What’s wrong with game theory

by John Quiggin on October 13, 2005

The latest Nobel Prize award to Aumann and Schelling has generated a bit of discussion about the value or otherwise of game theory. Generally speaking, economists are enthusiastic about game theory and other social scientists less so. Although I admire the work of Aumann and (even more) Schelling, as economists go, I’m a game-theory sceptic, for a fundamental reason I’ll try, probably unsuccessfully, to explain.

My main problem has to do with the idea of a strategy and its role in equilibrium concepts such as the famous Nash equilibrium. A game outcome is a Nash equilibrium if no player can gain by varying their own strategy, assuming that other players stick to their equilibrium strategy.

The problem here is to say what a “strategy” is. In a game like chess or poker, this is easy: the rules say what each player can do and when they can do it. The same is true in some special kinds of economic situations, such as auctions. But most of the time, there is no book of rules, so the set of strategies has to be described as part of the model.

If we look back at the Nash equilibrium idea, and put ourselves in the position of one of the players, it can be seen that there’s really no difficulty with the definition of our own strategy. We can look at the outcomes that are available, given the other player’s strategy, and pick whichever one is best for us. The way in which we label our choices doesn’t matter.

The critical problem is in the phrase “given the other player’s strategy”. In the absence of a rulebook, we can only know this if we know how the other player is going to react to this move (and the same holds in reverse for the other player). There was a large literature on this issue of “conjectural variations” before the rise of game theory, but it was generally felt to have ended in failure[1].

I’ve been trying to make this point for a decade or more, along with Simon Grant and Flavio Menezes, in a string of papers, some published and some not, most notably here (PDF files).

Although it’s easy enough to make the point in specific instances that if we choose a different assumption about strategies we get a different equilibrium, economic theorists strongly resist the argument that this is a general problem and that economic interactions with a well-defined strategy space are the exceptions rather than the rule.

At least, that’s the case in relation to finite games. For infinitely-repeated games, the strategy space gets very large, and the (in)famous Folk Theorem says, roughly, that anything can happen. This is really just the same problem in a different form.

This doesn’t mean game theory can’t be a useful source of insight, something Schelling in particular has shown. But it’s unlikely, in most cases, to yield definite and reliable predictions.

fn1. Digging around, I see the claim that we have witnessed in recent years a revival of Conjectural Variations in Game Theory

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10.14.05 at 2:34 am

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1

Brendan 10.13.05 at 6:25 am

Can I ask an idiot’s question, as a non-economist?

Actually two questions.

1: What, specifically, is wrong with the Historical School?

2: Why did the (to an outsider, slightly bizarre) emphasis in economics on mathematical laws, triumph over the Historical School’s emphasis on empirical work? I find this particularly weird since the main opponents of the Historical School, (the Austrian School) have also been sidelined in modern economics.

This might seem off topic, but it seems to me that the emphasis on game theory in contemporary economics would seem to derive from the view that economics is the mathematical approximation of how human beings ‘would’ behave in some abstract mathematical world, rather than how they do actually behave? (I’m aware that some game theorists use experimental or non-experimental studies, but these would seem to be in the minority. Or am I wrong about this?).

2

abb1 10.13.05 at 6:26 am

I thought the assumption is that the other player’s strategy is exactly the same as yours: looking at the outcomes that are available and picking whichever one is best for him. The set of outcomes that are available is the ‘rulebook’, no?

3

John m 10.13.05 at 6:42 am

Brendan,

A short yet cynical answer to your question:

Economics effectively tries to present itself as a science i.e. fundamentally predictable. Economists have a real world record of sequential failure which defies this presentation but explains why they like mathematical theories – because they are accurate and predicatable. Basically you’re assuming that Economics (and Economists for that matter) should aim to attempt to solve real world issues rather than to create and argue over academic abstractions.

4

abb1 10.13.05 at 7:01 am

Not necessarily, Brendan: suppose there are a dozen companies competing in a specific narrowly area of the market. They’re all trying to optimize their pricing strategy using software or maybe just expert intuition.

In this case you’re not trying to predict human behavior – you are creating a model that will allow you to develop a strategy for acheiving the optimal result, to find the best of all worst-case scenarios.

The only problem is that in the real world companies like to conspire instead of competing. But that’s illegal, so…

5

Kieran Healy 10.13.05 at 7:30 am

On the historical school, economists will echo Coase’s remark about the American institutionalists: their efforts amounted to a huge mass of descriptive material waiting for a theory, or a fire.

6

Henry 10.13.05 at 7:41 am

bq. This doesn’t mean game theory can’t be a useful source of insight, something Schelling in particular has shown. But it’s unlikely, in most cases, to yield definite and reliable predictions.

