.png){kind=icon}
.png){kind=icon}
Return
Equilibrium Selection in Replicator Equations Using Adaptive-Gain Control
.png){kind=icon}
PRE
AI
DOI：10.1109/TAC.2025.3567253.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
In this article, we deal with the equilibrium selection problem, which amounts to steering a population of individuals engaged in strategic game-theoretic interactions to a desired collective behavior. In the literature, this problem has been typically tackled by means of open-loop strategies, whose applicability is limited by the need of accurate a priori information on the game and a lack of robustness to uncertainty and noise. Here, we overcome these limitations by adopting a closed-loop approach using an adaptive-gain control scheme within a replicator equation-a nonlinear ordinary differential equation that models the evolution of the collective behavior of the population. For most classes of 2-action matrix games, we establish sufficient conditions to design a controller that guarantees convergence of the replicator equation to the desired equilibrium, requiring limited a priori information on the game. Numerical simulations corroborate and expand our theoretical findings.
Keywords:
Games
Mathematical models
Symmetric matrices
Sufficient conditions
Protocols
Linear matrix inequalities
Europe
Convergence
Artificial intelligence
Training
Adaptive-gain control
equilibrium selection
evolutionary game theory
replicator
Journal
IF:
7
Papers:
1.3W
Citations:
6.7W