Nonatomic potential games: the continuous strategy case

Man-Wah Cheung and Ratul Lahkar ()

Games and Economic Behavior, 2018, vol. 108, issue C, 341-362

Abstract: This paper studies large population (nonatomic) potential games with continuous strategy sets. We define such games as population games in which the payoff function is equal to the gradient of a real-valued function called the potential function. The Cournot competition model with continuous player set and continuous strategy set is our main example and is analyzed in detail. For general potential games, we establish that maximizers of potential functions are Nash equilibria. For a particular class of potential games called aggregative potential games, we characterize Nash equilibria using a one-dimensional analogue of the potential function, which we call the quasi-potential function. Finally, we show that a large population potential game is the limit of a sequence of finite-player potential games as the number of players approaches infinity.

Keywords: Potential games; Cournot competition model; Aggregative games; Externalities (search for similar items in EconPapers)
JEL-codes: C72 C73 D62 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (22)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:gamebe:v:108:y:2018:i:c:p:341-362

DOI: 10.1016/j.geb.2017.12.004

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