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.

翻译：相关均衡使得协调者能够通过推荐行动来影响自利智能体，这些行动确保没有参与者有动机偏离。然而，该机制的有效性依赖于对智能体成本结构的准确认知。当成本参数存在不确定性时，推荐行动可能不再满足激励相容性，导致智能体可能通过偏离推荐而获益。我们研究了一种机会约束相关均衡问题建模方法，该方法考虑了智能体成本的不确定性，并以预设置信水平保证激励相容性。我们推导了灵敏度分析结果，量化了单个激励约束中的不确定性如何影响预期协调结果。特别地，该分析通过将降低不确定性的边际效益与激励约束的对偶灵敏度相关联，刻画了信息的价值，为确定应优先获取哪些不确定性源的信息提供了指导。结果进一步表明，提高置信水平并非总是有益的，它可能在鲁棒性与系统效率之间引入权衡。数值实验证明，所提框架能够在不确定环境中保持协调性能，且与分析中建立的理论见解一致。