Steering Noncooperative Games Through Conjecture Design

TL;DR

This paper introduces a novel incentive design framework for dynamic noncooperative games that uses conjectures to steer players towards desirable equilibria, enabling efficient computation and application to large-scale systems.

Contribution

It proposes a unified conjecture-based incentive design approach that guarantees equilibrium existence and facilitates decentralized computation in noncooperative games.

Findings

Guarantee of equilibrium existence in both centralized and decentralized settings.

Framework enables decoupling of the game into independent optimization problems.

Application demonstrated on classical noncooperative games.

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.