Equilibria in a class of aggregative location games

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• 作者：Tobias Harks^a ; ^{tobias.harks@math.uni-augsburg.de" class="auth_mail" title="E-mail the corresponding author} ; Max Klimm^b ; ^{klimm@math.tu-berlin.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Pure Nash equilibrium ; Aggregative game ; Non-convex strategy set ; Cournot oligopoly ; Congestion game ; Queuing game
• 刊名：Journal of Mathematical Economics
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：61
• 期：Complete
• 页码：211-220
• 全文大小：581 K

文摘

Consider a multimarket oligopoly, where firms have a single license that allows them to supply exactly one market out of a given set of markets. How does the restriction to supply only one market influence the existence of equilibria in the game? To answer this question, we study a general class of aggregative location games where a strategy of a player is to choose simultaneously both a location out of a finite set and a non-negative quantity out of a compact interval. The utility of each player is assumed to depend solely on the chosen location, the chosen quantity, and the aggregated quantity of all other players on the chosen location. We show that each game in this class possesses a pure Nash equilibrium whenever the players’ utility functions satisfy the assumptions negative externality, decreasing marginal utility, continuity, and Location–Symmetry. We also provide examples exhibiting that, if one of the assumptions is violated, a pure Nash equilibrium may fail to exist.