Coordination Mechanisms with Partially Specified Probabilities

TL;DR

This paper explores how outcomes can be implemented when players have partial knowledge of data distributions and form beliefs via maximum-entropy inference, expanding the understanding of correlated equilibria.

Contribution

It provides characterizations of implementable outcomes under partial distribution knowledge and introduces a cross-entropy condition for canonical mechanisms.

Findings

Implementable outcomes match jointly coherent outcomes with unrestricted message spaces.

A single cross-entropy condition determines implementability in canonical mechanisms.

The framework applies to various examples and classes of games.

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.