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Subgame Perfect Cooperation in an Extensive Game

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Author Info

  • Parkash Chander

    ()
    (National University of Singapore and CORE, Universite Catholique de Louvain)

  • Myrna Wooders

    ()
    (Department of Economics, Vanderbilt University)

Abstract

This paper brings together two of the most important solution concepts of game theory �subgame-perfect Nash equilibrium of a non-cooperative game and the core of a cooperativegame. Our approach rests on two fundamental ideas: (1) Given an extensive game, the formationof a coalition leads to a new game where all the members of the coalition become one player. (2)At the origin of any subgame, the only possible coalitions consist of players who have decision nodes in the subgame. We introduce a concept of subgame perfect cooperative equilibrium, which we label the gamma-core of an extensive game. We provide a necessary and sufficient condition for the existence of the gamma-core of an extensive game of perfect information. As a motivating example, we formulate the problem of global warming as a dynamic game with simultaneous moves and show that if the payoff functions are quadratic, then the gamma-core of the game is nonempty.

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File URL: http://www.accessecon.com/pubs/VUECON/vu10-w08.pdf
File Function: First version, April 2010
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Bibliographic Info

Paper provided by Vanderbilt University Department of Economics in its series Vanderbilt University Department of Economics Working Papers with number 1008.

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Date of creation: Jun 2010
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Handle: RePEc:van:wpaper:1008

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Web page: http://www.vanderbilt.edu/econ/wparchive/index.html

Related research

Keywords: subgame perfect cooperation; extensive form game; subgame perfection; gamma-core;

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Cited by:
  1. Ehud Lehrer & Marco Scarsini, 2013. "On the Core of Dynamic Cooperative Games," Dynamic Games and Applications, Springer, vol. 3(3), pages 359-373, September.

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