Potential strategies Clause Samples

Potential strategies. Here we evaluate potential strategies (si) for each of the players, which includes a choice of action (ai ∈ {Ci, Ri }) for each of their potential types (ti ∈ Hi, Fi). The strategy for player i can therefore be represented as (ai |Hi, ai |Fi ). A strategy is a perfect Bayesian equilibrium strategy (si∗) for player i if it results in the maximum expected utility Ui, given the sequentially rational decisions of the other player. In this section, we are in- terested in identifying which combination of strategies, {si, sj }, are perfect Bayesian equi- librium strategies and yield a signed treaty between the players. To do this we evaluate combinations of strategies and whether or not they fall on the equilibrium path. P(C )j In the case that a treaty is signed (ai = Ci, aj = Cj), each player can update their belief that the other player is Honest. This belief of player i depends on the strategy of player j and is determined by Bayes rule λij = P(Hj |Cj) = P(Cj |Hj) P(Hj ) , noting that P(Hj) = λi.