Refinement derivatives and values of games

• 成果类型: Article
• 署名作者: Montrucchio, Luigi; Semeraro, Patrizia
• 署名单位: Collegio Carlo Alberto; University of Turin; University of Turin
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1070.0281
• 发表日期: 2008
• 页码: 97-118
• 关键词: cores; potentials

摘要

A definition of setwise differentiability for set functions is given through refining the partitions of sets. Such a construction is closely related to the one proposed by Rosenmuller [Rosenmuller, J. 1977. Extreme Games and Their Solutions. Springer-Verlag, Berlin], Epstein [Epstein, L. 1999. A definition of uncertainty aversion. Rev. Econom. Stud. 66 579-608], and Epstein and Marinacci [Epstein, L., M. Marinacci. 2001. The core of large differentiable TU games. J Econom. Theory 100 235-273]. We present several classes of transferable utility (TU) games that are differentiable and study differentiation rules. The last part of this paper applies refinement derivatives to the computation of value of games. Following Hart and Mas-Colell [Hart, S., A. Mas-Colell. 1989. Potential, value and consistency. Econometrica 57 589-614], we define an operator through the refinement derivative of the potential of the game. We show that this operator is a value, when restricted to the spaces pM(infinity) and POT2. The latter space is closely related to Myerson's balanced contributions axiom.