Coordination Mechanisms with Partially Specified Probabilities

2026-05-08

AI Summary

This study addresses the implementability of desired outcomes in strategic settings where only partial information about the data-generating process—such as expectations of a limited set of random variables—is known. It investigates implementation under players’ beliefs formed via maximum entropy inference, establishing that implementable outcomes are precisely those that are jointly coherent. The work extends the notion of correlated equilibrium by providing characterizations of implementability under both unrestricted message spaces and canonical mechanisms. A novel criterion based on level sets of cross-entropy is introduced to assess canonical mechanisms. By integrating tools from maximum entropy inference, cross-entropy analysis, correlated equilibrium theory, and convex analysis, the proposed framework demonstrates broad applicability across multiple classes of games, significantly expanding the scope of traditional correlated equilibrium concepts.

Abstract

We study which outcomes are implementable by disclosing coarse statistics of a data-generating process rather than its full distribution. Players observe data whose joint distribution is only partially known: they know the expectations of finitely many random variables and form beliefs by maximum-entropy inference. We obtain two characterizations. When message spaces are unrestricted, implementable outcomes coincide with jointly coherent outcomes, expanding the set of correlated equilibria. With canonical mechanisms, implementability reduces to a single cross-entropy condition: the target outcome must lie on the cross-entropy level set of some correlated equilibrium that passes through that equilibrium itself. Examples and several classes of games illustrate the reach of the framework.

Problem

• coordination mechanisms
• partially specified probabilities
• implementable outcomes
• maximum-entropy inference
• correlated equilibria

Innovation

• maximum-entropy inference
• partially specified probabilities
• correlated equilibrium
• cross-entropy condition
• coordination mechanisms