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An application of optimization theory to the study of equilibria for games: a survey

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  • Lina Mallozzi

Abstract

This contribution is a survey about potential games and their applications. In a potential game the information that is sufficient to determine Nash equilibria can be summarized in a single function on the strategy space: the potential function. We show that the potential function enable the application of optimization theory to the study of equilibria. Potential games and their generalizations are presented. Two special classes of games, namely team games and separable games, turn out to be potential games. Several properties satisfied by potential games are discussed and examples from concrete situations as congestion games, global emission games and facility location games are illustrated. Copyright Springer-Verlag 2013

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  • Lina Mallozzi, 2013. "An application of optimization theory to the study of equilibria for games: a survey," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(3), pages 523-539, September.
    • Handle: RePEc:spr:cejnor:v:21:y:2013:i:3:p:523-539
    DOI: 10.1007/s10100-012-0245-8
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    3. Robert P. Gilles & Lina Mallozzi & Roberta Messalli, 2023. "Emergent Collaboration in Social Purpose Games," Dynamic Games and Applications, Springer, vol. 13(2), pages 566-588, June.

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