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Incomplete stable structures in symmetric convex games

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Author Info
Slikker, M.
Norde, H. (Tilburg University, Center for Economic Research)

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Abstract

We study the model of link formation that was introduced by Aumann and Myerson (1988) and focus on symmetric convex games with transferable utilities. We show that with at most five players the full cooperation structure results according to a subgame perfect Nash equilibrium. Moreover, if the game is strictly convex then every subgame perfect Nash equilibrium results in a structure that is payoff equivalent to the full cooperation structure. Subsequently, we analyze a game with six players that is symmetric and strictly convex. We show that there exists a subgame Nash equilibrium that results in an incomplete structure in which two players are worse off than in the full cooperation structure, whereas four players are better off. Independent of the initial order any pair of players can end up being exploited.

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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 97.

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Date of creation: 2000
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Handle: RePEc:dgr:kubcen:200097

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Web page: http://center.uvt.nl

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Find related papers by JEL classification:
C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Feinberg, Yossi, 1998. "An Incomplete Cooperation Structure for a Voting Game Can Be Strategically Stable," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 2-9, July. [Downloadable!] (restricted)
  2. Roger B. Myerson, 1976. "Graphs and Cooperation in Games," Discussion Papers 246, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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Cited by:
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  1. Anne van den Nouweland, 2004. "The Formation of Communication Networks in Cooperative Games," University of Oregon Economics Department Working Papers 2004-2, University of Oregon Economics Department. [Downloadable!]
  2. Slikker, M. & Norde, H.W., 2004. "Symmetric convex games and stable structures," Discussion Paper 114, Tilburg University, Center for Economic Research. [Downloadable!]
  3. Slikker, M. & Gilles, R. & Norde, H. & Tijs, S., 2000. "Directed communication networks," Discussion Paper 84, Tilburg University, Center for Economic Research. [Downloadable!]
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