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In game theory, as in applications of other technologies that use RPT [Revealed Preference Theory], the purpose of the machinery is to tell us what happens when patterns of behavior instantiate some particular strategic vector, payoff matrix, and distribution of information—for example, a PD [Prisoner's Dilemma]—that we’re empirically motivated to regard as a correct model of a target situation. The motivational history that produced this vector in a given case is irrelevant to which game is instantiated, or to the location of its equilibrium or equilibria. As Binmore (1994, pp. 95–256) emphasizes at length, if, in the case of any putative PD, there is any available story that would rationalize cooperation by either player, then it follows as a matter of logic that the modeler has assigned at least one of them the wrong utility function (or has mistakenly assumed perfect information, or has failed to detect a commitment action) and so made a mistake in taking their game as an instance of the (one-shot) PD. Perhaps she has not observed enough of their behavior to have inferred an accurate model of the agents they instantiate. The game theorist’s solution algorithms, in themselves, are not empirical hypotheses about anything. Applications of them will be only as good, for purposes of either normative strategic advice or empirical explanation, as the empirical model of the players constructed from the intentional stance is accurate. It is a much-cited fact from the experimental economics literature that when people are brought into laboratories and set into situations contrived to induce PDs, substantial numbers cooperate. What follows from this, by proper use of RPT, not in discredit of it, is that the experimental setup has failed to induce a PD after all. The players’ behavior indicates that their preferences have been misrepresented in the specification of their game as a PD. A game is a mathematical representation of a situation, and the operation of solving a game is an exercise in deductive reasoning. Like any deductive argument, it adds no new empirical information not already contained in the premises. However, it can be of explanatory value in revealing structural relations among facts that we otherwise might not have noticed.
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