Verification of Correlated Equilibria in Concurrent Reachability Games

2026-04-27

AI Summary

This study addresses the verification of correlated equilibria and their subgame-perfect refinements in concurrent reachability games. Motivated by the safety and scalability requirements of multi-agent systems, it introduces—for the first time—the notion of subgame-perfect correlated equilibrium and conducts a systematic investigation integrating formal verification, game-theoretic analysis, computational complexity theory, and compact representations via Bayesian networks. The main contribution lies in establishing that, under standard representations, verifying correlated equilibria is P-complete, whereas its subgame-perfect refinement admits a solution in O(log²n) space, revealing a counterintuitive complexity separation. However, this gap vanishes when equilibria are represented using Bayesian networks, where both problems exhibit comparable computational complexity.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Cooperative Game Theory
• 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: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

As part of an effort to apply the rigorous guarantees of formal verification to multi-agent systems, the field of equilibrium analysis, also called rational verification, studies equilibria in multiplayer games to reason about system-level properties such as safety and scalability. While most prior work focuses on deterministic settings, recent probabilistic extensions enable the use of richer equilibrium concepts. In this paper, we study one such equilibrium concept -- correlated equilibria -- and introduce a natural refinement -- subgame-perfect correlated equilibria -- in the context of the verification problem. We characterize the computational complexity of verifying such equilibria and show a somewhat surprising separation (under standard complexity-theoretic assumptions): despite being more general, correlated equilibria yield a strictly harder P-complete verification problem than the subgame-perfect correlated equilibria verification problem, which can be solved in log-squared-space. We further analyze the setting where inputs are given succinctly via Bayesian networks, as the study of succinct representations is an important direction to connect static complexity-theoretic analysis to real-world program representations, and show that this complexity gap disappears under such representations.

Problem

• correlated equilibria
• concurrent reachability games
• verification
• computational complexity
• subgame-perfect

Innovation

• correlated equilibria
• subgame-perfect equilibrium
• concurrent reachability games
• computational complexity
• succinct representations