Scalable Coordination with Chance-Constrained Correlated Equilibria via Reduced-Rank Structure

Abstract: 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.