?” Perhaps Steven or Glenn could explain that distinction.

48

Glenn Bridgman 10.23.04 at 12:48 am

Cosma:
As far as I can see it, those “correlated” classical variables are simply a reformulation of the strategy one decides on beforehand without entanglement. Essentially, that “correlation” is a pair of functions q and k which take as input whether the question is the cat or dog one and output yes or no. The strategy steven describes can be thought of as q(x)=yes and k(x)=no for all x. This is the correlation you describe, and it maxes out at 3/4.

I lack the physics toolkit to analyze the quantum problem(sue me, I’m only a freshman:p), but evidently it maxes out at cos^2(pi/8), which is greater than 3/4, verifying your hypothesis.

49

Steven E. Landsburg 10.23.04 at 12:51 am

Glenn, unless I’ve misunderstood this one completely, I would say I can infer with 85 per cent probability that the event {DOG & PP=Yes} OR {CAT & PP=No} has occurred.

Yes, and you can infer with 100 percent probability that the other player will play an equilibrium strategy.

Better yet, if your friend writes down a poem, gives you a Xerox copy and keeps the original, you can infer with 100 percent probability that the poem in your pocket is identical to the poem in his pocket.

So what?

50

Brian Weatherson 10.23.04 at 12:54 am

Lindsay overstates the case that we can make precise inferences from the state of the particles, but it’s true that there is some information transferred. (This argued at greater length in chapter 6 of Tim Maudlin’s _Quantum Non-Locality_, which is available to read at Amazon on the search inside the book feature.)

Maudlin makes the nice point that Sherlock Holmes’s dog in the night story shows how nothing physical has to be transferred for information to be transferred. I’d add that nothing determinate has to be transferred for information (in the relevant sense) to be transferred. So the absence of any physical thing being transferred, and the absence of any determinate content being transferred don’t block the very natural inference that some information is transferred.

Imagine a variant of the game where we play in adjoining rooms, and after I make my choice I shout my answer as loud as I can. The walls are thick so there’s no way this can clearly get through, but it has some probabilistic effect because some particular loud noise might be me shouting. No one would say that here’s a better solution to the problem: if you get the dog question shout really bloody loud you’ll increase the other guy’s subjective probability that you got the dog question to 60%. Now your winning percentages can be well over 75%. This obviously doesn’t help with the original problem, and I don’t really how doing something involving fancy quantum effects that has a probabilistic effect on the other guy is an improvement over shouting bloody loud and having a probabilistic effect on the other guy.

(I suppose if I thought the particles were causally isolated then I would think that was a difference. But I don’t think that, again for reasons Maudlin outlines in his book.)

51

Steven E. Landsburg 10.23.04 at 1:01 am

Brian Weatherson: No one would say that here’s a better solution to the problem: if you get the dog question shout really bloody loud you’ll increase the other guy’s subjective probability that you got the dog question to 60%. Now your winning percentages can be well over 75%.

The difference being that this method does involve some (probabilistic) transfer of information about what question you got. The quantum channel doesn’t.

And now I think I’m off to dinner.

52

Glenn Bridgman 10.23.04 at 1:02 am

John: Look closely, you haven’t actually gained any information about your partners state(over the situation where there is no entanglement.)

Ogged: Honestly, I don’t know enough to feel safe giving a good solid definition. Call me back in about 2 years.

D^2: computers seem to do quite well using a dead line to communicate a 0 bit bit, I see no reason why not calling on your cell phone is any different. The fundamental question isn’t the map between various forms of data, but the process of selecting from the range of possible data.

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Steven E. Landsburg 10.23.04 at 1:02 am

Brian Weatherson: No one would say that here’s a better solution to the problem: if you get the dog question shout really bloody loud you’ll increase the other guy’s subjective probability that you got the dog question to 60%. Now your winning percentages can be well over 75%.

The difference being that this method does involve some (probabilistic) transfer of information about what question you got. The quantum channel doesn’t.

And now I think I’m off to dinner.

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Cosma 10.23.04 at 1:02 am

Glenn – I mean that the players can agree on strategies of the following form: if A is asked about cats, he looks at random variable X1, but if he’s asked about dogs he looks at random variable X2, and similarly player B looks at Y1 and Y2. X1 can be correlated with Y1, and have a different correlation with Y2. (This is the analog to making different quantum measurements depending on the question.) So they don’t have make answers which are just functions of the questions they get. Like I said, it’s Friday night, and I’ve got to go to dinner, so I’m not going to grind through the math, but my guess is that (i) classically correlated signals allow for an improvement over just having access to the questions, but (ii) not as much of an improvement as entangled signals. (Oh: and you want David Griffith’s quantum mechanics book, along with his electrodynamics book. They’re expensive, but they’re also the best textbooks you’ll ever read, at least in physics.)

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Dan Simon 10.23.04 at 1:04 am

This whole discussion reminds me of “quantum teleportation”: to the physics-ignorant, it sounds extremely exciting; to anyone with a modicum of knowledge of classical physics, it’s completely uninteresting; and to those who know a fair bit of quantum physics, it’s mildly interesting.

