Backward Induction and Nash Equilibrium
In the previous chapter, we have seen that the conjectures held by the players about the opponents’ behavior, and the revision of these conjectures during the game, may be represented by means of an assessment (σ, β). We have also seen alternative ways to specify optimal behavior against such assessments, formalized by the notions of best response and sequential best response. Roughly speaking, a criterion of rational decision making in extensive form games should give an answer to the following two questions: (1) for a given assessment (σ, β), which strategies may be viewed acceptable?, and (2) which assessments (o, β) may be viewed reasonable? Throughout this monograph, we shall assume that for a given assessment, players are expected to choose either a best response or a sequential best response against this assessment, depending on the concept, and hence the first question is answered by this assumption. The second question, however, is the most interesting one, and the remainder of this book is concerned with presenting and exploring rationality criteria that give different answers to the question which assessments are “reasonable” . In this chapter, we discuss a first series of rationality concepts that put restrictions on the behavioral conjecture profiles σ that may be held in a given assessment. All of these concepts are based on two influential ideas in the theory of extensive form games: backward induction and Nash equilibrium.
KeywordsNash Equilibrium Positive Probability Terminal Node Perfect Information Subgame Perfect Equilibrium
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