I’d agree – but what I like about game theoretic arguments is that game theory provides a version of double entry book-keeping – that is that if you do it right, the conclusions (the equilibrium) has to be compatible with the premises (the parameters, game form etc that you postulate). It’s a useful and valuable mental disciplining device to keep social scientists honest. That said, there’s an awful tendency to just-so stories even in the infinitely iterated version – I as an economist or social scientist go out and look for some stylized facts about an empirical situation, show that under reasonable parameter values there is a SGPE that seems to correspond vaguely to the actual outcomes if you squint at it in the right light, and go away convinced that I’ve actually proved something. Which of course I haven’t. What I’d like to see game theory doing is acknowledging that its best application is in a slightly more rigorous form of story-telling – something along the lines of Bates et al’s “analytic narratives” – where the evidence that game theory has value doesn’t flow from the mere demonstration that there’s an equilibrium, but from the kinds of evidence that, say, historians employ.

7

Dan K 10.13.05 at 7:42 am

I don’t mind game theory – it’s a valuable analytical tool for a certain class of behavior. The problem is that this class of behavior does not seem to be terribly relevant for understanding real world human behavior (which is John Q.’s point, really). But economics have a long history of relying on highly stylized representative anecdotes that share an unfortunate combination of a propensity for mathematical formalization and low empirical relevance. That’s not about to change soon, for reasons pointed out by john m.

8

Chris Bertram 10.13.05 at 8:01 am

One of the difficulties with applying game theory is that it is so hard to get agreement on when a real-world situation actually instantiates a game-theoretic structure.

Take PD for example. One friend of mine, a sociologist, sees PDs everywhere. That’s because he sees an apparent structure of payoffs like the PD embedded in all kinds of real-world situations (trades on the market, traffic meeting at intersections). But in most of those very situations, people don’t end up “defecting” because their _actual_ ordering of outcomes isn’t the one described by PD. But in that case, there was no PD … since the ordering of outcomes just is constitutive of a situation being a PD. (Or so someone like Binmore would say).

My sense is that people in different disciplines arguing about the utility of GT are often just arguing past one another because there is no cross-disciplinary consensus about what the application of GT would amount to.

9

duus 10.13.05 at 8:21 am

John.

thanks for the link to your “games without rules” paper. it’s very interesting.

10

Daniel 10.13.05 at 8:21 am

worth pointing out, I suppose, that Aumann’s claim to have invented the Folk theorem is at least as good as anyone else’s.

11

Lewis 10.13.05 at 8:24 am

I am reminded of the joke about the physicist asked to design a hen house. His report began: “Assume a spherical chicken….”

12

Tom 10.13.05 at 9:09 am

Breeding is making commercial chickens more and more spherical all the time, just as in Marx there is an argument for a historical tendency where actual capitalism is becoming more and more like Marx’s model.

13

Loren King 10.13.05 at 9:13 am

An enjoyable post and conversation. A few muddled thoughts, vaguely on point, and I hope not too distracting:

First, I’ve been wondering if (and have been trying recently to give some substance to the claim that) game theorists are often doing something more closely resembling normative argument than causal explanation. If game theory is really a very precise (arcane?) subsubfield of moral and political philosophy, then it’s explanatory failings are a bit beside the point.

This suspicion was buttressed recently when I listened to David Kreps try pointedly to talk with some sceptical humanists about “choice theory” instead of “rational choice theory.” The implication, I took it at the time, was that “rational” brings with it a bunch of normative baggage that muddies the descriptive and explanatory waters.

And indeed, these days when game theorists are interested in explaining how people actually behave (in divide the dollar settings, for instance), they seem more interested in norms, mechanisms of learning and adaptation, ‘focal points’ (Schelling, of course), and population parameters — the stuff, to be sure, of evolutionary just-so stories that Henry and no doubt all of us are rightly sceptical of, but still, at least a lurch toward descriptive accuracy and explanatory richness, instead of austere, elegant, but emprically dubious axioms and derivations.

Second, McKelvey and Palfrey’s statistical solution concept (the quantal response equilibrium) has allowed at least a bit more connection between statistical analysis of strategic behaviour and the high-flying fixed point theorems of the theorists. Curt Signorino in political science has been doing a bit of work along these lines, with some modest but suggestive results.

Third, and most muddled: some folks will claim that explanation doesn’t need always be strictly linked to prediction to be good science, and I want to muse on that point a bit. On the one hand, if we really understand the nuts and bolts of some causal process, then we can explain the mechanism at work, and predict future states, presumably.

