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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