Léonard Brice maps equilibrium complexity in multiplayer graph games

Léonard Brice’s latest paper, “Equilibria in Multiplayer Graph Games: An Algorithmic Study,” tackles a fundamental challenge in computer science verification: moving beyond two-player zero-sum games to model complex systems with multiple agents and objectives. The work, published on arXiv (2605.19954), formally analyzes five equilibrium notions—including Nash equilibrium—in the context of multiplayer graph games, where each player’s payoff is determined by infinite play.

The core contribution is complexity results for the constrained existence problem: given a game and payoff intervals for each player, does there exist an equilibrium profile where everyone’s payoff falls within those bounds? Brice provides tight computational bounds for all five equilibrium concepts, offering theoreticians and protocol designers clear guidance on which equilibria are tractable to verify. This directly impacts verification of robust multi-agent systems, autonomous vehicle coordination, and decentralized protocol design.