Chapter 7: Infinite Dynamic Games with Discrete Strategy Space: A Second Approach
7. Inﬁnite dynamic games with discrete strategy space: a second approach WEAKLY RENEGOTIATION-PROOF EQUILIBRIA The Concept1 7.1 7.1.1 In Chapter 6 it became clear that by requiring strategies to be renegotiation-proof the number of equilibria in repeated games could be substantially reduced. Moreover, requiring strategies to constitute a strongly perfect equilibrium reduced the set of equilibria even further. However, it turned out that for many games for which a renegotiation-proof equilibrium exists, no strongly perfect equilibrium can be found. For ﬁnite games an obvious way to deﬁne a Pareto-eﬃcient subgameperfect strategy involved a recursive deﬁnition. Now, in an inﬁnite time horizon, such a deﬁnition is not available, which leaves some leeway for ﬁnding an adequate formulation of what renegotiation-proofness means for supergames. Since Farrell and Maskin’s (1989a, b) deﬁnition has probably found the most widespread application in the literature, we concentrate exclusively on their concept of weakly and strongly renegotiationproof equilibria.2 It should be mentioned that the authors exclusively restrict the validity of their concept to two-player games and we follow this assumption in this chapter too. The possibility of an extension to N-player games will be discussed in Chapter 14. Farrell and Maskin’s deﬁnition of a weakly renegotiation-proof equilibrium (WRPE) takes up the central idea of the previous chapter that an equilibrium strategy should have no Pareto-dominated continuation payoﬀ in any subgame. In particular, in the ‘punishment subgame’ the punisher should not ﬁnd it attractive to skip the punishment. Once more,...
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