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What is game theory?

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This SEP article on practical reason does a pretty good job of explaining what I was getting at earlier. These parts particularly:

Among the substantive norms of practical reason, those of instrumental rationality have seemed least controversial to philosophers. Instrumental rationality, in its most basic form, instructs agents to take those means that are necessary in relation to their given ends. In the modern era, this form of rationality has widely been viewed as the single unproblematic requirement of practical reason. The instrumental principle makes no assumptions about the prospects for rational scrutiny of peoples' ends. Rational criticism of this kind apparently presupposes that there are objective reasons and values, providing standards for assessment of ends that are independent from psychological facts about what people happen to be motivated to pursue. In line with the naturalistic attitude sketched in section 2, however, it may be doubted whether such independent standards can be reconciled with the metaphysical commitments of contemporary scientific practice. A world that is shorn of objective values or norms leaves no room for rational criticism of peoples' ends, but only for Weberian Zweckrationalität: the rational determination of means to the realization of ends that are taken to be given, as a matter of human psychological fact.

This line of thought can be traced back to the philosophy of David Hume, who famously asserted that ‘Reason is, and ought only to be the slave of the passions’ (Hume 1978, 415). Those attracted to the Humean approach should bear in mind, however, that instrumental rationality is itself the expression of an objective normative commitment. The instrumental principle says that we are rationally required to take the means that are necessary to achieve our ends; if the principle represents a binding norm of practical reason, then we are open to rational criticism to the extent we fail to exhibit this kind of instrumental consistency, regardless of whether we want to comply with the principle or not. If naturalism really entails that there can be no objective norms or values, it may be wondered how an exception can possibly be made for the instrumental requirement. A more consistently naturalistic position would be to reject even Zweckrationalität in favor of a skeptical attitude towards practical reason in all its forms (Hampton 1998)—an attitude that may well correspond to the intentions of the historical Hume (compare Dreier 1997, Millgram 1995). Further questions can be raised about the plausibility of the suggestion that the instrumental norm exhausts the requirements of practical reason. The norm says that one should take the means that are necessary relative to one's psychologically-given ends. But how can the fact that a given means exhibits this kind of necessity give a person reason to choose the means, if the end is not itself something it would be valuable to achieve in some way? The instrumental principle seems to function as a binding norm of practical reason only if it is taken for granted that there are additional, independent standards for the assessment of our ends (Korsgaard 1997; Quinn 1993).

[...]

Humean proponents of structural approaches to practical reason have attempted to accommodate the rational criticism of individual ends, without departing from the spirit of Zweckrationalität, by expanding their view to encompass the totality of an agent's ends. Thus, even if there are no reasons or values that are ultimately independent of an agent's given ends, the possibility remains that we could criticize particular intrinsic desires by reference to others in an agent's subjective motivational set. An agent's desire for leisure, for instance, might be subordinated insofar as its satisfaction would frustrate the realization of other goals that are subjectively more important to the agent, such as professional success. Practical reason, it might be suggested, is a holistic enterprise, properly concerned not merely with identifying means to the realization of individual ends, but with the coordinated achievement of the totality of an agent's ends.

Many philosophers take this holistic approach to be the most promising way of thinking about the tasks of practical reason. It defines an important and difficult problem for practical reason to address, without departing from the metaphysically modest assumption that there is no court of appeal for the rational criticism of an agent's ends that is independent of those ends themselves. The holistic approach finds its most sophisticated and influential expression in the maximizing conception of practical rationality. According to the maximizing conception, the fundamental task of practical reason is to determine which course of action would optimally advance the agent's complete set of ends. Thus it is widely accepted that the rational action for a given agent to take is the one whose subjective expected utility—reflecting both the utility of possible outcomes, from the agent's point of view, and the agent's beliefs about the probability of those outcomes—is the highest.

Therefore, the individual end of getting Sally could be judged to be irrational. This is a good article to read for those interested in praxeology.

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Neodoxy replied on Tue, Dec 4 2012 9:43 PM

I can't for the life of me understand why it is that Mises so ardently rejected game theory. He seems to have argued that game theory is inapplicable to the market economy because A it is a game which different than what people do in the economy and B because all participants in the market economy must benefit from a transaction in order to make it.

Both of these premises seem utterly bogus to me in terms of actually criticizing market theory. In my mind game theory, when done properly, is extremely praxeological and not that different from Mises' method itself. This is similar to my complaint in MES where Rothbard denied that economic analysis can say anything about the various actions of any form of market structure.

