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

2026-04-01

AI Summary

This work addresses the challenges of scalability and incentive compatibility in large-scale multi-agent coordination under cost uncertainty, where traditional correlated equilibria suffer from exponential computational complexity and fail to guarantee incentive compatibility. The authors propose a low-rank representation of chance-constrained correlated equilibria, revealing for the first time that such equilibria can be expressed as convex combinations of a finite set of chance-constrained pure Nash equilibria. This insight circumvents the need to solve high-dimensional optimization problems. By integrating chance-constrained optimization, correlated equilibrium theory, and low-rank structural analysis, the method significantly enhances computational tractability while preserving probabilistic incentive compatibility. Evaluated in a multi-airline coordination scenario, the approach achieves substantially improved computational efficiency, reduces system-wide delay costs compared to current practices, and maintains low deviation rates and strong coordination performance under uncertainty.

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.

Problem

• correlated equilibria
• chance-constrained
• scalable coordination
• cost uncertainty
• computational tractability

Innovation

• chance-constrained correlated equilibrium
• reduced-rank structure
• scalable coordination
• convex combination of pure Nash equilibria
• computational tractability