The point of quantum game theory isn’t really to advance game theory–and certainly not the applied kind favored by economists–but rather to explore the theoretical implications of quantum information theory. These guys (with respect to Cleve et al.–Richard was a colleague of mine in grad school, and is a terrific, very smart guy) used to play the same, er, game in the field of (quantum) complexity theory, and they just hopped the fence and applied the same ideas to game theory. The game goes like this: take the small set of well-known counterintuitive quantum information theoretic ideas, pick one, find a new theoretical context in which its effects haven’t yet been considered, and then point out that its effects are, well, counterintuitive.

Of course, the theoretical context typically never took quantum information theory into account because it was derived from a practical context in which quantum information theory was irrelevant. That’s why this discussion has gotten so heated, hostile, and frankly devoid of content here on Crooked Timber–half the room is shouting, “theoretically, this result is unassailable”, the other half is shouting, “practically speaking, this result doesn’t make a lick of sense”, and in all likelihood, both sides are right.

So relax, everybody. It’s absolutely true that a very natural extension of standard game theoretic models to allow for quantum phenomena leads to some bizarre results. (Indeed, anyone familiar with quantum computing, quantum cryptography, or quantum information theory in general should have expected this.) It’s also absolutely true that the relationship between these theoretical models and real life is, to say the least, complicated, and it is most probably safe for the time being to assume that these models have absolutely no practical significance whatsoever.

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Glenn Bridgman 10.23.04 at 1:06 am

Brian, whatever form it takes, you are still engaging in some causal transfer of information, IE, your partners choice of answer depends on which question you got. That isn’t the case with the use of a quantum particle.

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Steven E. Landsburg 10.23.04 at 1:06 am

cosma: my guess is that (i) classically correlated signals allow for an improvement over just having access to the questions, but (ii) not as much of an improvement as entangled signals.

No, if you do the math, you’ll find that the classically correlated signals have no value whatsoever.

And now I’m really off to dinner.

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Glenn Bridgman 10.23.04 at 1:15 am

Cosma, if you think about it, our two methods of describing the classical correlation are identical. Essentially, my q function maps cat->X1 and dog->X2 and the k function maps cat->Y1 and dog->Y2. Since the problem is symmetric, whether X1 and X2 are yes or no doesn’t itself matter, only there relationship to Y1 and Y2 is important. We are thus left with either X1=Y1 or X1!=Y1 and likewise with the 2’s. Thus, there are only 4 total deterministic classical strategys, the maximum of which is X1!=Y1 and X2!=Y2, which gives us 3/4 on average.

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junius ponds 10.23.04 at 1:17 am

>Oh: and you want David Griffith’s quantum mechanics book, along with his electrodynamics book. They’re expensive, but they’re also the best textbooks you’ll ever read, at least in physics< Not only that, but some kind soul is collecting solutions to the problems in both books at solutionarchive.org.

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Abiola Lapite 10.23.04 at 1:22 am

“Maybe I’m misunderstanding, but it seems to me that exploiting a known correlation is an example of transferring information.”

No, it isn’t, as all the required information was transferred ahead of time, when the two players agreed to coordinate their strategies. The bottom line is that Steven Landsburg is in the right in this argument; entanglement does make a difference.

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Lindsay Beyerstein 10.23.04 at 1:22 am

I definitely overstated the case.

Brian, would it be correct to say the following: If you know that there a correlation between the state of your particle and your partner’s answer, then you have some information about what answer your partner gave?

Relativity forbids a signal traveling faster than light. What does quantum theory say about the causal connections between entangled particles?

I object to Steven’s proposed solution because it seems like Steven is simply exploiting the remarkable property of entangled particles to mirror each other faster than a light signal allows.

To the extent that you have evidence about what your partner is doing, your correlation problem is diminished. Steven’s solution only promises the level of success you’d get by applying common sense to less than perfectly reliable evidence about your partner’s state. That’s why it’s not impressive as a solution to the correlation problem. There’s no value added beyond a remarkable new form of evidence.

D-squared beat me to the punch when he pointed out that we can show this by simply stipulating that the participants can’t yoke themselves by quantum mechanisms.

Steven argues that an 85% success rate represents a better solution to the coordination problem than the 75% success rate achievable by the best traditional correlation problem solution.

All’s I’m saying is that to the extent that you have evidence about your partner’s state, you aren’t really solving a coordination problem.

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Detached Observer 10.23.04 at 1:27 am

Steven Landsburg wrote, “Suppose the rooms have been sealed off from each other in such a way that we couldn’t possibly send a light signal from one to the other without ten minutes of digging. What’s patently silly about being required to submit our answers within ten minutes?”

What’s not patently silly about sealing off rooms from each other in such a way that one couldn’t possibly send a light signal from one to the other without ten minutes of digging?

I realize that, yes, you can come up with a contrived scenario where you can “communicate” only via quantum techniques. I don’t dispute that it is of some theoretical interest, but when you wrote that “game theory changes dramatically players have access to quantum technology” you really oversold your case.

(Please don’t reply by saying that according to your definition of communication, the players are not communicating when they measure the correlated spins).

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Donald Johnson 10.23.04 at 1:34 am

I’d love to have seen Daniel ridicule Landsburg’s libertarian fanaticism and would have cheered him on from the sidelines. Instead we got physics envy disguised as resentment. This was a waste of time, DD.

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Steven E. Landsburg 10.23.04 at 1:38 am

lindsey: All’s I’m saying is that to the extent that you have evidence about your partner’s state, you aren’t really solving a coordination problem.

The point that I believe you’re missing is that you don’t have evidence about your partner’s state. No such evidence is transmitted. None.

