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Epsilon cores of games with limited side payments Nonemptiness and equal treatment

  • Myrna Wooders

    ()

    (University of Warwick)

  • Alexander Kovalenkov

    ()

    (University of North Carolina)

We introduce the concept of a parameterized collection of games with limited side payments, ruling out large transfers of utility. With convexity of the payoff set of the grand coalition, we show that (1) a game with limited side payments has a nonempty epsilon-core and (2) when some degree of side-paymentness within nearly effective small groups is assumed and large transfers are prohibited, then all payoffs in the epsilon-core treat similar players similarly. A bound on the distance between epsilon-core payoffs of any two similar players is given in terms of the parameters describing the game. These results add to the literature showing that large games with small effective groups have the properties of competitive markets. For prior equal treatment results for large games see especially Wooders (1980,1994a,b), Shubik and Wooders (1982) and Wooders (1983, Theorem 3) available at http://www.warwick.ac.uk/fac/soc/Economics/wooders/.

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Article provided by AccessEcon in its journal Economics Bulletin.

Volume (Year): 28 (2001)
Issue (Month): 5 ()
Pages: A0

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Handle: RePEc:ebl:ecbull:eb-01aa0008
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  1. Le Breton,Michel & Owen,Guillermo & Weber,Shlomo, 1991. "Strongly balanced cooperative games," Discussion Paper Serie A 338, University of Bonn, Germany.
  2. Shapley, Lloyd S & Shubik, Martin, 1969. "On the Core of an Economic System with Externalities," American Economic Review, American Economic Association, vol. 59(4), pages 678-84, Part I Se.
  3. Peter J. Hammond, . "On f-Core Equivalence with General Widespread Externalities," Working Papers 95004, Stanford University, Department of Economics.
  4. Billera, Louis J., 1974. "On games without side payments arising from a general class of markets," Journal of Mathematical Economics, Elsevier, vol. 1(2), pages 129-139, August.
  5. Mamoru Kaneko & Myrna Holtz Wooders, 1982. "Cores of Partitioning Games," Cowles Foundation Discussion Papers 620, Cowles Foundation for Research in Economics, Yale University.
  6. Martin Shubik & Myrna Holtz Wooders, 1982. "Near-Markets and Market Games," Cowles Foundation Discussion Papers 657, Cowles Foundation for Research in Economics, Yale University.
  7. Mamoru Kaneko, 1980. "The Central Assignment Game and the Assignment Markets," Cowles Foundation Discussion Papers 563, Cowles Foundation for Research in Economics, Yale University.
  8. Wooders, Myrna Holtz, 1994. "Equivalence of Games and Markets," Econometrica, Econometric Society, vol. 62(5), pages 1141-60, September.
  9. Kaneko, Mamoru & Wooders, Myrna Holtz, 1989. "The core of a continuum economy with widespread externalities and finite coalitions: From finite to continuum economies," Journal of Economic Theory, Elsevier, vol. 49(1), pages 135-168, October.
  10. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
  11. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, vol. 1(1), pages 9-25, June.
  12. Mas-Colell, Andreu, 1975. "A further result on the representation of games by markets," Journal of Economic Theory, Elsevier, vol. 10(1), pages 117-122, February.
  13. Charles M. Tiebout, 1956. "A Pure Theory of Local Expenditures," Journal of Political Economy, University of Chicago Press, vol. 64, pages 416.
  14. Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July.
  15. Mas-Colell, Andreu, 1979. "A refinement of the core equivalence theorem," Economics Letters, Elsevier, vol. 3(4), pages 307-310.
  16. Bennett, Elaine & Wooders, Myrna, 1979. "Income distribution and firm formation," Journal of Comparative Economics, Elsevier, vol. 3(3), pages 304-317, September.
  17. Wooders, Myrna Holtz & Zame, William R, 1984. "Approximate Cores of Large Games," Econometrica, Econometric Society, vol. 52(6), pages 1327-50, November.
  18. Garratt, Rod & Qin, Cheng-Zhong, 1997. "On a Market for Coalitions with Indivisible Agents and Lotteries," Journal of Economic Theory, Elsevier, vol. 77(1), pages 81-101, November.
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