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

TL;DR

This paper introduces a scalable approximation method for computing chance-constrained correlated equilibria in large systems, reducing computational complexity while maintaining effective agent coordination under uncertainty.

Contribution

The authors develop a convex combination approach that simplifies the computation of chance-constrained correlated equilibria by leveraging a finite set of pure equilibria, enabling tractable solutions.

Findings

Significant reduction in computation time for large-scale multi-agent coordination.

Lower system delay costs compared to current operational practices.

Consistent achievement of lower deviation rates under cost uncertainty.

Abstract

Chance-constrained correlated equilibrium enables coordination of noncooperative agents under cost uncertainty through probabilistic incentive-compatibility guarantees. However, computing such equilibria becomes intractable in large-scale systems 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.