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：相关均衡使得协调者能够通过推荐行动影响自利智能体，前提是任何智能体都没有偏离推荐行动的动机。然而，该机制的有效性依赖于精确掌握智能体的成本结构。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条件，导致智能体能够从偏离中获益。本文研究了一种考虑智能体成本不确定性的机率约束相关均衡问题建模，该模型能以预设置信水平保证激励相容性。我们推导了灵敏度结果，量化了个体激励约束不确定性对期望协调结果的影响。特别地，本文通过关联降低不确定性的边际收益与激励约束的对偶灵敏度，刻画了信息的价值，为识别应优先获取信息来源的不确定性类型提供指导。研究进一步表明，提高置信水平并非总是有利的，这可能在鲁棒性与系统效率之间引入权衡。数值实验展示了这一权衡：在中等置信水平下，CC-CE方法可降低高达35%的实际协调成本，而所提出的信息增益指标能持续识别有效的降不确定性来源。