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My main issue with game theory is that the players (usually) are not supposed to change the rules of the game. In most classic examples they are prohibited from communicating, promising and threatening. Also, quite often there is no long-term interaction, so the players are induced to screw each other instead of cooperating. Thus results of such analysis are not directly applicable to real life, where actors are not so handicapped.

In other words, game theory is fine for analysing toy examples, and maybe getting some insights from them. It does NOT prove anything about the real world problems (at least in the cases which I saw).

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Andris Birkmanis:

My main issue with game theory is that the players (usually) are not supposed to change the rules of the game. In most classic examples they are prohibited from communicating, promising and threatening. Also, quite often there is no long-term interaction, so the players are induced to screw each other instead of cooperating. Thus results of such analysis are not directly applicable to real life, where actors are not so handicapped.

In other words, game theory is fine for analysing toy examples, and maybe getting some insights from them. It does NOT prove anything about the real world problems (at least in the cases which I saw).

Signaling and bargaining games are all about communication and what the best message to sends is. Also, repeated interaction games have been extraordinarily popular for the last 35 years or so. 

 

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They may be popular among the experts, but the kind of stuff fed to the masses is very different.

On an unrelated track, do we count, e.g., mechanism design as "game theory", too?

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Raoul replied on Wed, Dec 5 2012 3:13 AM

I think GT includes some fun and interesting aspects, but, when it grows overreffined, it's both useless and uncorrect.

Now, it seems to me it's today required to master the GT, because it's the new language of economics. GT is a way to put old wine in new bottles. So, even if I don't like that, I'm feeling compelled to learn it (one day or another). 

I see that, for instance, in antitrust economics. Because all pro-antitrust arguments were debunked, pro-antitrust theorist took the old arguments, gave them new names and new formal presentation, and claim these new arguments were un-refuted.

So the use of learning GT is to show that in the new bottles there's only old bad wine.

Beside, there's a question I wonder about the mathematical version of GT. Does not the Knightian-Misesian theory of probability refute it? Example. If X has three possibilities A, B and C open to him, the (basic--maybe it's a strawman) game theorist is going to say, that the probabilities that X takes each course of action are A = 33%, B = 33% and C = 33%. Now, because these events aren't homogeneous, I'd answer that such probabilities are meaningless. Any thought?

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GT advises random mixes of strategies only under specific conditions, and even then the mix is not necessarily uniform. E.g., 33/33/33 split makes sense when playing rock/paper/scissors, but not when deciding whether to buy/sell/stay on the market.

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Raoul replied on Wed, Dec 5 2012 6:34 AM

So, is GT able to cope successfully with situations where the actor is deciding whether to buy/sell/stay on the market, i.e. where there's uncertainty in the Knightian meaning of the term? Are (good) game theorists able to integrate "uncertainty" without assuming a known distribution of risks?

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Well, the Knightian uncertainty is, by definition, unmeasurable. Which means, you cannot calculate it or with it. How are you going to use math with something like that?

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Raoul replied on Wed, Dec 5 2012 7:24 AM

Ok, my question should have been drafted this way: do (good) game theorists stop when confronted to uncertainty or do they ignore the problem and deal with uncertainty as if it was a quantifiable risk? And if they take into account the problem, how is it possible to have mathematical GT?

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Scientific theories are not hammers and they are not used like hammers.

Does an airplane pilot directly apply results from the theory of fluid dynamics when taking his real world decisions?

No. He is trained in reading instruments and situations and taking decisions following some practical guidelines and rules of thumb.

But he uses knowledge from fluid dynamics, indirectly. This knowledge maybe concealed from him in aspects of the machinery design concepts he does not necessarily fully understand.

It is the same thing all the time.

We seldom apply theoretical knowledge directly to "real world" problems. Theoretical knowledge reveals itself when dealing with theoretical problems abstracted from real world situations.

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The main purpose of game theory is to provide a theoretical framework whitin which some patterns of decision making can be analysed, disturbed, tested and perhaps better understood.

It is an strategy for understanding human affaris and other strategical situations, such as in biology and even other situations involving automatons taking decisions.

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When somebody claims to have conceived a pratical strategy form a decision process in the real world that is proven to be right by "game theory", he is either exaggerating in order to convince lay people, or he is practising pseudo-science.

You cannot prove stuff in the real world, only inside the logical framework of a theory.

Any scientific theory can only be, to a certain degree, a good or a bad fit to what we perceive to be actually happening.

 

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