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An explicit bound on " for nonemptiness of "-cores of games

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Kovalenkov, Alexander and Wooders, Myrna Holtz (1999) An explicit bound on " for nonemptiness of "-cores of games. Working Paper. University of Warwick, Department of Economics, Coventry.

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Abstract

We consider parameterized collections of games without side payments and determine a bound on E so that all suffciently large games in the collection have non-empty E-cores. Our result makes explicit the relationship between the required size of E for non-emptiness of the E-core, the parameters describing the collection of games, and the size of the total player set. Given the parameters describing the collection, the larger the game, the smaller the E that can bechosen.

Item Type: Working or Discussion Paper (Working Paper)
Subjects: H Social Sciences > HB Economic Theory
Q Science > QA Mathematics
Divisions: Faculty of Social Sciences > Economics
Library of Congress Subject Headings (LCSH): Game theory, Differential games, Mathematical models
Series Name: Warwick economic research papers
Publisher: University of Warwick, Department of Economics
Place of Publication: Coventry
Date: September 1999
Number: No.537
Number of Pages: 28
Status: Not Peer Reviewed
Access rights to Published version: Open Access
Funder: Departmento Governmental de Investigaciónes Cientificas y Técnológicas (DGICYT), Universitats of Catalonia (UCat), Social Sciences and Humanities Research Council of Canada (SSHRC), Universidad Autónoma de Barcelona (UAdB)
References: [1] Allen, B. (1994) \Incentives in market games with asymmetric information: Approximate (NTU) cores in large economies," in Social Choice, Welfare and Ethics, W. Barnett, H. Moulin, M. Salles amd N. Scho¯eld (eds.) Cambridge: Cambridge University Press. [2] Allen, B. (1995) \On the existence of core allocations in a large economy with incentive compatibility constraints," forthcoming in Topics in Game Theory and Mathematical Economics; Essays in Honor of Robert J. Aumann, M.H. Wooders (ed.) Fields Communication Volume, American Mathematical Society. [3] Billera, L.J. (1970) \Some theorems on the core of an n-person game without side payments", SIAM Journal of Applied Mathematics 18, 567-579. [4] Bondareva, O. N. (1962) \Theory of the core in an n-person game" (in Russian), Vestnik of Leningrad State University 13, 141-142. [5] Conley, J. and M.H.Wooders (2000) \Tiebout economies with di®erential genetic types and endogenously chosen crowding characteristics" Journal of Economic Theory (forthcoming). [6] Forges, F., A. Heifetz and E. Minelli (1999) \Incentive compatible core and competitive equilibrium in di®erential information economies," University of Cergy-Pontoise, Thema Discussion Paper No. 99-06. [7] Forges, F., and E. Minelli (1999) \A note on the incentive compatible core," University of Cergy-Pontoise, Thema Discussion Paper No. 99-02. [8] Hildenbrand, W. and A.P. Kirman (1988) Equilibrium Analysis, Advanced Textbooks in Economics, Amsterdam- New York - Oxford- Tokyo: North-Holland. [9] Kaneko, M. and M.H. Wooders (1982) \Cores of partitioning games," Mathematical Social Sciences 3, 313-327. [10] Kaneko, M. andM.H.Wooders (1996) \The non-emptiness of the f-core of a game without side payments," International Journal of Game Theory 25, 245-258. [11] Kovalenkov, A. and M.H. Wooders (1997a) \Approximate cores of games and economies with clubs," Autonomous University of Barcelona WP 390.97 and 391.97, revised. [12] Kovalenkov, A. and M.H. Wooders (1997b) \Epsilon cores of games and economies with limited side payments," Autonomous University of Barcelona WP 392.97. [13] Maschler, M., B. Peleg, and L. Shapley (1979) \Geometric properties of the kernel, nucleolus and related solution concepts," Mathematics of Operations Research 4, 303-338. [14] Scarf, H. E. (1965) \The core of an n-person game," Cowles Foundation Discussion Paper No. 182. [15] Scarf, H. E. (1967) \The core of an n-person game," Econometrica 35, 50-67. [16] Shapley, L. S. (1967) \On balanced sets and cores," Naval Research Logistics Quarterly 14, 453-460. [17] Shapley, L. S. and M. Shubik (1966) \Quasi-cores in a monetary economy with nonconvex preferences," Econometrica 34, 805-827. [18] Wooders, M. H. (1983) \The epsilon core of a large replica game," Journal of Mathematical Economics 11, 277-300. [19] Wooders, M. H. (1994a) \Equivalence of games and markets," Econometrica 62, 1141-1160. [20] Wooders, M. H. (1994b), \Approximating games and economies by markets," University of Toronto Working Paper No. 9415. [21] Wooders, M. H. and W.R. Zame (1984) \Approximate cores of large games," Econometrica 52, 1327-1350.
URI: http://wrap.warwick.ac.uk/id/eprint/1638

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