But on the other hand, I can explain in rich detail the themes and nuances of, say, a Neal Stephenson novel. Furthermore, based on my careful and broad readings, I might even be able to make some informed guesses about the sorts of books he’s likely to write in the future. But of course I cannot predict the details of his future projects. My explanation of his other books, and of his writing style more generally, still seems plausible, however.

If a significant part of social science is ‘figuring out the rules of the game’ in the same way we explain a text and an authorial style (I’m thinking of a Geertzian effort to make sense of apparently foolish choices, for instance), then we shouldn’t worry if these explorations aren’t especially predictive. We’d hope, I suppose, that our interpretive efforts to figure out the rules of the game might let theorists and other scientists then make at least rough predications about what’s likely to happen in that particular game.

14

Donald Johnson 10.13.05 at 9:15 am

PD = Prisoner’s dilemma, I assume. Actually, I’m sure, but I had to think about it for a minute and I’ve read John Maynard Smith (not his book on game theory though), so it’s possible others don’t know. Evolutionary biology is probably the place where game theory can be expected to have some real world relevance, I’d guess.

15

Peter 10.13.05 at 9:32 am

Currently, I am reading Klein’s Sources of Power. He goes into detail about trying to find actual uses of rational choice theory (RCT) type decisions being made by experts, and never found any. To explain what they were actually doing, he came up with the description of “recognition primed decionmaking” (RPD).

Game theory would be a good tool for RCT, except that people don’t make decisions that way. So the underlaying assumption is in error. Furthermore, RCT assumes that people actually think about the consequences of their actions. Another fatal blow for RCT.

Watching the idiots in the whitehouse make criminally stupid mistakes one after the other makes me pull out what’s left of my hair. Lately, I’ve been trying to figure out why people make bad (or worse) decisions. At least so I can learn how not to make them. I hope.

Next up, I’ll be looking for a couple of books by Schelling. Maybe he’ll have a better explanation of why people do boneheaded things.

16

C.J.Colucci 10.13.05 at 10:18 am

You mentioned both chess and poker, but wouldn’t the two games be fundamentally different? In chess, you know what material your opponent has, how much space he controls, and where he has positional advantages and disadvantages. If you have had an opportunity to study past the opponent’s past games, you can get a pretty good read on how he handles many situations. In poker, although you may have a sense of your opponent’s playing style (Doyle Brunson seems to have become less successful as a player after laying his ideas out in Supersystem), and you know the size of his chip stack, you don’t know (except to the extent that you can make an informed guess) what hand he holds. Does this difference in in formation make a significant difference in how game theory applies to the two games?

17

PLN 10.13.05 at 12:09 pm

CJ– no, it makes it more complicated but not all that different. With poker and other games of incomplete information, you simply have to condition your strategies on the distribution of chance outcomes you think possible. E.g., my opponent raises preflop all-in, my distribution of the hands in which he would do that is now 20% AA, 20% KK, 20% QQ, 30% AK, and 10% a uniform distribution over everything else (no, not really, but for simplicity).

Lack of information makes it a lot *harder* to calculate solutions, but not all that *different*. So long as you assume perfect recall (memory).

18

roger 10.13.05 at 12:12 pm

Abb1; doesn’t this generate a paradox: “I thought the assumption is that the other player’s strategy is exactly the same as yours: looking at the outcomes that are available and picking whichever one is best for him. The set of outcomes that are available is the ‘rulebook’, no?” Because if the player’s goal is to produce uncertainty in the other player, than sub-optimal routines would seem to be more advantageous in certain situations than optimal ones, depending on whether your optimal outcome depends on creating a maximum of uncertainty in the other player. This might be a variant of the Ellsburg’s famous “madman” theory that Kissinger supposedly adopted.

19

abb1 10.13.05 at 12:49 pm

Roger,
I misunderstood the post when I wrote that, thinking that he is talking about traditional applications. Clearly in a ‘Kissinger against Pol Pot’ situation the game theory is not going to do you any good, that’s quite obvious.

Now, in a typical ‘strategic pricing’ or ‘strategic bidding’ model, you’re choosing the best of all the possible worst-case scenarios as your strategy. So, if your competitors act irrational you’re likely to do better than you expected, you simply can’t do worse. And I think this is the most rational way to solve the prisoner’s dilemma too – to confess first.

