Strategic behavior in non-atomic games |
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| Institution: | 1. Faculty of Arts and Social Sciences, Sabanci University, Orhanli, Tuzla, 34956, Istanbul, Turkey;2. School of Economics, University of Surrey, Guildford, GU2 7XH, UK;1. Department of Economics, Towson University, United States;2. Department of Mathematics, Towson University, United States;1. Department of Economics, Indiana University, Bloomington, IN 47405, USA;2. European University in St. Petersburg, 3 Gagarinskaya Street, St. Petersburg, 191187, Russia;3. St. Petersburg Institute for Economics and Mathematics (Russian Academy of Sciences), 36-38 Serpukhovskaya Street, St. Petersburg, 190013, Russia;4. St. Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg, 199034, Russia;5. Department of Economics, Finance & Real Estate, Feliciano School of Business, Montclair State University, Montclair, NJ 07043, USA;1. Université de Franche-Comté, CRESE, 30 Avenue de l’Observatoire, 25009 Besançon, France;2. Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne, France;1. ICEF, NRU Higher School of Economics, Moscow, Russian Federation;2. Saïd Business School and St. Edmund Hall, University of Oxford, United Kingdom |
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| Abstract: | In order to remedy the possible loss of strategic interaction in non-atomic games with a societal choice, this study proposes a refinement of Nash equilibrium, strategic equilibrium. Given a non-atomic game, its perturbed game is one in which every player believes that he alone has a small, but positive, impact on the societal choice; and a distribution is a strategic equilibrium if it is a limit point of a sequence of Nash equilibrium distributions of games in which each player’s belief about his impact on the societal choice goes to zero. After proving the existence of strategic equilibria, we show that all of them must be Nash. We also show that all regular equilibria of smooth non-atomic games are strategic. Moreover, it is displayed that in many economic applications, the set of strategic equilibria coincides with that of Nash equilibria of large finite games. |
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| Keywords: | Nash equilibrium Strategic equilibrium Games with a continuum of players Equilibrium distributions |
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