This chapter offers a critical review of attempts to refine the idea of a Nash equilibrium. It begins by reiterating the arguments against a naïve interpretation of subgame-perfect equilibria using Selten's Chain-Store Game as an example. It then introduces assessment equilibria as a simplified version of Kreps and Wilson's sequential equilibrium. The idea is then used to analyze a boundedly rational version of the Centipede Game. Two signaling games — the Burning Money Game and Quiche — are used to discuss forward induction and the intuitive criterion, both of which are found wanting. The chapter ends with a brief discussion of rationalizability, which is a coarsening of the Nash equilibrium concept.
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