20

Marcus Stanley 10.13.05 at 1:04 pm

I think the use of game theory is precisely that it has NOT generally succeeded in “yielding definite and reliable predictions”. Game theory highlights the fact that even if you make heroic assumptions about rationality and clear preference orderings of outcomes, the result of strategic interaction between limited numbers of actors is unpredictable and highly sensitive to variation in norms, culture, behavior, etc. So game theory pulls us away from the (IMO hopeless) attempt to explain and predict human behavior using strict rationality assumptions and back toward culture and psychology. For example, I strongly doubt behavioral economics would be anything like as central as it is now unless the profession had first absorbed the lessons of game theory.

21

joe o 10.13.05 at 1:20 pm

Sources of Power is a very good book on how experts make decisions. It is very readable and convinsing.

22

roger 10.13.05 at 1:23 pm

The bidding situation is interesting. For instance, take the leveraged buyout. Surely the optimal course for the bidder, if the bidder and the owner of a company are trying to preserve the company — is not to damage the company in the course of the bidding. But in fact, a better strategy turned out to be merging the bidding process with one by which the buyout artist burdened the company with debts. That, in turn, spurred the use of damaging a company to preserve it by the management of companies, who might merge it with clearly unsuitable or expensive partners. Now of course you could say the equating the survival of the company with rationality is wrong — but, traditionally, rationality is identified with survival. It would seem, then, that you have to split the company as an abstract entity into various sectors — its management, the mass of its investors, potential buyers — and that you would need to game theorize under a number of time frames. This makes it much more difficult to say that computers or spreadsheets have solved the game theory problem by giving both sides constraints, since the constraints seem to change with micro shifts in the situations of the players, plus their time horizon.
Which is why, I think, mergers and acquisitions depend much more on outright irrationality — the vanity of the Ceo. It is much simpler.

23

radek 10.13.05 at 1:24 pm

Quick point, lots of Aumann’s work is on cooperative game theory, not non-cooperative game theory so there’s no strategies, but rather coalitions and the like. Cooperative game theory has fallen in a bit of disuse in economics though, outside of the pure theory folks.

And Marcus makes a good point.

24

abb1 10.13.05 at 1:42 pm

Roger,
this was again a complicated example. The example I’m familiar with is a spot market for electric power. Suppose you own a generator and you offer its capacity on the market. You can set a different price every day. If your price is too high – you won’t sell anything. If your (and everyone’s) price is too low – the spot-price will be low and you won’t make much profit.

Well, turns out if you have enough information about the market and the players on the market, you can calculate the optimal price. That’s not predicting Kissinger, but it’s something.

25

Jasmindad 10.13.05 at 3:42 pm

Peter said,
______
Currently, I am reading Klein’s Sources of Power. He goes into detail about trying to find actual uses of rational choice theory (RCT) type decisions being made by experts, and never found any. To explain what they were actually doing, he came up with the description of “recognition primed decionmaking” (RPD).

Game theory would be a good tool for RCT, except that people don’t make decisions that way. So the underlaying assumption is in error. Furthermore, RCT assumes that people actually think about the consequences of their actions. Another fatal blow for RCT.
______

The comment above deserves remarking on. People may behave rationally, i.e., as if they are explicitly following RCT, while in fact they are engaging in RPD. This happens when over time our responses evolve to those that are “rational”. In cognitive architecture research such as on Soar, this would be explained by “chunking,” a learning mechanism which puts away as rules little bits & pieces of rational behavior that at one time might indeed have been generated by deliberate rational behavior. This is an example of an explanation where rationality does not have to arise from being deliberately “rational” every instant.

In contrast are psychological and social phenomena where individual limits on rationality end up haring a different behavioral outcome in comparison with outcomes that would be predicted on the assumption of no limits to rationality. Herb Simon got the Nobel for his exploration of “bounded rationality.”

In short, one needs to be careful about what consequences follow from theories such as Klein’s.

26

Tom Slee 10.13.05 at 3:56 pm

Don’t get me wrong, I think game theory is immensely valuable. But I do sometimes think that whoever said “game theory tells us what we already know in a language no one understands” had a point.

27

Patrick 10.13.05 at 3:57 pm

I thought the value of rational choice theory and game theory was that it tells you what an objectively rational and completely self interested actor would consider, and how they would make a decision.

Then, when people don’t do that, you have a framework for figuring out *why,* and what parts of the rational calculus they’ve modified with their own tendencies.

Or if they do follow it, you have at least a prima facie explanation for why they did what they did.

28

Tracy W 10.13.05 at 4:30 pm

My general awareness of when game theory is used in economic policy advice is that it’s used a lot when deciding how to set up the rules. So you set up the end situation you (or the Government) want and from there work out what rules will, when combined with the players’ strategies, give you the outcome you want.

This is what economists try to do with designing auction rules. So not having a rule book isn’t a problem, as you’re using game theory to design the rulebook.

