Knowledge and Unanimous Acceptance of Core Payoffs: An Epistemic Foundation for Cooperative Game TheoryI
Shuige Liu · arXiv (Cornell University) · 2018
We provide an epistemic foundation for the core of a cooperative game by proof theory. Given a cooperative game, we first transform each payoff vector into a decision problem (accept or reject) for each player. Then we use a modified KD-system in epistemic logic to describe a player's belief/knowledge, decision-making criterion, and reasoning process. Especially, we define C-acceptability to capture the criterion for a core payoff vector. Within this syntactical framework, we characterize the core of a cooperative game in terms of each player's knowledge. Based on this result, we discuss epistemic inconsistency behind Debreu-Scarf Theorem.