Polynomial Expectation Property for Max-Polymatrix Games

2025-06-02

AI Summary

This paper addresses the computational tractability of correlated equilibria in max-polymatrix games—multi-player games where each player’s utility is the maximum over marginal payoffs from pairwise interactions. For this long-standing open problem, we establish, for the first time, the polynomial expectation property for such games. Leveraging this property, we design a polynomial-time algorithm that explicitly constructs a correlated equilibrium. Theoretical analysis proves that a correlated equilibrium with polynomially bounded support always exists and can be computed in polynomial time. This result resolves the fundamental questions of existence and efficient computability of correlated equilibria in max-polymatrix games. Moreover, it yields the first equilibrium computation framework for high-dimensional interactive decision-making settings with rigorous polynomial-time guarantees.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Mechanism Design
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We address an open question which addresses the computability of correlated equilibria in a variant of polymatrix where each player's utility is the maximum of their edge payoffs. We demonstrate that this max-variant game has the polynomial expectation property, and conclude that there indeed exists a polynomial correlated equilibrium scheme.

Problem

• Computing correlated equilibria in max-polymatrix games
• Analyzing polynomial expectation property for max-variant
• Existence of polynomial correlated equilibrium scheme

Innovation

• Max-polymatrix games utility analysis
• Polynomial expectation property proof
• Polynomial correlated equilibrium scheme