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Mas-Colell Bargaining Set of Large Games

  • Massimiliano Amarante
  • Luigi Montrucchio

We study the equivalence between the MB-set and the core in the general context of games with a measurable space of players. In the first part of the paper, we study the problem without imposing any restriction on the class of games we consider. In the second part, we apply our findings to specific classes of games for which we provide new equivalence results. These include non-continuous convex games, exact non-atomic market games and non-atomic non-exact games. We also introduce, and characterize, a new class of games, which we call thin games. For these, we show not only that the MB-set is equal to the core, but also that it is the unique stable set in the sense of von Neumann and Morgenstern. Finally, we study the relation between thin games, market games and convex games.

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Paper provided by Collegio Carlo Alberto in its series Carlo Alberto Notebooks with number 63.

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Length: 37 pages
Date of creation: 2007
Date of revision:
Handle: RePEc:cca:wpaper:63
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  1. Mas-Colell, Andreu, 1989. "An equivalence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 129-139, April.
  2. Dutta, Bhaskar & Ray, Debraj & Sengupta, Kunal & Vohra, Rajiv, 1989. "A consistent bargaining set," Journal of Economic Theory, Elsevier, vol. 49(1), pages 93-112, October.
  3. Dov Monderer & Ezra Einy & Diego Moreno, 1998. "The least core, kernel and bargaining sets of large games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(3), pages 585-601.
  4. Shitovitz, Benyamin, 1989. "The bargaining set and the core in mixed markets with atoms and an atomless sector," Journal of Mathematical Economics, Elsevier, vol. 18(4), pages 377-383, September.
  5. Yevgenia Apartsin & Ron Holzman, 2003. "The core and the bargaining set in glove-market games," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(2), pages 189-204, December.
  6. Vohra, Rajiv, 1991. "An existence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 19-34.
  7. Massimo Marinacci & Luigi Montrucchio, 2005. "Stable cores of large games," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(2), pages 189-213, 06.
  8. TamÂs Solymosi, 1999. "On the bargaining set, kernel and core of superadditive games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(2), pages 229-240.
  9. Massimiliano Amarante & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2006. "Cores of Non-Atomic Market Games," Carlo Alberto Notebooks 13, Collegio Carlo Alberto.
  10. Marinacci, Massimo & Montrucchio, Luigi, 2003. "Subcalculus for set functions and cores of TU games," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 1-25, February.
  11. Bezalel Peleg & Peter Sudholter, 2004. "Bargaining Sets of Voting Games," Discussion Paper Series dp376, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  12. L. Randall Wray & Stephanie Bell, 2004. "Introduction," Chapters, in: Credit and State Theories of Money, chapter 1 Edward Elgar Publishing.
  13. Philippe Robert-Demontrond & R. Ringoot, 2004. "Introduction," Post-Print halshs-00081823, HAL.
  14. Einy, Ezra & Holzman, Ron & Monderer, Dov, 1999. "On the Least Core and the Mas-Colell Bargaining Set," Games and Economic Behavior, Elsevier, vol. 28(2), pages 181-188, August.
  15. Einy, Ezra & Holzman, Ron & Monderer, Dov & Shitovitz, Benyamin, 1997. "Core Equivalence Theorems for Infinite Convex Games," Journal of Economic Theory, Elsevier, vol. 76(1), pages 1-12, September.
  16. Massimiliano Amarante & Fabio Maccheroni, 2006. "When an Event Makes a Difference," Theory and Decision, Springer, vol. 60(2), pages 119-126, 05.
  17. Diego Moreno & Benyamin Shitovitz & Ezra Einy, 1999. "The core of a class of non-atomic games which arise in economic applications," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(1), pages 1-14.
  18. Ron Holzman, 2001. "The comparability of the classical and the Mas-Colell bargaining sets," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(4), pages 543-553.
  19. Ehud Kalai & Eitan Zemel, 1980. "On Totally Balanced Games and Games of Flow," Discussion Papers 413, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  20. Massimo Marinacci & Luigi Montrucchio, 2003. "Cores and stable sets of finite dimensional games," ICER Working Papers - Applied Mathematics Series 07-2003, ICER - International Centre for Economic Research.
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