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Mas-Colell Bargaining Set of Large Games

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Author Info
Massimiliano Amarante
Luigi Montrucchio

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Abstract

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

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Length: 42 pages
Date of creation: 2007
Date of revision:
Handle: RePEc:cca:wpaper:63

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Related research
Keywords: Mas-Colell Bargaining Set; maximal excess game; core-equivalence; thin games; market games; convex games.;

Find related papers by JEL classification:
C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

This paper has been announced in the following NEP Reports:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Vohra, Rajiv, 1991. "An existence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 19-34. [Downloadable!] (restricted)
  2. 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. [Downloadable!]
  3. Mas-Colell, Andreu, 1989. "An equivalence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 129-139, April. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  5. TamÂs Solymosi, 1999. "On the bargaining set, kernel and core of superadditive games," International Journal of Game Theory, Springer, vol. 28(2), pages 229-240. [Downloadable!] (restricted)
  6. Massimiliano Amarante & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2006. "Cores of Non-Atomic Market Games," Carlo Alberto Notebooks 13, Collegio Carlo Alberto. [Downloadable!]
    Other versions:
  7. 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. [Downloadable!] (restricted)
  8. Massimo Marinacci & Luigi Montrucchio, 2005. "Stable cores of large games," International Journal of Game Theory, Springer, vol. 33(2), pages 189-213, 06. [Downloadable!] (restricted)
  9. 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. [Downloadable!] (restricted)
  10. 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, vol. 28(1), pages 1-14. [Downloadable!] (restricted)
  11. Ron Holzman, 2001. "The comparability of the classical and the Mas-Colell bargaining sets," International Journal of Game Theory, Springer, vol. 29(4), pages 543-553. [Downloadable!] (restricted)
  12. Massimiliano Amarante & Fabio Maccheroni, 2006. "When an Event Makes a Difference," Theory and Decision, Springer, vol. 60(2), pages 119-126, 05. [Downloadable!] (restricted)
  13. 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. [Downloadable!] (restricted)
  14. 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. [Downloadable!] (restricted)
    Other versions:
  15. 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. [Downloadable!]
  16. Dov Monderer & Ezra Einy & Diego Moreno, 1998. "The least core, kernel and bargaining sets of large games," Economic Theory, Springer, vol. 11(3), pages 585-601. [Downloadable!] (restricted)
  17. Yevgenia Apartsin & Ron Holzman, 2003. "The core and the bargaining set in glove-market games," International Journal of Game Theory, Springer, vol. 32(2), pages 189-204, December. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Daron Acemoglu & Davide Ticchi & Andrea Vindigni, 2008. "A Theory of Military Dictatorships," Carlo Alberto Notebooks 74, Collegio Carlo Alberto. [Downloadable!]
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  2. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2008. "Uncertainty Averse Preferences," Carlo Alberto Notebooks 77, Collegio Carlo Alberto. [Downloadable!]
  3. Ales Cerný & Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2008. "On the Computation of Optimal Monotone Mean-Variance Portfolios via Truncated Quadratic Utility," Carlo Alberto Notebooks 79, Collegio Carlo Alberto. [Downloadable!]
  4. Itzhak Gilboa & Fabio Maccheroni & Massimo Marinacci & David Schmeidler, 2008. "Objective and Subjective Rationality in a Multiple Prior Model," Carlo Alberto Notebooks 73, Collegio Carlo Alberto, revised 2008. [Downloadable!]
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