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Bargaining Set Solution Concepts in Dynamic Cooperative Games

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  • Hellman, Ziv

Abstract

This paper is concerned with the question of defining the bargaining set, a cooperative game solution, when cooperation takes place in a dynamic setting. The focus is on dynamic cooperative games in which the players face (finite or infinite) sequences of exogenously specified TU-games and receive sequences of imputations against those static cooperative games in each time period. Two alternative definitions of what a ‘sequence of coalitions’ means in such a context are considered, in respect to which the concept of a dynamic game bargaining set may be defined, and existence and non-existence results are studied. A solution concept we term ‘subgame-stable bargaining set sequences’ is also defined, and sufficient conditions are given for the non-emptiness of subgame-stable solutions in the case of a finite number of time periods.

Suggested Citation

  • Hellman, Ziv, 2008. "Bargaining Set Solution Concepts in Dynamic Cooperative Games," MPRA Paper 8798, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:8798
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    File URL: https://mpra.ub.uni-muenchen.de/8798/1/MPRA_paper_8798.pdf
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    References listed on IDEAS

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    1. Predtetchinski, Arkadi & Herings, P. Jean-Jacques & Peters, Hans, 2002. "The strong sequential core for two-period economies," Journal of Mathematical Economics, Elsevier, vol. 38(4), pages 465-482, December.
    2. P. Herings & A. Predtetchinski & A. Perea, 2006. "The Weak Sequential Core for Two-Period Economies," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(1), pages 55-65, April.
    3. Laurence Kranich & Andrés Perea & Hans Peters, 2005. "Core Concepts For Dynamic Tu Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 43-61.
    4. Predtetchinski, Arkadi, 2007. "The strong sequential core for stationary cooperative games," Games and Economic Behavior, Elsevier, vol. 61(1), pages 50-66, October.
    5. Gale, Douglas, 1978. "The core of a monetary economy without trust," Journal of Economic Theory, Elsevier, vol. 19(2), pages 456-491, December.
    6. Oviedo, Jorge, 2000. "The core of a repeated n-person cooperative game," European Journal of Operational Research, Elsevier, vol. 127(3), pages 519-524, December.
    7. Arkadi Predtetchinski & P. Herings & Hans Peters, 2004. "The strong sequential core in a dynamic exchange economy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 24(1), pages 147-162, July.
    8. Berden Caroline, 2007. "The Role of Individual Intertemporal Transfers in Dynamic TU-Games," Research Memorandum 030, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    9. Becker, Robert A & Chakrabarti, Subir K, 1995. "The Recursive Core," Econometrica, Econometric Society, vol. 63(2), pages 401-423, March.
    10. Laurence Kranich & Andres Perea & Hans Peters, 2000. "Dynamic Cooperative Games," Discussion Papers 00-06, University at Albany, SUNY, Department of Economics.
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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.

    More about this item

    Keywords

    Cooperative game; Repeated game; Bargaining set;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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