Cores of many-player games; nonemptiness and equal treatment
This paper provides sufficient conditions to ensure nonemptiness of approximate cores of many-player games and symmetry of approximate core payoffs (the equal treatment property). The conditions are: (a) essential superadditivity -- an option open to a group of players is to partition into smaller groups and realize the worths of these groups and (b) small group effectiveness (SGE) -- almost all gains to collective activities can be realized by cooperation only within members of some partition of players into relatively small groups. Another condition, small group negligibility (SGN), is introduced and shown to be equivalent to SGE. SGN dictates that small groups of players cannot have significant effects on average (i.e., per capita) payoffs of large populations; thus, SGN is a analogue, for games with a finite player set, of the condition built into models with a continuum of player that sets of measure zero can be ignored. SGE implies per capita boundedness (PCB), that the supremum of average or per capita payoffs is uniformly bounded above. Further characterization of SGE in terms of its relationship to PCB is provided. It is known that if SGE does not hold, then approximate cores of many-player games may be empty. Examples are developed to show that if SGE does not hold and if there are players of "scarce types" (in other works, players with scarce attributes) then even if there is only a finite number of types of players and approximate cores are non-empty, symmetry may be lost; moreover, even players of abundant types may be treated asymmetrically by the core.
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Volume (Year): 14 (2010)
Issue (Month): 1 (March)
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- Kovalenkov, Alexander & Wooders, Myrna, 2003.
"Approximate cores of games and economies with clubs,"
Journal of Economic Theory,
Elsevier, vol. 110(1), pages 87-120, May.
- Alexander Kovalenkov & Myrna Holtz Wooders, 2000. "Approximate Cores of Games and Economies with Clubs," Econometric Society World Congress 2000 Contributed Papers 1790, Econometric Society.
- Kovalenkov, Alexander & Wooders, Myrna Holtz, 2002. "Approximate Cores Of Games And Economies With Clubs," The Warwick Economics Research Paper Series (TWERPS) 634, University of Warwick, Department of Economics.
- Kovalenkov, Alexander & Wooders, Myrna Holtz, 1999. "Approximate Cores Of Games And Economies With Clubs," The Warwick Economics Research Paper Series (TWERPS) 535, University of Warwick, Department of Economics.
- Alexander Kovalenkov & Myrna H. Wooders, 1998. "Approximate cores of games and economies with clubs," Working Papers mwooders-00-01, University of Toronto, Department of Economics.
- Kovalenkov, Alexander & Wooders, Myrna Holtz, 2001.
"Epsilon Cores of Games with Limited Side Payments: Nonemptiness and Equal Treatment,"
Games and Economic Behavior,
Elsevier, vol. 36(2), pages 193-218, August.
- Myrna Wooders & Alexander Kovalenkov, 2001. "Epsilon cores of games with limited side payments Nonemptiness and equal treatment," Economics Bulletin, AccessEcon, vol. 28(5), pages A0.
- Khan, A & Polemarchakis, Heraklis M, 1978. "Unequal Treatment in the Core," Econometrica, Econometric Society, vol. 46(6), pages 1475-81, November.
- Allouch, Nizar & Wooders, Myrna, 2008. "Price taking equilibrium in economies with multiple memberships in clubs and unbounded club sizes," Journal of Economic Theory, Elsevier, vol. 140(1), pages 246-278, May.
- Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July.
- Eyal Winter & Myrna Wooders, 2008. "On large games with bounded essential coalition sizes," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(2), pages 191-206.
- Kannai, Yakar, 1970. "Continuity Properties of the Core of a Market," Econometrica, Econometric Society, vol. 38(6), pages 791-815, November.
- Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, vol. 1(1), pages 9-25, June.
- Hurwicz, Leonid, 1999. " Revisiting Externalities," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 1(2), pages 225-45.
- Green, Jerry R., 1972. "On the inequitable nature of core allocations," Journal of Economic Theory, Elsevier, vol. 4(2), pages 132-143, April.
- Martin Shubik & Myrna Holtz Wooders, 1982. "Near-Markets and Market Games," Cowles Foundation Discussion Papers 657, Cowles Foundation for Research in Economics, Yale University.
- Wooders, Myrna Holtz & Zame, William R, 1984. "Approximate Cores of Large Games," Econometrica, Econometric Society, vol. 52(6), pages 1327-50, November.
- Wooders, Myrna Holtz, 1994. "Equivalence of Games and Markets," Econometrica, Econometric Society, vol. 62(5), pages 1141-60, September.
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