Econophysicobabble

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.

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.

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.

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.

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.

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

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

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.

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?

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

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.

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?

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

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

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.

“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.

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.

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.

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

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.

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.

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.

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?

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.

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.

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?

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.

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.

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.

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.

>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.

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.

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.

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.

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.

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?

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.

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.

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.

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?

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?)

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.

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.

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.

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.)

>(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_.

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

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.

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.

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.

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?

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.

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.

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?

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.

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

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.

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.

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.

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.

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.

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.

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.

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?