Kovalenkov, Alexander and Wooders, Myrna Holtz (1999) A law of scarcity for games. Working Paper. University of Warwick, Department of Economics, Coventry.

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Abstract

The "law of scarcity" is that scarceness is rewarded; recall, for example, the diamonds and water paradox. In this paper, furthering research initiated in Kelso and Crawford (1982, Econometrica 50, 1483-1504) for matching models, we demonstrate a law of scarcity for cores and approximate cores of games.

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, Demand (Economic theory), Monotonic functions, Approximation theory, Small groups
Series Name:	Warwick economic research papers
Publisher:	University of Warwick, Department of Economics
Place of Publication:	Coventry
Date:	December 1999
Number:	No.546
Number of Pages:	15
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
Funder:	Social Sciences and Humanities Research Council of Canada (SSHRC), Universitats of Catalonia (UCat), Universidad Autónoma de Barcelona (UAdB)
Adapted As:	Kovalenkov, A. and Wooders, M.H. (2003). Laws of scarcity for a finite game: exact bounds on estimations. [Coventry] : University of Warwick, Economics Department. (Warwick economic research papers, no.691).
References:	[1] Crawford, V.P. (1991) “Comparative statics in matching models,” Journal of Economic Theory 54, 389-400. [2] Crawford, V. and E. Knoer (1981) “Job matchings with heterogeneous firms and workers,” Econometrica 49, 437-50. [3] Engl, G. and S. Scotchmer (1996) “The core and the hedonic core: Equivalence and comparative statics” Journal of Mathematical Economics 26, 209-248. [4] Engl, G. and S. Scotchmer (1997) “The law of supply in games, markets and matching models,” Economic Theory 9, 539-550. [5] Epstein, L.G. (1981) “Generalized duality and integrability,” Econometrica 49, 655-578. [6] Hildenbrand, W. (1994) Market Demand: Theory and Empirical Evidence, Princeton: Princeton University Press. [7] Kelso, A.S. and V.P. Crawford (1982) “Job matching, coalition formation, and gross substitutes,” Econometrica 50, 1483-1504. [8] Kovalenkov, A. and M.H. Wooders (1999a) “Approximate cores of games and economies with clubs,” University ofWarwick Department of Economics Working Paper No. 535, combining Autonomous University of Barcelona WP. 390.97 and 391.97, on-line at http: //www.warwick.ac.uk/fac/soc/Economics/wooders/online.html. [9] Kovalenkov, A. and M.H. Wooders (1999b) “An explicit bound on ε for nonemptiness of ε-cores of games,” University of Warwick Department of Economics Working Paper No. 537, combining Autonomous University of Barcelona WP 393.97 and 394.97, on-line at http: //www.warwick.ac.uk/fac/soc/Economics/wooders/on-line.html. [10] Roth, A. (1984) “The Evolution of the labor market for medical residents and interns: A case study in game theory,” Journal of Political Economy 92, 991-1016. [11] Roth, A. and M. Sotomayer (1990) Two-sided Matching; A Study in Gametheoretic Modeling and Analysis, Cambridge: Cambridge University Press. [12] Scotchmer, S. and M.H. Wooders (1988) “Monotonicity in games that exhaust gains to scale,” Hoover Institution Working Paper in Economics E-89-23, on-line at http://www.warwick.ac.uk/fac/soc/Economics/wooders/on-line.html. [13] Shapley, L.S. (1962) “Complements and substitutes in the optimal assignment problem,” Navel Research Logistics Quarterly 9, 45-48. [14] Shubik, M. and M.H.Wooders (1982) “Near markets and market games,” Cowles Foundation Discussion Paper No. 657, published as “Clubs, near markets and market games” in Topics in Mathematical Economics and Game Theory; Essays in Honor of Robert J. Aumann, (1999) M.H. Wooders ed., American Mathematical Society Fields Communication Volume 23, 233-256, on-line at http: //www.warwick.ac.uk/fac/soc/Economics/wooders/on-line.html. [15] Wooders, M.H. (1979) “A characterization of approximate equilibria and cores in a class of coalition economies”, Stony Brook Department of Economics Working Paper No. 184, 1977, Revised 1979, on-line at http: //www.warwick.ac.uk/fac/soc/Economics/wooders/on-line.html. [16] Wooders, M.H. (1980) “Asymptotic cores and asymptotic balancedness of large replica games” Stony Brook Department of Economics Working Paper No. 215, 1979, Revised and extended 1980, on-line at http: //www.warwick.ac.uk/fac/soc/Economics/wooders/on-line.html. [17] Wooders, M.H. (1983) “The epsilon core of a large replica game,” Journal of Mathematical Economics 11, 277-300. [18] Wooders, M.H. (1992a) “Inessentiality of large groups and the approximate core property; An equivalence theorem,” Economic Theory 2, 129-147. [19] Wooders, M.H. (1992b) “Large games and economies with effective small groups” University of Bonn SFB Discussion Paper No. B-215, published in Game Theoretic Approaches to General Equilibrium Theory, (1994) J.-F. Mertens and S. Sorin eds., Dordrecht- Boston- London: Kluwer Academic Publishers. [20] Wooders, M.H. (1994a) “Equivalence of games and markets,” Econometrica 62, 1141-1160. [21] Wooders, M.H. (1994b) “Approximating games and economies by markets,” University of Toronto Working Paper No. 9415. [22] Wooders, M.H. (1999) “Multijurisdictional economies, the Tiebout Hypothesis, and sorting,” Proceedings of the National Academy of Sciences 96: 10585-10587, on-line at http://www.pnas.org/perspective.shtml. [23] Wooders, M.H. andW.R. Zame (1987) “Large games; Fair and stable outcomes,” Journal of Economic Theory 42, 59-93.
URI:	http://wrap.warwick.ac.uk/id/eprint/1631

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