Abstract
The theory of non cooperative games with potential function was introduced by Monderer and Shapley in 1996. Such games have interesting properties, among which is the existence of equilibria in pure strategies. The paper by Monderer and Shapley has inspired many game theory researchers. In the present paper, many classes of multiobjective games with potential functions are studied. The notions of generalized, best-reply and Pareto potential games are introduced in a multicriteria setting. Some properties and Pareto equilibria are investigated.
Highlights
Potential scalar games have an attractive feature in common: every maximizer of the potential function, a real valued function on strategy profile, is an equilibrium (NE for short) for the game
In 1996, Monderer and Shapley ([4]) introduced potential games. They proved that the exact potential games have interesting relations with the games introduced by Rosenthal, and all potential games have at least an equilibrium in pure strategies: the maximum of a potential function corresponds to an equilibrium of the potential game
We investigate the finite improvement property (FIP for short), the cycle of the best reply property and the relations between the equilibria of a potential game and those of the coordination game
Summary
Potential scalar games have an attractive feature in common: every maximizer of the potential function, a real valued function on strategy profile, is an equilibrium (NE for short) for the game. It is natural to ask if the same is valid for multiobjective games, called vector games, with the suitable changes, considering Pareto equilibria instead of Nash equilibria and defining suitable best-reply correspondences This problem was partially investigated in [1,2]. Many other classes of potential games were considered in the literature as generalized, best-reply potential, Nash potential (see [14,15] and references therein). We study these classes in a multicriteria setting,. The paper is organized as follows: Section 2 gives a background about results, definitions and known notations; in Sections 3–5 we study respectively generalized, best-reply, Pareto potential games in the vector case.
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