In Search of Lost Correlation: Correlated Equilibrium via Marginal Actions

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.