Unfortunately there is no reason to believe that economists in government are far brighter than economists in business, so there is generally an iterative process as the players figure out how to game the rules. But this happens with every set of regulations or laws and therefore is not a strong criticism of game theory.

Also, game theory has taught environmental regulators that it’s a very good idea to avoid rules that set up a prisoners’ dilemma situation with no way for parties to evolve stable cooperative strategies. (Yes, I know that a lot of people cooperate in prisoner’s dilemma experiments. But if you set it up so people can’t know who they’re playing against and therefore can’t cooperate and play multiple games, cooperation goes down over time. I assisted my uni professor in running one of these experiments).

As for maths in economics, I think it’s important as putting your thinking into mathematics makes it clear what you’re assuming and what you aren’t. I find it very hard to rigorously handle the interactions of several variables while working entirely in prose. By rigorously I mean not forgetting about one of them (or one or more of the possible interactions) halfway through. Perhaps the maths should be burnt afterwards – but it’s an important step for all us sub-genius folk.

29

Jonas Grumby 10.13.05 at 8:43 pm

CJ – As an erstwhile math student, I wanted to throw in my barely-relevant 2 cents.

The 2 cases you cite are fundamentally different in that chess is a finite complete-information game, and as such there exists a well-defined perfect strategy that allows the advantaged player (presumably white, though it’s not known) to never lose (i.e. to always at least tie). Tic-tac-toe is the analog game where this is known to every 10 year.
In the real world (even the one of spherical chickens), there aren’t any interesting complete information games.

30

Maria 10.13.05 at 9:28 pm

Regarding the application of Schelling’s insights, I recommend this article in Slate , pointing out the reality of the dangers of thinking that Game Theory is always applicable.

31

Ian Whitchurch 10.13.05 at 11:56 pm

The place to start, in my opinion, is what killed my intention to go for a career in Economics.

Econometrica, 1984, round about page 1040.

Several articles about Rationalisable expectations.

Essentially, what these articles argues – and that I didnt have the maths to follow – is that expectations were not rational, but rationalisable, because information is costly, and information about information is also costly.

The logic is that the single most valuable fact about price information was that they embodied that someone was putting a value on what you held, but that information embodied what they thought someone else would pay for that information.

This “fit” with what I saw in “the real world” specifically what Alan Bond overpaid for Kerry Packer’s Channel Nine (“You only get one Alan Bond in your life, and I’ve had mine”).

Now, you cannot rationally assess what someone else would pay for an asset – you can only make a rationalisable view on that, because you need to make a n-th order decision on what you will pay to verfity what you think is true about the information you hold.

This is because after you do that you need to figure what you’ll pay to verify if what you think is true. And then you’ll need to figure out what you’ll pay to verify what you paid to verify what you think is true, about what you think is true, and so on. And so infinitum.

I thought you could solve this with automata – build a similation of market, with automata that carry out various strategies,and then successful automata copy themselves, and we could figure out how markets work that way.

But then I couldnt see a solution to automata that change strategy.

Ian Whitchurch

32

john m. 10.14.05 at 4:22 am

Comment #32:

“…most people act the way you expect”
This is exactly wrong, particularly when considering economics. Simple example: why buy an iPOD over a Zen? The Zen is cheaper and functionally equivocal. Answer: because the iPOD looks better. This is an aesthetic appeal and is a wholly emotional reaction. Economic models simply cannot factor an intangible such as this into any model as they cannot reliably predict human reactions any more than any human can. Ask the record companies who turned down the Beatles if you’re unsure of this line of argument…

33

Ruchira 10.15.05 at 1:03 am

jonas grumby:

“In the real world (even the one of spherical chickens), there aren’t any interesting complete information games.”

If you mean “interesting” the way most people do then this is clearly not true, since chess itself is interesting. For a game with more than two players, I suggest you look at Puerto Rico:
http://www.boardgamegeek.com/game/3076
The only element of incomplete information is that the plantation tiles are shuffled, but this is a rather minor element of gameplay and I contend that if you laid out all the plantation tiles face up in a sequence at the beginning it would still be an interesting game.

I’m guessing what you are referring to is the following: in a generic finite extensive-form game of complete information, backward induction yields a unique pure strategy Nash equilibrium. However, note the word “generic”–it *is* possible to construct interesting examples. I did so in my thesis:
http://math.berkeley.edu/~datta/thesis.pdf
on pp. 48-52 (pp. 60-64 of the PDF). In this example, unlike in generic extensive-form games, there are mixed Nash equilibria, and for various reasons the game is unpredictable; both the first and last players will randomize their moves.

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