Correlated equilibria provide a mechanism for coordinating noncooperative agents through incentive-compatible recommendations, but their guarantees degrade under uncertainty in agents' cost structures. Chance-constrained correlated equilibrium addresses this issue by enforcing incentive compatibility with probabilistic guarantees, but computing such equilibria remains intractable in large-scale coordination problems due to the exponential growth of the joint action space. We develop an approximation method for computing chance-constrained correlated equilibria by showing that these equilibria admit a representation as convex combinations of a finite set of chance-constrained pure Nash equilibria, enabling tractable computation without solving the full correlated equilibrium program. Numerical experiments on large-scale multi-airline coordination scenarios demonstrate substantial reductions in computation time while achieving lower system delay costs compared to current operational practice. Under cost uncertainty, the proposed method consistently achieves lower deviation rate compared to the full formulation while achieving comparable coordination performance.

翻译：相关均衡通过激励兼容的建议为非合作智能体提供了一种协调机制，但在智能体的成本结构存在不确定性时其保证性能会下降。机会约束相关均衡通过施加具有概率保证的激励兼容性来解决这一问题，但由于联合动作空间的指数级增长，在大规模协调问题中计算此类均衡仍然难以处理。我们开发了一种近似方法来计算机会约束相关均衡，通过证明这些均衡可表示为有限个机会约束纯纳什均衡的凸组合，从而无需求解完整的相关均衡规划即可实现可计算性。在大规模多航空公司协调场景的数值实验中，与当前运营实践相比，该方法在计算时间上实现了显著降低，同时获得了更低的系统延迟成本。在成本不确定性条件下，所提方法在实现可比协调性能的同时，其偏离率始终低于完整规划方案。