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Cores of Partitioning Games

  • Mamoru Kaneko

    (University of Tsukuba)

  • Myrna Holtz Wooders

    (University of Toronto)

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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File URL: http://cowles.econ.yale.edu/P/cd/d06a/d0620.pdf
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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 620.

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Length: 25 pages
Date of creation: Feb 1982
Date of revision:
Publication status: Published in Mathematical Social Sciences (1982), 3: 313-327
Handle: RePEc:cwl:cwldpp:620
Note: CFP 566.
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Order Information: Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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  1. Dierker, Egbert, 1971. "Equilibrium Analysis of Exchange Economies with Indivisible Commodities," Econometrica, Econometric Society, vol. 39(6), pages 997-1008, November.
  2. Shubik, Martin, 1971. "The "Bridge Game" Economy: An Example of Indivisibilities," Journal of Political Economy, University of Chicago Press, vol. 79(4), pages 909-12, July-Aug..
  3. 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.
  4. Henry, Claude, 1972. "Market Games with Indivisible Commodities and Non-convex Preferences," Review of Economic Studies, Wiley Blackwell, vol. 39(1), pages 73-76, January.
  5. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
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