Chance-Constrained Correlated Equilibria for Robust Noncooperative Coordination

2026-03-14

AI Summary

This work addresses the loss of incentive compatibility in conventional correlated equilibria under uncertainty in agents’ cost parameters, which can lead to coordination failure. To overcome this limitation, the paper proposes a chance-constrained correlated equilibrium framework that enforces incentive compatibility with a prescribed confidence level, thereby enabling robust non-cooperative coordination. Leveraging stochastic optimization and duality theory, the authors develop a sensitivity analysis to quantify the value of information and characterize the trade-off between confidence levels and system efficiency. Both theoretical analysis and numerical experiments demonstrate that the proposed framework effectively preserves coordination performance under uncertainty, validating strategic prioritization of information acquisition and revealing an intrinsic balance between robustness and efficiency.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Game Theory and Economic Paradigms: Coordination and Collaboration
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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 that the proposed framework maintains coordination performance in uncertain environments and are consistent with the theoretical insights developed in the analysis.

Problem

• correlated equilibria
• incentive compatibility
• cost uncertainty
• chance constraints
• noncooperative coordination

Innovation

• chance-constrained correlated equilibrium
• incentive compatibility
• cost uncertainty
• sensitivity analysis
• value of information