Common p-Belief with Plausibility Measures: Extended Abstract

An epistemic probability model has a common prior if P i = P j for all i, j A .To simplify notation, we write W, ( i ) iA , F , P when P is the common prior.Remark 2.2.We could also allow a different -algebra F i for each P i , but this complexity is unnecessary for the purpose of this paper.Given a state w and an agent i A , the set i (w) represents i's information at state w.With this interpretation in mind, we can now define the agents' knowledge and posterior beliefs.Definition 2.3 (Knowledge).Suppose that W, ( i ) iA , F , (P i ) iA is an epistemic probability model.The knowledge operator for agent i A is the function K i : (W ) (W ) where: for all E W ,If w K i (E) we say that agent i knows that E in w. 3 Definition 2.4 (Posterior Belief).Given an epistemic probability model W, ( i ) iA , F , (P i ) iA .The posterior belief for i at state w is the (possibly partial) function P i,w : (W ) [0, 1] where: for all E W ,Suppose that W, ( i ) iA , F , (P i ) iA is an epistemic-probability model.We write K(E) for the event that everyone knows E, and C(E) for the event that E is common knowledge. 4Formally, everyone knows is a function K : (W ) (W ) where: for all E W ,