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Subgame Perfect Cooperation in an Extensive Game

Author

Listed:
  • 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.

Suggested Citation

  • Parkash Chander & Myrna Wooders, 2010. "Subgame Perfect Cooperation in an Extensive Game," Vanderbilt University Department of Economics Working Papers 1008, Vanderbilt University Department of Economics.
    • Handle: RePEc:van:wpaper:1008
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    References listed on IDEAS

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    Cited by:

    1. Roberto Serrano, 2021. "Sixty-seven years of the Nash program: time for retirement?," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(1), pages 35-48, March.
    2. Wang, Ying, 2021. "Fund-raising and Allocation of Green Climate Fund: Taking Global Pareto Optimality and Fiscal Balance into Consideration," MPRA Paper 106861, University Library of Munich, Germany.
    3. Giorgos Stamatopoulos, 2021. "On the core of economies with multilateral environmental externalities," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 23(1), pages 158-171, February.
    4. Jeong, Seungwon (Eugene) & Lee, Joosung, 2024. "The groupwise-pivotal referral auction: Core-selecting referral strategy-proof mechanism," Games and Economic Behavior, Elsevier, vol. 143(C), pages 191-203.
    5. Ehud Lehrer & Marco Scarsini, 2013. "On the Core of Dynamic Cooperative Games," Dynamic Games and Applications, Springer, vol. 3(3), pages 359-373, September.
    6. Chander, Parkash, 2017. "Subgame-perfect cooperative agreements in a dynamic game of climate change," Journal of Environmental Economics and Management, Elsevier, vol. 84(C), pages 173-188.

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    More about this item

    Keywords

    subgame perfect cooperation; extensive form game; subgame perfection; gamma-core;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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