Scaling Chance-Constrained Correlated Equilibrium Computation for Exclusive Resource-Assignment Games

2026-09-11

AI Summary

本文针对资源分配博弈中机会约束相关均衡计算的复杂性问题，提出了一种精确单一分配限制方法，显著降低了计算时间。

Abstract

The chance-constrained correlated equilibrium concept provides a robust coordination technique for self-interested agents whose costs are uncertain to a central coordinator, but the number of joint actions considered in its computation grows exponentially with the number of agents. We propose an exact-one resource-assignment restriction for games in which agents compete for shared resources and simultaneous use of a resource is undesirable or unsafe. The restriction allows each resource to be assigned to exactly one agent, reducing the number of joint actions considered from O(2^(nr)) to O(n^r) for n agents and r resources. The resulting problem is solved over the restricted joint action set while retaining all incentive constraints associated with unilateral deviations. We show that the feasible set of the restricted problem is exactly the convex hull of the chance-constrained pure Nash equilibria contained in the exact-one assignment set, yielding a necessary and sufficient condition for nonemptiness. We further derive a sufficient condition under which all chance-constrained pure Nash equilibria of the unrestricted game are retained by the restriction. Numerical experiments in a vertiport departure-corridor coordination scenario demonstrate a 99.81% reduction in median computation time relative to the unrestricted formulation while achieving equivalent coordination performance.

Problem

• chance-constrained correlated equilibrium
• exclusive resource-assignment games
• self-interested agents
• uncertain costs
• joint actions

Innovation

• exact-one resource-assignment
• chance-constrained correlated equilibrium
• reduced joint action set
• convex hull of equilibria
• computation time reduction