his is of course exactly the type of problem that beliefs system solve in general games Here, however, the situation is much simpler, because the domain of uncertainty(the sets of payoff types)are fixed throughout the game In Perfect Bayesian equilibria(see OR for details), the information conveyed by strat- egy profiles is complemented by measures ui(h)E A(i) associated with each nonterminal history In interpreting the definitions, it is important to remember that, just like the probabilities Pi,ui(h) represents the beliefs of players other than i about Player i's type. These beliefs are common to all players, which is reasonable: after all, the priors pi are common, and all players observe exactly the same occurrences as the play progresses The key condition in the definition of a PbE is the requirement that these beliefs be action-determined. That is: if Player i does not move at a history h, then the beliefs about her should not change at h; and if Player i does move, than beliefs about her should only be affected by her own action at h(not by somebody else's action Just like the consistency requirement in SE, this complements Bayesian updating with restrictions on beliefs following unexpected actions (i.e. on beliefs at off-equilibrium histo-This is of course exactly the type of problem that beliefs system solve in general games. Here, however, the situation is much simpler, because the domain of uncertainty (the sets of payoff types) are fixed throughout the game. In Perfect Bayesian equilibria (see OR for details), the information conveyed by strat￾egy profiles is complemented by measures µi(h) ∈ ∆(Θi) associated with each nonterminal history. In interpreting the definitions, it is important to remember that, just like the probabilities pi , µi(h) represents the beliefs of players other than i about Player i’s type. These beliefs are common to all players, which is reasonable: after all, the priors pi are common, and all players observe exactly the same occurrences as the play progresses. The key condition in the definition of a PBE is the requirement that these beliefs be action-determined. That is: if Player i does not move at a history h, then the beliefs about her should not change at h; and if Player i does move, than beliefs about her should only be affected by her own action at h (not by somebody else’s action). Just like the consistency requirement in SE, this complements Bayesian updating with restrictions on beliefs following unexpected actions (i.e. on beliefs at off-equilibrium histo￾ries). 6