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Bargaining Set Solution Concepts in Repeated Cooperative Games

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  • Ziv Hellman

Abstract

This paper is concerned with the question of extending the definition of the bargaining set, a cooperative game solution, when cooperation takes place in a repeated setting. The focus is on situations 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 repeated game bargaining set may be defined, and existence and non-existence results are studied. A solution concept we term subgame-perfect bargaining set sequences is also defined, and sufficient conditions are given for the nonemptiness of subgame-perfect solutions in the case of a finite number of time periods.

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Bibliographic Info

Paper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp523.

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Length: 26 pages
Date of creation: Oct 2009
Date of revision:
Handle: RePEc:huj:dispap:dp523

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  1. Laurence Kranich & Andres Perea & Hans Peters, 2000. "Dynamic Cooperative Games," Discussion Papers 00-06, University at Albany, SUNY, Department of Economics.
  2. Maschler, Michael, 1976. "An advantage of the bargaining set over the core," Journal of Economic Theory, Elsevier, vol. 13(2), pages 184-192, October.
  3. P. Herings & A. Predtetchinski & A. Perea, 2006. "The Weak Sequential Core for Two-Period Economies," International Journal of Game Theory, Springer, vol. 34(1), pages 55-65, April.
  4. 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.
  5. 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).
  6. Predtetchinski, Arkadi, 2007. "The strong sequential core for stationary cooperative games," Games and Economic Behavior, Elsevier, vol. 61(1), pages 50-66, October.
  7. Mas-Colell, Andreu, 1989. "An equivalence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 129-139, April.
  8. Gale, Douglas, 1978. "The core of a monetary economy without trust," Journal of Economic Theory, Elsevier, vol. 19(2), pages 456-491, December.
  9. Arkadi Predtetchinski & P. Herings & Hans Peters, 2004. "The strong sequential core in a dynamic exchange economy," Economic Theory, Springer, vol. 24(1), pages 147-162, 07.
  10. 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.
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