2023 Reports

Cooperative Analysis of Incomplete Information

Liu, Qingmin

We propose a theory of cooperative games with incomplete information. The theory concerns stable interactions that cannot be undermined by coalitions and is built on a criterion of rational counterfactual reasoning, which requires that in every counterfactual scenario of coalitional deviation, every individual player formulate a belief and act optimally, and in doing so they collectively prevent the counterfactual scenario from actualizing. We equip the criterion with weak consistency and strong consistency to reflect the alignment of players’ beliefs and incentives in deviating coalitions, and demonstrate their implications through two applications. We identify a condition of comonotonic differences that preserves the efficiency of stable matching with incomplete information, where Tarski’s fixed point theorem is a useful tool. We show that mutual costly signaling unravels outcome-relevant incomplete information in networks.

Keywords: Cooperative Games, Incomplete Information, Matching, Network Formation