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Subgame Perfect Cooperation in an Extensive Game

  • Parkash Chander

    ()

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

  • Myrna Wooders

    ()

    (Department of Economics, Vanderbilt University)

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
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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
Contact details of provider: Web page: http://www.vanderbilt.edu/econ/wparchive/index.html

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  1. Germain, M. & Toint, Ph. & Tulkens, H. & de Zeeuw, A.J., 2003. "Transfers to sustain dynamic core-theoretic cooperation in international stock pollutant control," Other publications TiSEM 8953bc6e-fc65-4fd7-a2d1-6, Tilburg University, School of Economics and Management.
  2. Debraj Ray & Rajiv Vohra, 1998. "A Theory of Endogenous Coalition Structures," Working Papers 98-1, Brown University, Department of Economics, revised Jan 1998.
  3. Perry, M. & Rany, P., 1992. "A Non-Cooperative View of Coalition Formation and the Core," UWO Department of Economics Working Papers 9203, University of Western Ontario, Department of Economics.
  4. Gale, Douglas, 1978. "The core of a monetary economy without trust," Journal of Economic Theory, Elsevier, vol. 19(2), pages 456-491, December.
  5. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
  6. FORGES, Françoise & MERTENS, Jean-François & VOHRA, Rajiv, 2001. "The ex ante incentive compatible core in the absence of wealth effects," CORE Discussion Papers 2001001, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Bloch, Francis, 1996. "Sequential Formation of Coalitions in Games with Externalities and Fixed Payoff Division," Games and Economic Behavior, Elsevier, vol. 14(1), pages 90-123, May.
  8. Germain, Marc & Toint, Philippe & Tulkens, Henry & de Zeeuw, Aart, 2003. "Transfers to sustain dynamic core-theoretic cooperation in international stock pollutant control," Journal of Economic Dynamics and Control, Elsevier, vol. 28(1), pages 79-99, October.
  9. CHANDER, Parkash, . "The gamma-core and coalition formation," CORE Discussion Papers RP 1993, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  10. Becker, Robert A & Chakrabarti, Subir K, 1995. "The Recursive Core," Econometrica, Econometric Society, vol. 63(2), pages 401-23, March.
  11. Dockner Engelbert J. & Van Long Ngo, 1993. "International Pollution Control: Cooperative versus Noncooperative Strategies," Journal of Environmental Economics and Management, Elsevier, vol. 25(1), pages 13-29, July.
  12. Roy Radner & Prajit K. Dutta, 2005. "A Strategic Analysis of Global Warming: Theory and Some Numbers," Working Papers 05-03, New York University, Leonard N. Stern School of Business, Department of Economics.
  13. repec:dau:papers:123456789/5454 is not listed on IDEAS
  14. Serrano Roberto, 1995. "A Market to Implement the Core," Journal of Economic Theory, Elsevier, vol. 67(1), pages 285-294, October.
  15. Reinganum, Jennifer F & Stokey, Nancy L, 1985. "Oligopoly Extraction of a Common Property Natural Resource: The Importance of the Period of Commitment in Dynamic Games," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(1), pages 161-73, February.
  16. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
  17. CHANDER, Parkash, 2010. "Cores of games with positive externalities," CORE Discussion Papers 2010004, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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