Chapter 6: Finite Dynamic Games with Discrete Strategy Space: A Second Approach
INTRODUCTION 6.1 In Section 4.4 we demonstrated that in games with two or more stage game Nash equilibria (NE) all payoﬀ vectors can be sustained by subgameperfect equilibrium strategies which give each player more than in his/her worst NE provided discount factors are close to 1. Such an abundance of equilibria was also found in supergames where even weaker conditions must be satisﬁed to derive folk theorem type of results. Thus, although we strengthened the equilibrium concept for dynamic games by requiring strategies not only to be an NE but also to be a subgame-perfect equilibrium (SPE), the set of equilibrium payoﬀs remains large. A concept which is capable of reducing (though not eliminating) this lack of predictability in repeated games is the concept of renegotiation-proofness. Though there emerged many versions of this concept, in the context of ﬁnite games the interpretation seems not very controversial (Benoît and Krishna 1993; Bergin and MacLeod 1993; Bernheim et al. 1987; Fudenberg and Tirole 1996, pp. 174ﬀ.). The subsequent discussion is based on Benoît and Krishna’s deﬁnition which is restricted to two-player games. In this case their concept coincides with Bernheim et al.’s deﬁnition of coalitionproof equilibria, which we discuss in Chapter 15. In the above-cited literature it is argued that threats which imply a lower payoﬀ to deviators and punishers alike will be subject to renegotiations and therefore lose their credibility. If defection occurs, it is in the interest of all players to treat bygones as...
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