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The weak-core of a game in normal form with a continuum of players

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  • Askoura, Y.

Abstract

This paper deals with the weak-core of normal form games with a continuum set of players and without side payments. This concept is an approximation of the core introduced by Weber, Shapley and Shubik. The weak-core is slightly larger than Aumann's [alpha]-core when adapted to large anonymous games. A non-emptiness result is obtained based on the well known Scarf's non-vacuity theorem for finite games.

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  • Askoura, Y., 2011. "The weak-core of a game in normal form with a continuum of players," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 43-47, January.
    • Handle: RePEc:eee:mateco:v:47:y:2011:i:1:p:43-47
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    1. Hart, Sergiu & Hildenbrand, Werner & Kohlberg, Elon, 1974. "On equilibrium allocations as distributions on the commodity space," Journal of Mathematical Economics, Elsevier, vol. 1(2), pages 159-166, August.
    2. Kannai, Yakar, 1970. "Continuity Properties of the Core of a Market," Econometrica, Econometric Society, vol. 38(6), pages 791-815, November.
    3. Mas-Colell, Andreu, 1975. "A model of equilibrium with differentiated commodities," Journal of Mathematical Economics, Elsevier, vol. 2(2), pages 263-295.
    4. Starr, Ross M, 1969. "Quasi-Equilibria in Markets with Non-Convex Preferences," Econometrica, Econometric Society, vol. 37(1), pages 25-38, January.
    5. HILDENBRAND, Werner, 1968. "The core of an economy with a measure space of economic agents," LIDAM Reprints CORE 26, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Wooders, Myrna Holtz & Zame, William R, 1984. "Approximate Cores of Large Games," Econometrica, Econometric Society, vol. 52(6), pages 1327-1350, November.
    7. SCHMEIDLER, David, 1973. "Equilibrium points of nonatomic games," LIDAM Reprints CORE 146, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Anderson, Robert M, 1985. "Strong Core Theorems with Nonconvex Preferences," Econometrica, Econometric Society, vol. 53(6), pages 1283-1294, November.
    9. Kannai, Yakar, 1972. "Continuity Properties of the Core of a Market: A Correction," Econometrica, Econometric Society, vol. 40(5), pages 955-958, September.
    10. Rath, Kali P, 1992. "A Direct Proof of the Existence of Pure Strategy Equilibria in Games with a Continuum of Players," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(3), pages 427-433, July.
    11. Hildenbrand, Werner & Schmeidler, David & Zamir, Shmuel, 1973. "Existence of Approximate Equilibria and Cores," Econometrica, Econometric Society, vol. 41(6), pages 1159-1166, November.
    12. W. Hildenbrand, 1968. "The Core of an Economy with a Measure Space of Economic Agents," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(4), pages 443-452.
    13. Khan, M. Ali & Rath, Kali P. & Sun, Yeneng, 1997. "On the Existence of Pure Strategy Equilibria in Games with a Continuum of Players," Journal of Economic Theory, Elsevier, vol. 76(1), pages 13-46, September.
    14. Weber, S., 1981. "Some results on the weak core of a non-side-payment game with infinitely many players," Journal of Mathematical Economics, Elsevier, vol. 8(1), pages 101-111, March.
    15. Mas-Colell, Andreu, 1984. "On a theorem of Schmeidler," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 201-206, December.
    16. Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July.
    17. 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.
    18. Kaneko, Mamoru & Wooders, Myrna Holtz, 1996. "The Nonemptiness of the f-Core of a Game without Side Payments," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(2), pages 245-258.
    19. Ali Khan, M. & Yamazaki, Akira, 1981. "On the cores of economies with indivisible commodities and a continuum of traders," Journal of Economic Theory, Elsevier, vol. 24(2), pages 218-225, April.
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    2. Yang, Zhe, 2017. "Some infinite-player generalizations of Scarf’s theorem: Finite-coalition α-cores and weak α-cores," Journal of Mathematical Economics, Elsevier, vol. 73(C), pages 81-85.
    3. Yang, Zhe & Song, Qingping, 2022. "A weak α-core existence theorem of generalized games with infinitely many players and pseudo-utilities," Mathematical Social Sciences, Elsevier, vol. 116(C), pages 40-46.
    4. Yang, Zhe, 2018. "Some generalizations of Kajii’s theorem to games with infinitely many players," Journal of Mathematical Economics, Elsevier, vol. 76(C), pages 131-135.
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