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

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.

Figures (4)

• Figure 3: Illustrative example of a coordination scenario inspired by airport virtual queueing systems. A central coordinator recommends which aircraft to release ① but does not enforce aircraft-level decisions directly. Released aircraft contribute to shared congestion $c(t)$ ( ②-- ③) and to queueing delay $\delta_f(t)$ ④, while departures are governed by runway service rates $\mu_r$ ⑤. Airlines retain autonomy over whether to follow the recommendations ⑥, creating a noncooperative coordination problem.
• Figure 4: Scalability comparison between Full-CCCE and RR-CCCE. Wall-clock computation time (log scale) is shown as a function of the number of eligible aircraft per epoch. The horizontal dotted line indicates the epoch duration (4 minutes), representing the real-time constraint for online deployment.
• Figure 5: Comparison of realized delay cost across coordination mechanisms. Full-CCCE and RR-CCCE outperform FCFS as traffic increases. RR-CCCE exhibits a performance gap relative to Full-CCCE due to approximation. Average marked by $\circ$.
• Figure 6: Performance under cost uncertainty ($\alpha=90\%$, six airlines). (a) Delay cost distribution as a function of cost noise level $\sigma$. All correlated equilibrium-based methods maintain comparable delay cost as uncertainty increases. (b) Deviation rate versus $\sigma$. The uncertainty-aware formulation reduces deviation rates, with the reduced-rank approach maintaining consistently low deviation levels across all $\sigma$. Horizontal lines indicate mean values.

Theorems & Definitions (8)

• Definition 1: Correlated equilibrium aumannaumann_2
• Example 1: Coordination via correlated equilibrium
• Definition 2: Chance-constrained CE j_vq
• Definition 3: Chance-constrained pure Nash equilibrium
• Lemma 1
• proof
• Theorem 1
• proof