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

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  • Myrna Wooders

    ()
    (University of Warwick)

  • Alexander Kovalenkov

    ()
    (University of North Carolina)

Abstract

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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Bibliographic Info

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. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, Elsevier, vol. 1(1), pages 9-25, June.
  2. Kaneko, Mamoru, 1982. "The central assignment game and the assignment markets," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 205-232, September.
  3. Charles M. Tiebout, 1956. "A Pure Theory of Local Expenditures," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 64, pages 416.
  4. Le Breton, M & Owen, G & Weber, S, 1992. "Strongly Balanced Cooperative Games," International Journal of Game Theory, Springer, Springer, vol. 20(4), pages 419-27.
  5. Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July.
  6. Wooders, Myrna Holtz & Zame, William R, 1984. "Approximate Cores of Large Games," Econometrica, Econometric Society, Econometric Society, vol. 52(6), pages 1327-50, November.
  7. Bennett, Elaine & Wooders, Myrna, 1979. "Income distribution and firm formation," Journal of Comparative Economics, Elsevier, vol. 3(3), pages 304-317, September.
  8. Garratt, Rod & Qin, Cheng-Zhong, 1997. "On a Market for Coalitions with Indivisible Agents and Lotteries," Journal of Economic Theory, Elsevier, Elsevier, vol. 77(1), pages 81-101, November.
  9. Mas-Colell, Andreu, 1979. "A refinement of the core equivalence theorem," Economics Letters, Elsevier, Elsevier, vol. 3(4), pages 307-310.
  10. Mas-Colell, Andreu, 1975. "A further result on the representation of games by markets," Journal of Economic Theory, Elsevier, Elsevier, vol. 10(1), pages 117-122, February.
  11. 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, Elsevier, vol. 49(1), pages 135-168, October.
  12. Mamoru Kaneko & Myrna Holtz Wooders, 1982. "Cores of Partitioning Games," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 620, Cowles Foundation for Research in Economics, Yale University.
  13. Martin Shubik & Myrna Holtz Wooders, 1982. "Near-Markets and Market Games," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 657, Cowles Foundation for Research in Economics, Yale University.
  14. Hammond, Peter J., 1999. "On f-core equivalence with general widespread externalities," Journal of Mathematical Economics, Elsevier, vol. 32(2), pages 177-184, October.
  15. Shapley, Lloyd S & Shubik, Martin, 1969. "On the Core of an Economic System with Externalities," American Economic Review, American Economic Association, American Economic Association, vol. 59(4), pages 678-84, Part I Se.
  16. 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.
  17. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, Econometric Society, vol. 50(6), pages 1483-1504, November.
  18. Wooders, Myrna Holtz, 1994. "Equivalence of Games and Markets," Econometrica, Econometric Society, Econometric Society, vol. 62(5), pages 1141-60, September.
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Cited by:
  1. Wooders, Myrna H., 2001. "Some corrections to claims about the literature in Engl and Scotchmer (1996)," Journal of Mathematical Economics, Elsevier, vol. 36(4), pages 295-309, December.
  2. Wooders, Myrna, 2008. "Small group effectiveness, per capita boundedness and nonemptiness of approximate cores," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 888-906, July.
  3. Ehud Lehrer & Marco Scarsini, 2013. "On the Core of Dynamic Cooperative Games," Dynamic Games and Applications, Springer, Springer, vol. 3(3), pages 359-373, September.
  4. Myrna Wooders, 2009. "Cores of Many-Player Games; Nonemptiness and Equal Treatment," Vanderbilt University Department of Economics Working Papers, Vanderbilt University Department of Economics 0918, Vanderbilt University Department of Economics.
  5. Myrna Wooders, 2009. "Market Games and Clubs," Vanderbilt University Department of Economics Working Papers, Vanderbilt University Department of Economics 0919, Vanderbilt University Department of Economics.
  6. Tovey, Craig A., 2010. "The instability of instability of centered distributions," Mathematical Social Sciences, Elsevier, Elsevier, vol. 59(1), pages 53-73, January.
  7. Nizar Allouch & Myrna Wooders, 2004. "Price taking equilibrium in club economies with multiple memberships and unbounded club sizes," Cahiers de la Maison des Sciences Economiques, Université Panthéon-Sorbonne (Paris 1) b04109, Université Panthéon-Sorbonne (Paris 1).
  8. Wooders, M. & Selten, R. & Cartwright, E., 2001. "Some First Results for Noncooperative Pregames : Social Conformity and Equilibrium in Pure Strategies," The Warwick Economics Research Paper Series (TWERPS), University of Warwick, Department of Economics 589, University of Warwick, Department of Economics.
  9. Allouch, Nizar & Wooders, Myrna, 2008. "Price taking equilibrium in economies with multiple memberships in clubs and unbounded club sizes," Journal of Economic Theory, Elsevier, Elsevier, vol. 140(1), pages 246-278, May.
  10. Allouch, Nizar & Wooders, Myrna, 2002. "Competitive Pricing In Socially Networked Economies," The Warwick Economics Research Paper Series (TWERPS), University of Warwick, Department of Economics 639, University of Warwick, Department of Economics.

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