Detached observer: (Please don’t reply by saying that according to your definition of communication, the players are not communicating when they measure the correlated spins).

My reply is that by any reasonable definition of communication, the players are not communicating when they measure the correlated spins. Please don’t reply by saying that according to your definition of communication, the players can be communicating even when they’re not communicating.

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g 10.23.04 at 1:40 am

dsquared, your phone-my-wife-at-5pm example is broken. Let’s suppose your convention is that you ensure that her phone rings at exactly 5pm. Then, to do that, you need to make the call a little earlier than 5pm; say at 4.59:59pm. The information your wife “instantaneously” gets when one day the phone doesn’t ring at 5pm is that at 4.59:59pm you were for some reason unable or unwilling to call her. That isn’t an instantaneous transfer of information; it took the same amount of time as the phone call would have.

Oh, and Dan Simon’s analysis is spot on.

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Glenn Bridgman 10.23.04 at 1:41 am

Lindsay, using entanglement yields no additional information about your partners state over the classical scenerio. None at all. There is no causal relationship between the particles.

Detached, say you don’t want to hear it as much as you want, but its the truth. If it wasn’t the truth, we could have instaneous communication, but that’s not possible.
Put another way, if there was some information being transfered in this game, then we could use that transfered information to reconstruct communications at faster than light speeds.

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EKR 10.23.04 at 1:42 am

D^2 writes:
“Glenn: When I’m overseas, I have an arrangement with my wife that I’ll call her at 5pm every day to let her know I’m alright. On the day she doesn’t get a call, at 5pm, instantaneously, her information set changes. Obviously no information has been transmitted, because you can’t transmit information by not making a phone call, but there has been a kind of communication. It’s something similar that’s going on in the game-theory example.”

I’m not sure it’s fair to say that her information set changes instantaneously. Remember that there’s an inherent time delay corresponding to the speed of light delay in your calling or not calling. To sharpen the point, imagine that you’re on Alpha Centauri. In order to call at 5 PM, you needed to place the call at 5 PM four years ago. When the clock strikes 5:01 and you don’t call, your wife only knows that something was wrong on Alpha Centauri 4 years ago, not what the story is now. That’s a pretty funny definition of instantaneous.

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dsquared 10.23.04 at 1:48 am

Cosma: Steven is right on this one; a classical signal can’t do any better than 3/4 win. The precise issue here is that the quanglement of the two particles gives the players a way of making their choices conditional on one another which classical physics can’t achieve, and whether or not this is “information” in the physical sense, as Dan Simon points out, from an economic point of view it turns this into a communication game.

After all, if instead of an entangled particle I simply had magic powers which allowed me to control Steven’s brain at a distance without him realising, then he would get no information about the state of my particle, but we would always win, and I doubt that anyone would consider this to be attacking the fundamentals of game theory.

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dsquared 10.23.04 at 1:51 am

This was a waste of time, DD

How can you say that when you have no idea what else I was proposing to do with the time?

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Glenn Bridgman 10.23.04 at 1:52 am

Yargh…
D^2, in your bizarre mind control scenerio, Steven is still basing his choice on your state. This isn’t the case with quantanglment.

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Lindsay Beyerstein 10.23.04 at 1:52 am

I have no attachment to the word “communication.” Clearly, your partner is not sending you a signal. No physical signal travels between you and your partner.

On the other hand, your background theory plus the state of your particle gives you evidence of your partner’s state.

Suppose someone was advocating a theological solution to the coordination problem. She says that if you are righteous and equipped, God tells you what your partner is doing, but God only tells the truth 85% of the time. In that case, clearly, your partner is not communicating with you, but you still have relatively reliable guidance. Or, imagine that God doesn’t communicate with you directly. God tells you that when your mood ring turns blue, there’s an 85% chance that your partner is in state X. When your ring turns blue, you apply common sense to achieve an 85% success rate.

No one should credit the theologian with having solved the coordination problem, even if she were correct about the theological details.

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Steven E. Landsburg 10.23.04 at 1:54 am

dsquared: After all, if instead of an entangled particle I simply had magic powers which allowed me to control Steven’s brain at a distance without him realising, then he would get no information about the state of my particle, but we would always win, and I doubt that anyone would consider this to be attacking the fundamentals of game theory.

On the contrary. If/when someone discovers a mechanism for controlling other people’s brains without their realizing it, the consequences for game theory will be enormous.

The reason nobody studies such consequences is that there is no such mechanism.

Quantum entanglement is real. Whether it will, at some time in the future, be of importance for game theory depends on how technology develops.

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dsquared 10.23.04 at 1:55 am

Glen: but in the quanglement case, his choice is still conditioned on my choice in a way in which it isn’t in a noncommunication game. This was my fundamental point of game theory and it remains; a noncommunication game is defined, rigorously, as one in which players strategies must be chosen conitionally on information sets which are independent of one another. Choices based on entangled quanta aren’t independent.

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Steven E. Landsburg 10.23.04 at 1:58 am

lindsey: On the other hand, your background theory plus the state of your particle gives you evidence of your partner’s state.

What, exactly, do you mean by “state”?

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Lindsay Beyerstein 10.23.04 at 2:02 am

There are causal connections in play. Creating entangled particles requires causal intervention. You and your partner are causally connected by your prior agreement to abide by the dictates of your (causally acquired) quantum theory.

