Steering Noncooperative Games Through Conjecture Design
Francesco Morri, Hélène Le Cadre, David Salas, Didier Aussel
TL;DR
The paper addresses steering noncooperative multi-agent games toward desirable equilibria by designing conjectures about opponents' reactions, combining mechanism design, incentive design, and opponent modeling into a unified framework. It introduces a centralized conjecture-design problem that optimizes conjectures to realize a target equilibrium via a global objective $\\mathscr{F}(x)$, with existence guaranteed under mild regularity and pseudo-convexity conditions; the resulting equilibrium aligns with the designer's target. A decentralized variant is developed where players use fixed conjectures and targets provided by a coordinator, preserving existence guarantees and enabling parallel computation. Applications to the tragedy of the commons, Olsder's paradox, and a large-scale coordination game illustrate improved outcomes over Nash equilibria, including cases with no equilibrium under standard formulations, and the framework extends to saddle games with stronger consistency constraints. Altogether, the conjecture-design approach offers a scalable, principled path to incentive design and opponent modeling in large-scale multi-agent systems, with potential integration into fully decentralized and learning-based paradigms.
Abstract
In dynamic noncooperative games, each player makes conjectures about other players' reactions before choosing a strategy. However, resulting equilibria may be multiple and do not always lead to desirable outcomes. These issues are typically addressed separately, for example, through opponent modelling and incentive design. Drawing inspiration from conjectural variations games, we propose an incentive design framework in which a coordinator first computes an equilibrium by optimizing a predefined objective function, then communicates this equilibrium as a target for the players to reach. In a centralized setting, the coordinator also optimizes the conjectures to steer the players towards the target. In decentralized settings, players independently compute conjectures and update their strategies based on individual targets. We provide a guarantee of equilibrium existence in both cases. This framework uses conjectures not only to guide the system towards desirable outcomes but also to decouple the game into independent optimization problems, enabling efficient computation and parallelization in large-scale settings. We illustrate our theoretical results on classical representative noncooperative games, demonstrating its application potential.