Refinement Derivatives and Values of Games
AbstractA definition of set-wise differentiability for set functions is given through refining the partitions of sets. Such a construction is closely related to the one proposed by Rosenmuller (1977) as well as that studied by Epstein (1999) and Epstein and Marinacci (2001). We present several classes of TU games which are differentiable and study differentiation rules. The last part of the paper applies refinement derivatives to the calculation of value of games. Following Hart and Mas-Colell (1989), we define a value operator through the derivative of the potential of the game. We show that this operator is a truly value when restricted to some appropriate spaces of games. We present two alternative spaces where this occurs: the spaces pM( ) and POT2. The latter space is closely related to Myerson's balanced contribution axiom.
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Bibliographic InfoPaper provided by Collegio Carlo Alberto in its series Carlo Alberto Notebooks with number 9.
Length: 41 pages
Date of creation: 2006
Date of revision:
TU games; large games; non-additive set functions; value; derivatives;
Find related papers by JEL classification:
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
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- Epstein, Larry G, 1999. "A Definition of Uncertainty Aversion," Review of Economic Studies, Wiley Blackwell, vol. 66(3), pages 579-608, July.
- 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.
- Calvo, Emilio & Santos, Juan Carlos, 1997. "Potentials in cooperative TU-games," Mathematical Social Sciences, Elsevier, vol. 34(2), pages 175-190, October.
- 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.
- 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.
- 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.
- Neyman, Abraham, 2002. "Values of games with infinitely many players," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 56, pages 2121-2167 Elsevier.
- Massimo Marinacci & Luigi Montrucchio, 2003. "Ultramodular functions," ICER Working Papers - Applied Mathematics Series 13-2003, ICER - International Centre for Economic Research.
- Massimo Marinacci & Luigi Montrucchio, 2005. "Stable cores of large games," International Journal of Game Theory, Springer, vol. 33(2), pages 189-213, 06.
- Massimiliano Amarante & Luigi Montrucchio, 2010. "The bargaining set of a large game," Economic Theory, Springer, vol. 43(3), pages 313-349, June.
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