Steering Noncooperative Games Through Conjecture Design
Authors: Francesco Morri, Hélène Le Cadre, David Salas, Didier Aussel
Organizations: Inria, Univ. Lille CNRS, Centrale Lille · Instituto de Ciencias de la Ingeniería Universidad de O’Higgins · Laboratoire PROMESUPR 8521 Université de Perpignan, Tecnosud
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.
Figures & tables
Figure 1 : We report the conjectured objective functions in Fig. 1(a) - 1(c) , and the real one for player 1 in Fig. 1(b) . In all plots we highlight the position of the equilibria.
Equilibrium
J1
J2
NE
19984
5284
CCE
32321
14124
SO
38040
21404
Table 1 : Returns obtained by both players in NE, CCE and SO.
Settings
N=2
N=5
N=10
N=15
N=20
N=30
N=50
Symmetric
CW
CW
CS
CS
D
D
D
Asymmetric
CS
CS
CS
D
D
D
D
Table 2 : Best algorithm from the Coordination Game.
Figure 2 : Comparison of learning a strategy in the saddle game for different algorithms. Each one is ran for 103 steps with different learning steps.