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Subcalculus for set functions and cores of TU games

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  • Massimo Marinacci
  • Luigi Montrucchio

Abstract

This paper introduces a subcalculus for general set functions and uses this framework to study the core of TU games. After stating a linearity theorem, we establish several theorems that characterize mea- sure games having finite-dimensional cores. This is a very tractable class of games relevant in many economic applications. Finally, we show that exact games with Þnite dimensional cores are generalized linear production games.

Suggested Citation

  • Massimo Marinacci & Luigi Montrucchio, 2001. "Subcalculus for set functions and cores of TU games," ICER Working Papers - Applied Mathematics Series 09-2001, ICER - International Centre for Economic Research.
    • Handle: RePEc:icr:wpmath:09-2001
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    References listed on IDEAS

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    1. Louis J. Billera & Joseph Raanan, 1981. "Cores of Nonatomic Linear Production Games," Mathematics of Operations Research, INFORMS, vol. 6(3), pages 420-423, August.
    2. Hart, Sergiu & Neyman, Abraham, 1988. "Values of non-atomic vector measure games : Are they linear combinations of the measures?," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 31-40, February.
    3. Marinacci, Massimo & Montrucchio, Luigi, 2004. "A characterization of the core of convex games through Gateaux derivatives," Journal of Economic Theory, Elsevier, vol. 116(2), pages 229-248, June.
    4. Epstein, Larry G. & Marinacci, Massimo, 2001. "The Core of Large Differentiable TU Games," Journal of Economic Theory, Elsevier, vol. 100(2), pages 235-273, October.
    5. Larry G. Epstein, 1999. "A Definition of Uncertainty Aversion," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(3), pages 579-608.
    6. AUMANN, Robert J. & DREZE, Jacques H., 1974. "Cooperative games with coalition structures," LIDAM Reprints CORE 217, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. DELBAEN, Freddy, 1974. "Convex games and extreme points," LIDAM Reprints CORE 159, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Mongin Philippe, 1995. "Consistent Bayesian Aggregation," Journal of Economic Theory, Elsevier, vol. 66(2), pages 313-351, August.
    9. 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.
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    Citations

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    Cited by:

    1. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2011. "Classical Subjective Expected Utility," Working Papers 400, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    2. Nobusumi Sagara & Milan Vlach, 2011. "A new class of convex games on σ-algebras and the optimal partitioning of measurable spaces," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(3), pages 617-630, August.
    3. M. Amarante & F. Maccheroni & M. Marinacci & L. Montrucchio, 2006. "Cores of non-atomic market games," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(3), pages 399-424, October.
    4. Salvatore Modica & Marco Scarsini, 2003. "The convexity-cone approach to comparative risk and downside risk," ICER Working Papers - Applied Mathematics Series 01-2003, ICER - International Centre for Economic Research.
    5. Castagnoli, Erio & Maccheroni, Fabio & Marinacci, Massimo, 2002. "Insurance premia consistent with the market," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 267-284, October.
    6. Massimiliano Amarante & Luigi Montrucchio, 2007. "Mas-Colell Bargaining Set of Large Games," Carlo Alberto Notebooks 63, Collegio Carlo Alberto.
    7. 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.
    8. Marinacci, Massimo & Montrucchio, Luigi, 2004. "A characterization of the core of convex games through Gateaux derivatives," Journal of Economic Theory, Elsevier, vol. 116(2), pages 229-248, June.
    9. Fabio Maccheroni & William H. Ruckle, 2001. "BV as a dual space," ICER Working Papers - Applied Mathematics Series 29-2001, ICER - International Centre for Economic Research.
    10. Massimo Marinacci & Luigi Montrucchio, 2003. "Ultramodular functions," ICER Working Papers - Applied Mathematics Series 13-2003, ICER - International Centre for Economic Research.
    11. Enrico Diecidue & Fabio Maccheroni, 2002. "Coherence without Additivity," ICER Working Papers - Applied Mathematics Series 10-2002, ICER - International Centre for Economic Research.
    12. Luigi Montrucchio & Patrizia Semeraro, 2006. "Refinement Derivatives and Values of Games," Carlo Alberto Notebooks 9, Collegio Carlo Alberto.
    13. Massimo Marinacci & Luigi Montrucchio, 2002. "The convexity-cone approach to comparative risk and downside risk," ICER Working Papers - Applied Mathematics Series 18-2002, ICER - International Centre for Economic Research.
    14. Luigi Montrucchio & Patrizia Semeraro, 2008. "Refinement Derivatives and Values of Games," Mathematics of Operations Research, INFORMS, vol. 33(1), pages 97-118, February.

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