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Glenn Bridgman 10.23.04 at 2:04 am

Lindsay, evidence implys you have information pertaining to your partners state. You don’t. Quantanglement transfers no such thing.

As for your God scenerio, you are still positing a causative effect, which circumvents the rules by being simply a very complicated version of you writing your answer down and showing it to the other guy.

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Steven E. Landsburg 10.23.04 at 2:07 am

Lindsay (sorry for misspelling your name before; I’m reading it off a tiny screen): Can you please tell me exactly what piece of information you think is being transferred?

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Glenn Bridgman 10.23.04 at 2:10 am

Sure they are. My state has no influence on your state. Voila, they’re independent.

The quantum example would work even if they were to be measured at the exact same instant. No other phenomonon we know of allows for that.

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Reimer Behrends 10.23.04 at 2:21 am

Steven, I am quite unclear why using quantum mechanics in your example does not constitute communication in the Shannon-Weaver sense. You are “reproducing at one point either exactly or approximately a message selected at another point” [Shannon 1948]. Note that a physical process connecting source and destination is not necessary; for example, Shannon explicitly considers the case where the source can generate only one message, and where you can therefore generate the message precisely at the destination without any physical communication taking place.

(By the way, how can one have such a long comment thread about the nature of communication and information on an academic blog without Shannon-Weaver being mentioned at least once?)

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Steven E. Landsburg 10.23.04 at 2:23 am

reimer: You are “reproducing at one point either exactly or approximately a message selected at another point”

What message is that?

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Chad Orzel 10.23.04 at 2:26 am

Despite what they tell you, physicists are human beings. They eat, fart and have sex more or less like the rest of us.

Actually, the sex is much better, thanks to quantum entanglement. Just thought you’d like to know.

As to the current pissing contest, I think Dan Simon has it about right.

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Detached Observer 10.23.04 at 2:33 am

Steven Landsburg wrote “My reply is that by any reasonable definition of communication, the players are not communicating when they measure the correlated spins. Please don’t reply by saying that according to your definition of communication, the players can be communicating even when they’re not communicating”

Any reasonable definition of communication? At least acknowledge that reasonable people can certainly conceive of communication as something different than the physical transmission of information.

Anyway, we are no longer debating science but dictionary definitions here.

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John Quiggin 10.23.04 at 2:39 am

John S says “File these snipes at Landsburg under “US writers for the masses – must be critised” along with CT’s swipes against Thomas Friedman and Nicholas Kristof and make your own minds up.”

If you do a search on Kristof, you’ll find more favorable references than otherwise – perhaps you meant David Brooks.

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Glenn Bridgman 10.23.04 at 2:40 am

The act of communication is restricting(probalistically or not) the set of all possible communications to a subset of that same set. The set of all possible states for your partner to be in is not restricted, thus, no communication takes place.

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Steven E. Landsburg 10.23.04 at 2:40 am

Let me try an example that I think will speak to the confusion of several people who are posting here:

You and I sit in separate rooms. Once per minute, we each receive a red or green tennis ball through our mailslots.

Every time we observe our tennis balls, they turn out to be the same color. (We know this because we write down the colors and compare what we’ve written down later). Sometimes we both get red; sometimes we both get green.

Sometimes I wear sunglasses, but it doesn’t seem to affect my vision; I write down the colors I see, and they always match yours.

And ditto when you wear sunglasses.

However, whenever we *both* wear sunglasses, we always see the colors differently. If I see red, you see green, and vice versa.

We have no communication and have not agreed in advance about whether to wear our sunglasses (this is the analogue of not knowing in advance whether we’ll be asked about cats and dogs).

Now. A tennis ball comes through my mail slot. I either do or do not put on my sunglasses. I see that it’s red.

What information has been transferred?

I contend that a) the answer is none, and b) although the example is not physically possible, it is identical in every relevant respect to the situation in the dog/cat game. In fact we could *play* the dog cat game this way and win all the time; we just agree that if we’re asked about cats we’ll leave the glasses off and if we’re asked about dogs we’ll put them on.

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Steven E. Landsburg 10.23.04 at 2:44 am

detached observer: At least acknowledge that reasonable people can certainly conceive of communication as something different than the physical transmission of information.

Sure. But reasonable people can’t conceive of communication as something that involves no transmission of information whatsoever, physical or not.

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Dan Simon 10.23.04 at 2:45 am

Quantum entanglement is real. Whether it will, at some time in the future, be of importance for game theory depends on how technology develops.

No, whether it will, at some time in the future, be of importance for game theory depends on how game theory as an academic discipline develops–and frankly, few non-game theorists care about that. The more interesting question is whether, at some time in the future, quantum entanglement will be of importance in any of the practical scenarios in which game theory might be expected to be of use. Can you come up with even one, even remotely plausible such scenario? (No “say you’re locked in a room…” hypotheticals, please.)

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Steven E. Landsburg 10.23.04 at 2:50 am

dan simon: Can you come up with even one, even remotely plausible such scenario?

Short answer: no. Longer answer: This, perhaps, is a plausible scenario for how a plausible scenario might develop: We certainly engage in strategic interaction that take place via email (I submit auction bids via email, for example.) At some time in the future, it is plausible that my email will be composed on a computer that uses quantum channels to transmit information. And—I was going to say that this is the speculative part, but I think i’ts not even precise enough to be called speculation—perhaps the technology of those computers will allow me to make use of entanglement between particles in my computer and particles in yours.

