Chance-Constrained Correlated Equilibria for Robust Noncooperative Coordination

TL;DR

This paper introduces a chance-constrained correlated equilibrium framework that manages uncertainty in agents' costs, balancing robustness and efficiency, and guides information acquisition to improve coordination.

Contribution

It develops a novel chance-constrained formulation for correlated equilibria under uncertainty, with sensitivity analysis and an information-gain metric to enhance robustness.

Findings

CC-CE reduces coordination cost by up to 35% at optimal confidence levels.

Sensitivity analysis links uncertainty reduction to incentive constraint dual sensitivities.

The information-gain metric effectively identifies key uncertainty sources.

Abstract

Correlated equilibria enable a coordinator to influence the self-interested agents by recommending actions that no player has an incentive to deviate from. However, the effectiveness of this mechanism relies on accurate knowledge of the agents' cost structures. When cost parameters are uncertain, the recommended actions may no longer be incentive compatible, allowing agents to benefit from deviating from them. We study a chance-constrained correlated equilibrium problem formulation that accounts for uncertainty in agents' costs and guarantees incentive compatibility with a prescribed confidence level. We derive sensitivity results that quantify how uncertainty in individual incentive constraints affects the expected coordination outcome. In particular, the analysis characterizes the value of information by relating the marginal benefit of reducing uncertainty to the dual sensitivities of the incentive constraints, providing guidance on which sources of uncertainty should be prioritized for information acquisition. The results further reveal that increasing the confidence level is not always beneficial and can introduce a tradeoff between robustness and system efficiency. Numerical experiments demonstrate this tradeoff: CC-CE reduces realized coordination cost by up to 35% at intermediate confidence levels, while the proposed information-gain metric consistently identifies effective uncertainty sources to reduce.