A payoff dynamics model for generalized Nash equilibrium seeking in population games

This paper studies the problem of generalized Nash equilibrium seeking in population games under general affine equality and convex inequality constraints. In particular, we design a novel payoff dynamics model to steer the decision-making agents to a generalized Nash equilibrium of the underlying game, i.e., to a self-enforceable state where the constraints are satisfied and no agent has incentives to unilaterally deviate from her selected strategy. Moreover, using Lyapunov stability theory, we provide sufficient conditions to guarantee the asymptotic stability of the corresponding equilibria set in stable population games. Auxiliary results characterizing the properties of the equilibria set are also provided for general continuous population games. Furthermore, our theoretical developments are numerically validated on a Cournot game considering various market-related and production-related constraints. (C)& nbsp;2022 Elsevier Ltd. All rights reserved.

Automated summary

This paper investigates the problem of seeking generalized Nash equilibrium in population games with general affine equality and convex inequality constraints. A novel payoff dynamics model is designed to guide decision-making agents to a generalized Nash equilibrium, where constraints are satisfied and no agent has incentives to deviate from their selected strategies. The paper provides sufficient conditions for the asymptotic stability of the equilibria set in stable population games using Lyapunov stability theory. Additional results characterizing the properties of the equilibria set are also presented for general continuous population games. The theoretical developments are numerically validated using a Cournot game with various market-related and production-related constraints.