Consistency and Sequential Rationality
In Chapter 3 we have discussed some restrictions on assessments which, roughly speaking, reflect the requirement that players should believe that opponents act optimally. In the concepts of Nash equilibrium and normal form perfect equilibrium, this requirement is only imposed at the beginning of the game, whereas in other concepts such as backward induction, subgame perfect equilibrium and quasi-perfect equilibrium, it is imposed at every stage of the game. The concepts discussed so far did not explicitly involve the belief system, however, since explicit restrictions were put on the behavioral conjecture profile only. In this chapter we discuss some rationality criteria which impose explicit conditions on the belief system as well. We consider two types of restrictions. The first type, which we refer to as consistency conditions, should guarantee that the behavioral conjectures and the beliefs in a given assessment should not contradict one another. For instance, the beliefs held by a player at an information set should be in accordance with his beliefs held at earlier information set, which, in turn, should be compatible with the behavioral conjecture held by this player about the opponents’ behavior. Conditions of the second type are similar to those presented in Chapter 3, as they require players to attach positive probability only to those opponents’ strategies that constitute sequential best responses. By imposing this requirement at every information set we obtain the notion of sequential rationality. If we impose it only at those information sets that are not avoided by the initial conjectures, the weaker notion of weak sequential rationality results.
KeywordsNash Equilibrium Belief System Terminal Node Perfect Information Subgame Perfect Equilibrium
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