In Search of Lost Correlation: Correlated Equilibrium via Marginal Actions

2026-03-02

AI Summary

This study addresses the problem of characterizing which marginal distributions over individual agents’ action frequencies can be generated by some correlated equilibrium, when only these marginals are observable and the full joint distribution over action profiles is unavailable. By introducing a novel “no-arbitrage” condition—requiring that no external observer can secure a positive expected payoff by independently contracting with each agent and unilaterally deviating from the prescribed strategy—the paper provides the first complete characterization of the set of marginal distributions induced by correlated equilibria. This characterization naturally extends to the special case of Nash equilibria. The results establish necessary and sufficient conditions for inferring the underlying equilibrium structure of a game solely from local, marginal observations, thereby offering a rigorous theoretical foundation for equilibrium identification under partial information.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Mechanism Design
• Cognitive Modeling & Cognitive Systems: Agent Architectures

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• correlated equilibrium
• marginal actions
• no arbitrage
• simultaneous move game
• Nash equilibrium

Innovation

• correlated equilibrium
• marginal actions
• no arbitrage condition
• Nash equilibrium
• inverse game theory