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.

翻译：相关均衡可通过协调者推荐行动实现自我利益主体的协同，此时任何参与者均无偏离动机。但当成本参数存在不确定性时，这种机制的有效性依赖于对主体成本结构的精确认知——推荐行动可能不再满足激励相容条件，导致参与主体通过偏离获得收益。本文研究考虑成本不确定性的机会约束相关均衡问题，该模型以预设置信度保证激励相容条件成立。我们推导出敏感性分析结果，量化个体激励约束的不确定性对预期协调结果的影响。具体而言，通过将降低不确定性的边际效益与激励约束的对偶敏感性相关联，本文刻画了信息的价值，为优先获取何种不确定性来源提供指导。研究进一步揭示：提高置信水平并非总是有益的，这将在鲁棒性与系统效率间引入权衡。数值实验验证了该权衡：在中等置信水平下，所提CC-CE方法可使实际协调成本降低高达35%，同时所提出的信息增益指标能持续识别有效的不确定性缩减来源。