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In Search of Lost Correlation: Correlated Equilibrium via Marginal Actions

Christopher P. Chambers, Maxime Cugnon de Sévricourt, Christopher Turansick

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.

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.
Paper Structure (7 sections, 2 theorems, 27 equations, 2 tables)

This paper contains 7 sections, 2 theorems, 27 equations, 2 tables.

Table of Contents

  1. Introduction
  2. Related Literature
  3. The Model
  4. Correlated Equilibrium
  5. Nash Equilibrium
  6. Conclusion
  7. Proofs

Key Result

Theorem 2.3

A marginal strategy profile $p$ is compatible with a correlated equilibrium if, and only if, it is unexploitable by action-wise transfer schemes.

Theorems & Definitions (9)

  • Definition 2.1
  • Definition 2.2
  • Theorem 2.3
  • Example 2.4
  • Example 2.5
  • Definition 2.6
  • Theorem 2.7
  • proof : Proof of \ref{['th:correlated_eq']}
  • proof : Proof of \ref{['th:Nash']}