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Cores of partitioning games

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  • Kaneko, Mamoru
  • Wooders, Myrna Holtz

Abstract

A generalization of assignment games, called partitioning games, is introduced. Given a finite set N of players, there is an a priori given subset pi of coalitions of N and only coalitions in pi play an essential role. Necessary and sufficient conditions for the non-emptiness of the cores of all games with essential coalitions pi are developed. These conditions appear extremely restrictive. However, when N is "large," there are relatively few "types" of players, and members of pi are "small" and defined in terms of numbers of players of each type contained in subsets, then approximate cores are non-empty.
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Suggested Citation

  • Kaneko, Mamoru & Wooders, Myrna Holtz, 1982. "Cores of partitioning games," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 313-327, December.
    • Handle: RePEc:eee:matsoc:v:3:y:1982:i:4:p:313-327
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    1. Martin Shubik & Myrna Holtz Wooders, 1982. "Approximate Cores of a General Class of Economies. Part I: Replica Games, Externalities, and Approximate Cores," Cowles Foundation Discussion Papers 618, Cowles Foundation for Research in Economics, Yale University.
    2. Shubik, Martin, 1971. "The "Bridge Game" Economy: An Example of Indivisibilities," Journal of Political Economy, University of Chicago Press, vol. 79(4), pages 909-912, July-Aug..
    3. Claude Henry, 1972. "Market Games with Indivisible Commodities and Non-convex Preferences," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 39(1), pages 73-76.
    4. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    5. Dierker, Egbert, 1971. "Equilibrium Analysis of Exchange Economies with Indivisible Commodities," Econometrica, Econometric Society, vol. 39(6), pages 997-1008, November.
    6. Myrna Holtz Wooders, 1981. "The Epsilon Core of a Large Game," Cowles Foundation Discussion Papers 612, Cowles Foundation for Research in Economics, Yale University.
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