In Search of Lost Correlation: Correlated Equilibrium via Marginal Actions

TL;DR

This paper characterizes the sets of marginal action distributions that can result from correlated equilibria in finite games, using a no arbitrage condition, and extends the results to Nash equilibria.

Contribution

It introduces a novel characterization of marginal distributions from correlated equilibria using no arbitrage conditions, applicable to both correlated and Nash equilibria.

Findings

Sets of marginal distributions consistent with correlated equilibria are characterized.

The no arbitrage condition is key to identifying feasible marginal distributions.

Results extend to Nash equilibria, broadening their applicability.

Abstract

In this paper, we study which data can be induced by a correlated equilibrium given a known finite simultaneous move game. We assume that an analyst has access to the frequency of each agent's actions but does not have access to the distribution over joint action profiles. We characterize which sets of marginal distributions over actions arise from some correlated equilibria via a type of no arbitrage condition. An outside observer is unable to make a profit in expectation by independently contracting with each agent and collecting a portion of the total utility gained via unilateral deviation. This characterization naturally extends to Nash equilibria.