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junius ponds 10.23.04 at 3:01 am

>(By the way, how can one have such a long comment thread about the nature of communication and information on an academic blog without Shannon-Weaver being mentioned at least once?)< I thought so too, but I was waiting for someone familiar with information theory (which wouldn't include me) to speak up. However, any string of bits generated by a number of EPR pairs and held by Alice and Bob has no structure, being random, and I suspect the Shannon entropy "strebt einem Maximum zu," as it were. Nevertheless, A & B's actions _can be correlated by the string if they agreed on a protocal beforehand_.

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morinao 10.23.04 at 3:13 am

So the idea is that Alice and Bob themselves don’t communicate because they never see each other’s answer, but their entangled quantum particles can talk to each other once they’re passed back to the verifier? Is this like Searle’s Chinese Box?

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Steven E. Landsburg 10.23.04 at 3:19 am

I have posted my final words on this subject to http://www.marginalrevolution.com , in a post titled “Quantum Game Theory Revisited”

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PG 10.23.04 at 3:21 am

Ooh, I wish I’d checked CT earlier today. The Case for Looting was one of the most idiotic attempts to apply economic thinking that I’ve ever seen.

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junius ponds 10.23.04 at 3:23 am

I was hoping Landsburg would explain the protocol without recourse to linear algebra I haven’t learned (e.g. traces of matrices.) My point was, in the simple, toy case of measurements on (|1>|1> + |0>|0>)/sqrt(2) with respect to |1>&|0>, actions of A&B can be coordinated and each can infer what the other is doing from the protocol, but as neither A nor B can affect the statistics of measurements of the other, neither can encode what question he or she has been asked.

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junius ponds 10.23.04 at 3:27 am

That is, the toy protocol is: Measure in |0>&|1> on the particle. If |1>, do X; If |0> do Y. Presumably the authors have cooked up just the sort of protocol that coordinates A&B to defeat the game by exploiting correlations in their measurement outcomes, just as this one does. However, it involves measurements in several sets of basis vectors, and is accordingly more complicated.

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Reimer Behrends 10.23.04 at 3:48 am

Steven, the message is a pair drawn from the set { cat, dog } x { yes, no }. That is not particularly relevant, though, as the Shannon-Weaver model is not interested in semantic meaning, but in how communication reduces information entropy (what we informally call uncertainty) for the receiver.

A communication system consists of a source that produces messages, modeled as a stochastic process, an encoder that translates messages in a form suitable for the communication channel/signal, a decoder that translates them back, and a destination where the message can be observed.

Prior to communication, all messages are equiprobable; therefore the entropy for the receiver (check the link above for the math) is at its maximum. You then choose and encode your message using a quantum-mechanical process; at the receiving end, your partner uses a matching process to decode the message; because messages are no longer equiprobable, information entropy for your partner has been reduced; therefore, communication has taken place.

Note that it is not relevant for this model that you cannot freely choose your messages, but do so by observing a quantum-mechanical event; it would be the same, communication-wise, if you derived your message silently from a coin flip that both you and your partner can observe and that is interpreted according to a pre-arranged convention. This is the precise idea that underlies the so-called one-time pad, a cipher that is unbreakable in the information-theoretic sense. Quantum-mechanic implementations of one-time pads have been suggested; nobody has stopped calling the process communication because of the involvement of quantum mechanics.

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matt 10.23.04 at 3:49 am

Is the definition of information as “a difference that makes a difference” relevant here?

For my money, information is passed from A to B if 1) A is able to pick either message M0 or M1 and 2) and after B’s measurement, B goes (w.h.p.) into state S0 or S1, depending on which message A picked.

Are these two criteria met in the present case?

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Jack 10.23.04 at 4:07 am

Why isn’t choosing the orientation of the measuring device according to the question asked a signal? As i understand it this step is necessary to establish the correct correlations.

It looks awfully much as if information is being transmitted. What are the probabilities of the misere version of the game where you try to avoid winning the game?
If I assume that the other player is trying to answer to achieve a “win” the question is can I improve on the chances of achieving the win or loss that I want.

Knowing the answer the other player will give I have a 75% chance of transmitting a win and a 75% chance of correctly transmitting a no.
It’s quite noisy but if I can agree on a coding system i can use it to transmit a signal over repeated games.

With the help of the quantum bit I can apparently improve that to about 85% in each case. This will enable me to increase the bandwidth of this channel by adopting a more efficient coding system and therefore I can transmit more information in a fixed time. Information is clearly being transmitted. I think it is only the sub-bit quantity that is confusing.

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Glenn Bridgman 10.23.04 at 4:26 am

This is my last post for a while, as I am heading out to imbibe large amounts of cheap beer.

Reimer, the quantum measurment doesn’t reduce information entropy at all. The set reduction only occurs after your decision has been made, IE, it doesn’t affect your decision. My opponent could not first reduce his message set and then cause me to say yes or no as a result.

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GT 10.23.04 at 4:36 am

Steven (and others),

If I understand this correctly, and chances are I don’t, the quantum particles are linked in a manner such that when you measure one there is an 85% chance that the other will have the same result.

So if you agree to give a certain answer based on the measurement you increase the chances of both getting it right wothout direct communication.

Is this correct?

