The semantics of preference-based belief operators

摘要

In epistemic analyses of games, it is common to use subjective belief operators. There are numerous examples where KD45 operators like 'belief with probability 1' (e.g., Tan & Werlang [26]), 'belief with primary probability 1, (Brandenburger [10]) and 'conditional belief with probability 1, (Ben-Porath [7]) are applied. More recently, Brandenburger &; Keisler [13] and Battigalli & Siniscalchi [6] have proposed nonmonotonic subjective belief operators called 'assumption' and 'strong belief, respectively. These operators all have in common that they are based on subjective probabilities ― arising from a probability distribution, a lexicographic probability system, or a conditional probability system ― that represent the preferences of the player as a decision maker. Thus, in game theory there is a prevalence of preference-based belief operators.