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Sandwich Games

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  • Roee Teper

Abstract

The extension of set functions (or capacities) in a concave fashion, namely aconcavi cation, is an important issue in decision theory and combinatorics. It turns out thatsome set-functions cannot be properly extended if the domain is restricted to be bounded.This paper examines the structure of those capacities that can be extended over a boundeddomain in a concave manner. We present a property termed the sandwich property that isnecessary and sufficient for a capacity to be concavfi able over a bounded domain. We showthat when a capacity is interpreted as the product of any sub group of workers per a unit oftime, the sandwich property provides a linkage between optimality of time allocations andefficiency.

Suggested Citation

  • Roee Teper, 2014. "Sandwich Games," Working Paper 5863, Department of Economics, University of Pittsburgh.
    • Handle: RePEc:pit:wpaper:5863
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    References listed on IDEAS

    as
    1. Lehrer, Ehud & Teper, Roee, 2015. "Subjective independence and concave expected utility," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 33-53.
    2. Yaron Azrieli & Ehud Lehrer, 2007. "Extendable Cooperative Games," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 9(6), pages 1069-1078, December.
    3. Ehud Lehrer, 2009. "A new integral for capacities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(1), pages 157-176, April.
    4. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    5. Biswas, A. K. & Parthasarathy, T. & Potters, J. A. M. & Voorneveld, M., 1999. "Large Cores and Exactness," Games and Economic Behavior, Elsevier, vol. 28(1), pages 1-12, July.
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