If so, I don’t see how this is not a form of communication. If insetad of the quantum particles the participants had a couple of malfunctioning wireless receivers, so that 85% of the time they could link, the result would be the same.

It seems to me that the quantum particles are a form of communication because they are linked.

What am I missing?

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Reimer Behrends 10.23.04 at 4:58 am

Glenn, the problem is that in the information-theoretic sense the example is undistinguishable from a situation where you use an electronic or mechanical device to simulate the same effect (sharing of a randomly determined bit of information between two places). Try to see the quantum-mechanical device as a black box and tell me what it accomplishes in an information-theoretic sense that can’t be accomplished by other means. As a black box, it is a device with a switch at each end (with a “cat” and a “dog” position) that will produce a (random) bit of output at each end if consulted. If both switches are in the same position, there is a probability > .5 that both bits will be the same. There is nothing here that is an inherent property of quantum mechanics that I can see.

I would also like to add that I’m not too enamored of the example in general: what it comes down to is sharing one bit of information between two places. The cat/dog stuff and other requirements drop a couple of xor-operations on top of that problem, thus obscuring rather than illuminating it.

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John Quiggin 10.23.04 at 5:03 am

The revised post at Marginal Revolution makes it clear that the quantum physics part of a story is a red herring. In this post, the entire argument is replicated using polarizing sunglasses and coloured light in place of the entangled particles. This is all classical physics. And the strategy works 100 per cent, just like Daniel’s.

Apparently, we could have avoided a whole lot of disagreement if Daniel had posted this example in the first place.

It seems that the real point of the post is that the way in which economists and information theorists have defined the term “communication” is wrong, and that when you define it correctly, following the usage of physicists, the standard results no longer apply.

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GT 10.23.04 at 5:11 am

John,

I thought I was missing something but it seems not.

If the two participants are asked theses questions over several days and they agree to ahead of time to give a certain answer based on how the sky looks from their windows (assume they are in the same neighborhood) they may not be directly communicating but they certainly are using a signaling system.

I still don’t get what Steven was trying to say.

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Tara Gosset 10.23.04 at 5:24 am

Thanks for the tennis ball example.

I have glasses that somehow coordinate with the other guy’s glasses to ensure that we see different colors.

The glasses coordinate with each other, but they don’t communicate with each other?

This seems to get us back to the original point. What we have is faster-than-light communication between the glasses.

If the glasses communicate, then I read the glasses, I’m at least benefiting from communication even if I’m not directly communicating.

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Tara Gosset 10.23.04 at 5:30 am

If the problem is that we are using a classical physics definition of “communicate”, then

Bah.

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junius ponds 10.23.04 at 5:43 am

If I’m reading Reimer correctly, he’s missing the point — nonlocal “steering” — of entanglement. Do both participants have this box, and if so, how do they communicate?

>what it comes down to is sharing one bit of information between two places. The cat/dog stuff and other requirements drop a couple of xor-operations on top of that problem, thus obscuring rather than illuminating it.< Precisely what I was trying to say earlier with the toy protocol. CSCH and that protocol both exploit (noncausal) statistical correlation. >I have glasses that somehow coordinate with the other guy’s glasses to ensure that we see different colors.< Yes, quite right. But you can't communicate with these glasses, because you can't select the colors to see. Are these glasses "communicating" themselves? I suppose it's an issue of interpretation; certainly we can't DO anything with this sort of "information transmission," because all the "information" contained in the wave function is _inaccessible_. Likewise, are conscious beings necessary for collapse of the state vector? In this case, who cares?

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matt 10.23.04 at 5:45 am

The apparent dispute between Landsburg and his opponent(s) is on whether communication is going on in the EPR example. I think underlying this, though, is a conflation between two cases of communication.

There are (at least) two different for A and B to end up in correlated states. One is for A to pick a state and send a message to B, triggering B to enter a correlated state. Another is for some intermediary C to pick a state, broadcast a message, with the result that A and B go into states correlated with C (and thus correlated with each other).

Right now, I’ll assert, both you and I see the words “Crooked Timber” on our screens. It doesn’t follow that I’ve communicated with you. On the other hand, we both currently see the words, “Right now, I’ll assert…” because in this case I have communicated with you.

In the EPR example, as far as I can tell, A and B do not communicate with one another. Rather, isn’t the guy who originally entangled the two particles at least something like a broadcasting intermediary?

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Dan Simon 10.23.04 at 5:48 am

This, perhaps, is a plausible scenario for how a plausible scenario might develop: We certainly engage in strategic interaction that take place via email (I submit auction bids via email, for example.) At some time in the future, it is plausible that my email will be composed on a computer that uses quantum channels to transmit information. And—-I was going to say that this is the speculative part, but I think i’ts not even precise enough to be called speculation—-perhaps the technology of those computers will allow me to make use of entanglement between particles in my computer and particles in yours.

There’s still one huge piece missing from this story. Even in the unlikely event that quantum channels one day become available in practical game theoretic settings, how on earth would they ever become available even in the complete absence of classical ones between the same parties?

As far as I know, there are no examples of a quantum channel being of (even theoretical) game theoretic use in the presence of a parallel classical channel. And I see no indication in the result of Cleve et al. that such an example is any closer to being discovered than I would have expected it to be before the paper was written–that is to say, very, very far away.

