Chance-Constrained Correlated Equilibria for Robust Noncooperative Coordination
Computer Science and Game TheoryMultiagent Systems
Summary
The authors study how to help a group of self-interested agents coordinate their actions when their costs are uncertain. They propose a method that makes sure agents want to follow recommendations with a certain level of confidence, even if the exact costs aren’t known. Their analysis shows how knowing more about specific uncertainties can improve coordination and that aiming for too much confidence might reduce overall efficiency. They also test their approach through simulations, confirming its usefulness when costs are uncertain.
Authors
Jaehan Im, Ufuk Topcu, David Fridovich-Keil
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.