Chance-Constrained Correlated Equilibria for Robust Noncooperative Coordination
This addresses robust coordination in multi-agent systems for applications like robotics or economics, but it is incremental as it extends existing correlated equilibrium concepts with chance constraints.
The paper tackles the problem of coordinating self-interested agents under uncertain cost structures by proposing a chance-constrained correlated equilibrium framework that guarantees incentive compatibility with a prescribed confidence level, and numerical experiments show it maintains coordination performance in uncertain environments.
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.