Nash equilibrium seeking in full-potential population games under capacity and migration constraints

Abstract

This brief proposes a novel decision-making model for generalized Nash equilibrium seeking in the context of full-potential population games under capacity and migration constraints. The capacity constraints restrict the mass of players that are allowed to simultaneously play each strategy of the game, while the migration constraints introduce a networked interaction structure among the players and rule the strategic switches that players can make. In this brief, we consider both decoupled capacity constraints regarding individual strategies, as well as coupled capacity constraints regarding disjoint groups of strategies. As main technical contributions, we prove that the proposed decision-making protocol guarantees the forward time invariance of the feasible set, and we provide sufficient conditions on the connectivity level of the migration graph to guarantee the asymptotic stability of the set of generalized Nash equilibria of the underlying game when the game is a full-potential population game with concave potential function. Furthermore, we also provide an alternative discrete-time analysis of the proposed evolutionary game dynamics, which allows us to formulate a population-game-inspired distributed optimization algorithm that guarantees the hard satisfaction of the constraints over all iterations. Finally, the theoretical results are validated numerically on a constrained networked congestion game.