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We provide an epistemic foundation for cooperative games by proof theory viastudying the knowledge for players unanimously accepting only core payoffs. Wefirst transform each cooperative game into a decision problem where a playercan accept or reject any payoff vector offered to her based on her knowledgeabout available cooperation. Then we use a modified KD-system in epistemiclogic, which can be regarded as a counterpart of the model for non-cooperativegames in Bonanno (2008), (2015), to describe a player's knowledge,decision-making criterion, and reasoning process; especially, a formula calledC-acceptability is defined to capture the criterion for accepting a core payoffvector. Within this syntactical framework, we characterize the core of acooperative game in terms of players' knowledge. Based on that result, wediscuss an epistemic inconsistency behind Debreu-Scarf Theorem, that is, theincrease of the number of replicas has invariant requirement on eachparticipant's knowledge from the aspect of competitive market, while requiresunbounded epistemic ability players from the aspect of cooperative game.

Knowledge and Unanimous Acceptance of Core Payoffs: An Epistemic Foundation for Cooperative Game Theory