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Glenn Bridgman 10.23.04 at 6:00 am

(I apologize in advance for any ridiculousness in this post, I am slightly inebriated:p)

John, with all due respect, you don’t understand the tennis ball analogy. It’s not classical physics, because there is no way we could make a situation that worked like that in the classical world. The quantum aspect is essential.

Reimar, what happens if we both consult the black box at precisely the same time?

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bad Jim 10.23.04 at 9:13 am

Of all the comment threads on the Bush “wolves” commercial, this has to be the strangest, hands down.

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g 10.23.04 at 10:52 am

John: it isn’t true that polarizing glasses work the same way for purely classical reasons. That peculiar property of polarizing filters is a quantum effect. Isn’t it?

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Jack 10.23.04 at 11:15 am

I can’t see that there is any game theory content to this beyond the use of a slightly unreliable messenger.

The real puzzle would be the apparent speed of communication but I think that is at least partially illusory. It’s rather like looking at the same thing at the same time. There is real oddness is how the way you look at things at one end has an effect on the way things appear at the other but I’m not sure what that has to do with game theory.

I’d be more interested in something like a quantum minority game agent. Could you make a good one with fewer bits of memory than normal?

The game has to be sufficiently complicated that simple prepared responses do not have 100% success and this is probably the simplest example.

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Stephen Bullock 10.23.04 at 11:44 am

Hi Matt:

In the EPR example, as far as I can tell, A and B do not communicate with one another. Rather, isn’t the guy who originally entangled the two particles at least something like a broadcasting intermediary?

————–o——————–
So the classical players can meet
a week before the game starts
to contrive who says yes and who
says no. If suitable devices exist, why couldn’t quantum-enabled
players bring a thousand quantum
bits each to this meeting, entangle them,
load them afterwards into their two personally
owned qubit storage devices
and then play the game with them a week later?

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Jack 10.23.04 at 12:43 pm

Or they could bring cell phones.

I think there is some signalling done by the choice of polarity to examine the electron with. In any case it is clear that information is being exchanged because if I have, say, a thousand tests I can send more bits with a given level of reliability using he quantum technique than with the prearranged system alone.

If this is indeed true and all the maths has been done properly there is an action at a distance issue but I still don’t see the game theory issue. There are some issues in computability where quantum machines can make certain calculations with a significantly greater speed/lower order of growth than purely classical machines but here it seems to be purely about communication as Daniel originally said.

Communication is happening because I can use the greater probabilities of transmitting a chosen bit to convey more information in a given time.

This is not, except for its speed, a particularly quantum issue. I can mimic the device classically given a very little time.

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Reimer Behrends 10.23.04 at 2:06 pm

Junius, there is only one box, and both parties have access to it; or, alternatively, two boxes whose behavior is interdependent. Just as with Steven’s setup where you have essentially two small “quantum machines” whose behavior is interdependent.

Glenn, it will take a fraction of a microsecond to come up with the answer. It’s a box with a switch at each end, each with two positions labelled cat and dog (you can use a pair of computers connected by a network, with one of them running the necessary code and the other one serving as a dumb client to implement it). Whenever one participant flips a switch it will alter the output for that participant to make sure that the game is won. It’s a simple little state machine whose implementation I might give as a programming task for first year computer science students.

If you want to mirror the original experiment precisely, introduce a middle position for the switch and don’t show anything for either party until they’ve moved their switch into either the cat or dog position.

What seems to throw people for a loop is that you can determine message content with high likelihood without an apparent physical connection. But even that is nothing new in principle: When a sender transmits a data block followed by a checksum over a noisy channel, we will know that checksum with high likelihood even _before_ it has been transmitted (and with certainty, if the channel is noiseless). The reverse happens when during cryptographic communication both sides exchange a session key and then generate a bit stream from it: the bit stream is completely predictable on both sides; thus, once the session key has been transmitted securely, the bit stream does not need to be transmitted by a physical process, but is inferred by the receiving end (in mathematical terms, that works because the bit stream does not reduce information entropy). By exchanging entangled particles, we do something similar.

The above should not be read to imply that nothing interesting is taking place when using the quantum-mechanical approach. According to the experiment (correct me if I’m wrong, I’m not a physicist), it basically allows you to determine for independent random events x1 and x2 two values y1 and y2 such that p(x1, y1, x2, y2) holds for a certain non-trivial predicate p with high likelihood. That in itself is remarkable without an apparent physical connection; but I don’t see how you can, based on any existing definition somewhere in the scientific literature that I am aware of, say that no communication is taking place and I don’t see how it should affect game theory.

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Steve Carr 10.23.04 at 3:59 pm

I’m sure someone’s already made this point and I missed it in the 114 previous posts, but in Landsburg’s revised example, he writes: “When we look at them, they’re always opposite colors. We know this, for example, because we each write down the sequence of colors we see and compare them afterward.”

Surely even Landsburg would have to agree that comparing sequences of colors counts as “communication” and an exchange of information. And without that communication, there’s no way to win the game (not consistently), because the people wouldn’t know that they’re seeing opposite colors.

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zaoem 10.23.04 at 7:43 pm

From Steven Landsburg’s example: “All we have to do is agree to leave off the sunglasses when we’re asked about cats, put them on when we’re asked about dogs, answer yes when we see a red ball, and answer no when we see a green.”

Surely this type of agreement follows from cheap talk.

