Abstract
This paper studies the characterizations of (weakly) Pareto-Nash equilibria for multiobjective population games with a vector-valued potential function called multiobjective potential population games, where agents synchronously maximize multiobjective functions with finite strategies via a partial order on the criteria-function set. In such games, multiobjective payoff functions are equal to the transpose of the Jacobi matrix of its potential function. For multiobjective potential population games, based on Kuhn-Tucker conditions of multiobjective optimization, a strongly (weakly) Kuhn-Tucker state is introduced for its vector-valued potential function and it is proven that each strongly (weakly) Kuhn-Tucker state is one (weakly) Pareto-Nash equilibrium. The converse is obtained for multiobjective potential population games with two strategies by utilizing Tucker’s Theorem of the alternative and Motzkin’s one of linear systems. Precisely, each (weakly) Pareto-Nash equilibrium is equivalent to a strongly (weakly) Kuhn-Tucker state for multiobjective potential population games with two strategies. These characterizations by a vector-valued approach are more comprehensive than an additive weighted method. Multiobjective potential population games are the extension of population potential games from a single objective to multiobjective cases. These novel results provide a theoretical basis for further computing (weakly) Pareto-Nash equilibria of multiobjective potential population games and their practical applications.
Highlights
In the current technological, social and economic environments, large populations of small anonymous agents are involved in strategical interactions with multiple objectives
We focus on the characterizations of Pareto-Nash equilibria of multiobjective potential population games (MPPG), where agents aim at synchronously maximizing all the objective functions, and their decision-making preference order is a partial one on the so-called criteria-function set
Referred to [2,16], we review the model of multiobjective population games (MPG) and Pareto-Nash equilibria and weighted Nash equilibria
Summary
Social and economic environments, large populations of small anonymous agents are involved in strategical interactions with multiple objectives. Population games [1] provide a unified framework for describing strategy interactions within a mass of small anonymous agents with a single decision-making objective. To efficiently model interactions in large populations with multiple objectives, multiobjective population games (MPG) are further proposed [2]. To our best knowledge, up to now, no published results on agents’ incentives to change strategies are available for MPG. MPG with agents’ strategy-switching incentives are of high research and practical importance
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