Kreps and Wilson suggest the following definition Definition 3 Fix a finite general extensive game T. An assessment(B, u)is consistent iff there exists a sequence of assessments(6m, u") converging to(B, p) and such that(i) Bi(Ii(a)>0 for every iE N, I Ti and a E A(D); and(ii)un is derived from Bn via Bayes It is easy to see that this definition captures the intended restrictions. Note that(ii) makes sense because, since every action in the game receives positive probability, every information set is also reached with positive probability, so Bayes'rule always applies Myerson suggests the following argument. Almost all elements of the set B of behavioral strategy profiles satisfy Condition (i) in Definition 3: that is, Condition(i) is generically satisfied. Also, Condition(ii) is very reasonable, so we definitely want all assessments(B, u) such that B satisfies(i) to be deemed consistent if and only if u is derived from B by Bayes' rule. Finally, it seems reasonable(and convenient) to assume that the set of consistent assessments is closed; hence, it makes sense to define it to be precisely the closure of the set of assessments satisfying()and(ii This may not appear to be a tremendously compelling argument; however, let me add that, for certain classes of games, consistency is equivalent to much simpler conditions on beliefs(when the latter are represented in an appropriate format ) Also, consistency can be characterized for general games in a manner that does not involve limits(although the characterization is not tremendously appealing) We are finally ready to define sequential equilibrium Definition 4 Fix a finite general extensive game T. An assessment (B, u) is a sequential equilibrium of r iff it is consistent and sequentially rational Perfect Bayesian equilibrium Some people find the definition of sequential equilibrium unwieldy(this refers in particular to the consistency requirement ). Also, consistency is only defined for finite games, so sequential equilibrium does not really apply to relatively simple games such as Bayesian extensive games with observed actions where type sets are infinite In such games, just like in a Bayesian game with simultaneous moves, one must specify a strategy for each payoff-type of each player. That is, we must specify type-contingent strategies. Hence, upon reaching a history h, players may be able to make inferences about their opponents' types based on the (equilibrium) strategy profile. However, at histories off the anticipated path of play, it is clear that the strategy profile does not convey any information about opponents' typesKreps and Wilson suggest the following definition. Definition 3 Fix a finite general extensive game Γ. An assessment (β, µ) is consistent iff there exists a sequence of assessments (β n , µn ) converging to (β, µ) and such that (i) β n i (Ii)(a) > 0 for every i ∈ N, I ∈ Ii and a ∈ A(I); and (ii) µ n is derived from β n via Bayes’ rule. It is easy to see that this definition captures the intended restrictions. Note that (ii) makes sense because, since every action in the game receives positive probability, every information set is also reached with positive probability, so Bayes’ rule always applies. Myerson suggests the following argument. Almost all elements of the set B of behavioral strategy profiles satisfy Condition (i) in Definition 3: that is, Condition (i) is generically satisfied. Also, Condition (ii) is very reasonable, so we definitely want all assessments (β, µ) such that β satisfies (i) to be deemed consistent if and only if µ is derived from β by Bayes’ rule. Finally, it seems reasonable (and convenient) to assume that the set of consistent assessments is closed; hence, it makes sense to define it to be precisely the closure of the set of assessments satisfying (i) and (ii). This may not appear to be a tremendously compelling argument; however, let me add that, for certain classes of games, consistency is equivalent to much simpler conditions on beliefs (when the latter are represented in an appropriate format). Also, consistency can be characterized for general games in a manner that does not involve limits (although the characterization is not tremendously appealing). We are finally ready to define sequential equilibrium. Definition 4 Fix a finite general extensive game Γ. An assessment (β, µ) is a sequential equilibrium of Γ iff it is consistent and sequentially rational. Perfect Bayesian equilibrium Some people find the definition of sequential equilibrium unwieldy (this refers in particular to the consistency requirement). Also, consistency is only defined for finite games, so sequential equilibrium does not really apply to relatively simple games such as Bayesian extensive games with observed actions where type sets are infinite. In such games, just like in a Bayesian game with simultaneous moves, one must specify a strategy for each payoff-type of each player. That is, we must specify type-contingent strategies. Hence, upon reaching a history h, players may be able to make inferences about their opponents’ types based on the (equilibrium) strategy profile. However, at histories off the anticipated path of play, it is clear that the strategy profile does not convey any information about opponents’ types. 5