I am still kind of puzzled by the relevance of all this. It strikes me that the notion that quantum theory “solves” coordination dilemmas is rather obvious in that it essentially captures an assumption about connectedness between actors, as do more common solution concepts to coordination dilemmas that focus on norms. Can we really separate quantum game theory from those more common assumptions that actors have a set of shared assumptions about their connectedness (“appropriate behavior”)?

117

Chad Orzel 10.23.04 at 8:07 pm

Let me try an example that I think will speak to the confusion of several people who are posting here:

You and I sit in separate rooms. Once per minute, we each receive a red or green tennis ball through our mailslots.

{etc.}

I haven’t read the original paper in detail, so it entirely possible that there’s some subtlety in the physics of the situation that this second example misses. If the tennis ball thing is a good analogue for what’s happening, though, I would be inclined to say that there’s nothing inherently quantum about this whole thing.

The really important feature, from a quantum standpoint, of the EPR experiment, is that the state of the particles is indeterminate until one is measured. If all you care about is that there’s a particular correlation between the two particles, then it’s just a convoluted dodge around the rules of the game, and might just as well be done by exchanging classical tennis balls, or looking at a particular part of the sky at the time of the question (as somebody upthread suggested).

I suspect that the physics has gotten mangled somewhere in the journey from one scenario to the other. I’m already feeling faintly ashamed of myself for wasting this much time on such a silly argument, though, so I’m probably not going to try to track down the mistake.

118

junius ponds 10.23.04 at 8:25 pm

I read EPR last year. EPR argue that quantum mechanics is incomplete because properties corresponding to noncommuting observables as measured by Alice can be predicted by Bob with perfect certainty, making both “elements of reality” according to a criterion they lay out. The buried assumption is locality. A hidden variables theory, as Einstein would have it, would have two canonically conjugate variables both determinate… Bohm pulled off a _nonlocal_ hidden variables interpretation.

Nonlocality is what is really important here.

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junius ponds 10.23.04 at 8:29 pm

To wit:

>Junius, there is only one box, and both parties have access to it; or, alternatively, two boxes whose behavior is interdependent. Just as with Steven’s setup where you have essentially two small “quantum machines” whose behavior is interdependent.< A classical box that behaved in this manner would be impermissible because it would require propagation of signals at speeds less than or equal to c. EPR pairs exhibit the correlation without signaling.

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junius ponds 10.23.04 at 8:36 pm

>Alice can be predicted by Bob with perfect certainty< That is, without disturbing Alice's system, due to the locality assumption. Sorry, I should have made that more clear.

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junius ponds 10.23.04 at 8:44 pm

To people who think a causal influence (information transfer) is involved: since the statistics of measurements are unaffected, obviously you impute some physical reality to the wave function. I’m inclined to view it as a bookkeeping device, wholly belonging to the quantum formalism, but then again, I have a strong positivist streak — but so does the Copenhagen Interpretation. I have a feeling we’re never going to feel completely satisfied so long as we keep talking about collapse and so forth.

122

abb1 10.23.04 at 9:05 pm

Sounds like Reimer got it exactly right: the two particles together constitute a device.

Like a pair of those miraculous glasses or a phone line or a notepad with pencil or a talking God.

Same idea, different mechanics.

123

neil 10.24.04 at 3:13 am

A question to the game theorists: In what sense are two players not ‘communicating’ if they have devices to which they can provide input which they assume goes to the other player, or can receive output which they assume comes from the other player?

It seems like this pokes holes only in the definition of information flow in a physical system. Because physically, I can accept that there is no connection between the entangled particles; but I can’t accept that there is no way to transmit information over this channel. If the physics says there is, then we must have the definition of ‘transmit’ or ‘information’ wrong.

The more I think about it, the more it sounds like DD’s ‘calling my wife at 5pm’ analogy is the best one here. By not calling his wife, DD has sent no signal to his wife’s telephone device, but by monitoring the device she can nonetheless determine some information about his state.

There are lots of ways that the ramifications of quantum theory could affect everyday life, but this one is a big stretch.

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Eli 10.24.04 at 4:05 am

Once people get it settled that entanglement can’t transmit information (in the Shannon sense), it sure looks like this all comes down to disagreeing whether “no communication” means “no transmission of information” or “no interaction whatsoever”. Classically, there would be no difference, but in fact there is.

We’re assuming the players are allowed to coordinate their strategy. If they can do that in person, it’s natural also to allow them to prepare an entangled pair at that time. If they’re only allowed to do their strategizing over a purely classical channel, they’re more limited. I think the point is that you might want to pay attention to that kind of distinction when defining the rules of a game.

(Disclaimer: I only glanced at the paper itself.)

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Jack 10.24.04 at 7:06 pm

In the example presented information is being transmitted.

Just by cooperation I can control the awarding or not of the prize with 75% accuracy. By switching thd dial on an entangled electron spin detector I can improve the accuracy to 85%. That difference is information. In a single trial it would be hard to identify but over repeated examples I would be able to improve the bit rate for a given accuracy.

This is action at a distance which is not expected to be possible but is also a famous physics problem the ins and outs of which are not discussed here.

I’m surprised that this is interesting from a game theory point of view.

The problem may be that although the game presented is probably the simplest for which something interesting could happen it serves as a kind of Monty Hall problem obscuring the information transition. How do you have intuitions about a piece of information smaller than a bit?

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