Chapter 10: Strategy, Externality, and Rationality
It has been observed that much literature in game theory relies on simplifying assumptions that can frustrate the application of the theory, particularly to public policy. “Perfect recall” is one instance here. The objective of this chapter is to give arguments why several other assumptions are problematic. We will begin with a common (often tacit) assumption of non-cooperative game theory and then proceed to explore two further issues of cooperative game theory and an ambiguity in the concept of rationality. 10.1 “BEHAVIOR STRATEGIES SUFFICE” We now have the technical apparatus to reconsider the role of contingent and behavior strategies in game theory, and the idea that, thanks to Kuhn’s demonstration, “behavior strategies suffice.” As we recall from Chapter 3, Kuhn had demonstrated that an important family of games in extensive form can be analyzed by using behavior strategies only, choosing local (generally randomized) best responses. It was noted, however, that this analysis is not applicable to games of imperfect recall (CGT, 1997, pp. 146–68), nor to any cooperative game (Selten, 1964), nor does it recover all Nash equilibria (CGT, 1997, pp. 312–54). It was also stated in Chapter 3 that Kuhn’s reasoning does not apply to non-cooperative equilibrium concepts other than the Nash equilibrium. This will now be discussed. In particular, correlated strategies cannot be derived from the local determination of behavior strategies as best responses at each information set. Consider Game 10.1, shown in extensive form by Figure 10.1. No “story” or application will be given for...
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