The Library
Approximate cores of games and economies with clubs
Tools
Kovalenkov, Alexander and Wooders, Myrna Holtz (2001) Approximate cores of games and economies with clubs. Working Paper. Coventry: University of Warwick, Department of Economics. (Warwick economic research papers).

PDF
WRAP_Kovalenkov_twerp535rev.pdf  Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader Download (470Kb) 
Official URL: http://www2.warwick.ac.uk/fac/soc/economics/resear...
Abstract
We introduce the framework of parameterized collections of games and provide three nonemptiness of approximate core theorems for arbitrary games with and without sidepayments. The parameters bound (a) the number of approximate types of players and the size of the approximation and (b) the size of nearly effective groups of players and their distance from exact effectiveness. The theorems are based on a new notion of partitionbalanced profiles and approximately partitionbalanced profiles. The results are then applied to a new model of an economy with clubs. In contrast to the extant literature, our approach allows both widespread externalities and uniform results.
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):  Group theory, Clubs, Approximation theory, Small groups  Research, Game theory 
Series Name:  Warwick economic research papers 
Publisher:  University of Warwick, Department of Economics 
Place of Publication:  Coventry 
Date:  August 2001 
Number:  No.535 
Number of Pages:  41 
Status:  Not Peer Reviewed 
Access rights to Published version:  Open Access 
Description:  Original version, January 1997; this revision, August 2001 
Funder:  European Union (EU), Universidad Autónoma de Barcelona (UAdB), Universitats of Catalonia (UCat), Social Sciences and Humanities Research Council of Canada (SSHRC), Departmento Governmental de Investigaciónes Cientificas y Técnológicas (DGICYT) 
Adapted As:  Kovalenkov, A. and Wooders, M.H. (2002). Approximate cores of games and economies with clubs. [Coventry] : University of Warwick, Economics Department. (Warwick economic research papers, no.634). 
References:  [1] B. Allen, Incentives in market games with asymmetric information: Approximate NTU cores in large economies," Chapter 11 in Social Choice, Welfare, and Ethics: Proceedings of the Eighth International Symposium in Economic Theory and Econometrics (W.A. Barnett, H. Moulin, M. Salles, and N.J. Scho¯eld eds.), Cambridge: Cambridge University Press, 1994. [2] R.M. Anderson, An elementary core equivalence theorem, Econometrica 46 (1978), 14381487. [3] R.J. Aumann, Markets with a continuum of traders, Econometrica 32 (1964), 3950. [4] W.J. Baumol, J.C. Panzer and R.D. Willig, Contestable Markets and the Theory of Industry Structure, San Diego: Harcourt, Brace, Javanovitch, 1982. [5] E. Bennett and M. Wooders, Income distribution and ¯rm formation, Journal of Comparative Economics 3 (1979), 304317. [6] V. BÄohm, The limit of the core of an economy with production,International Economic Review 15 (1974), 143148. [7] J. Broome, Approximate equilibrium in economies with indivisible commodities, Journal of Economic Theory 5 (1972), 224249. [8] J. Buchanan, An economic theory of clubs, Economica 33 (1965), 114. [9] J. Conley, Convergence theorems on the core of a Public Goods Economy: Sufficient Conditions,Journal of Economic Theory 62 (1994), 16185. [10] J. Conley and M. Wooders, Tiebout economies with di®erential genetic types and endogenously chosen crowding characteristics, Journal of Economic Theory 98 (2001), 261294. [11] J. Conley and M.Wooders, Taste homogeneity of optimal jurisdictions in a Tiebout economy with crowding types and endogenous educational investment choices, Richerche Economiche 50 (1996), 367387. [12] J. Conley and M. Wooders, Equivalence of the core and competitive equilibrium in a Tiebout economy with crowding types, Journal of Urban Economics (1997), 421440. [13] J. Conley and M. Wooders, Anonymous pricing in Tiebout economies and economies with clubs,in Topics in Public Finance, (D. Pines, E. Sadka, and I. Zilcha eds.), Cambridge: Cambridge University Press 1998. [14] V.P. Crawford, Comparative Statics in Matching Markets,Journal of Economic Theory 54 (1991), 389400. [15] N. Dagan, R. Serrano and O. Volij, Bargaining, Coalitions and Competition, Economic Theory 15 (2000):279296. [16] G. Debreu, New concepts and techniques for equilibrium analysis,International Economic Review 3 (1962), 257273. [17] G. Debreu and H. Scarf, A limit theorem on the core of an economy,International Economic Review 4 (1963), 235246. [18] F. Forges, A. Heifetz and E. Minelli, Incentive compatible core and competitive equilibria in di®erential information economies, Economic Theory 18(2001), 349365. [19] R. Garratt and CZ. Qin Cores and competitive equilibria with indivisibilities and lotteries, Journal of Economic Theory 68 (1996), 531543. [20] D.B. Gilles, Some Theorems on nperson Games, Ph.D. Dissertation, Department of Mathematics, Princeton University, Princeton 1953. [21] J. Greenberg and S. Weber, Strong Tiebout equilibrium with restricted preference domain, Journal of Economic Theory 38 (1986), 101117. [22] P.J. Hammond, On fcore equivalence with general widespread externalities, Journal of Mathematical Economics 32 (1999), 177184. [23] P.J. Hammond, M. Kaneko, and M. Wooders (1989) Continuum economies with ¯nite coalitions; Core, equilibrium and widespread externalities, Journal of Economic Theory 49 (1989), 113134. [24] W. Hildenbrand, Core and Equilibria of a Large economy, Princeton: Princeton University Press, 1974. [25] W. Hildenbrand and A.P. Kirman, Introduction to Equilibrium Analysis, Amsterdam Oxford: North Holland, 1976. [26] T. Ichiishi and J. SchÄa®er, The ¿core of a game without side payments,Carnegie Mellon University Graduate School of Industrial Administration Working Paper No. 97980, 1979. [27] M. Kaneko and M. Wooders, Cores of partitioning games, Mathematical Social Sciences 3 (1982), 313327. [28] M. Kaneko and M. Wooders, The core of a game with a continuum of players and ¯nite coalitions: The model and some results, Mathematical Social Sciences 12 (1986), 105137. [29] M. Kaneko and M. Wooders, The core of a continuum economy with widespread externalities and ¯nite coalitions: From ¯nite to continuum economics, Journal of Economic Theory 49 (1989), 135168. [30] M. Kaneko and M. Wooders, The nonemptiness of the fcore of a game without side payments, International Journal of Game Theory 25 (1996), 245258. [31] Y. Kannai, Continuity properties of the core of a market, Econometrica 38 (1970), 791815. [32] A.S. Kelso and V.P. Crawford, Job matching, coalition formation, and gross substitutes, Econometrica 50 (1982), 14831504. [33] H. Konishi, M. Le Breton, and S. Weber, Equilibrium in a ¯nite local public goods economy, Journal of Economic Theory 79 (1998), 224244. [34] A. Kovalenkov and M. Wooders, Epsilon cores of games and economies with limited side payments, Autonomous University of Barcelona WP 392.97, revised, Games and Economic Behavior (in press). [35] A. Kovalenkov and M.Wooders, An exact bound on " for nonemptiness of "cores of games,Autonomous University of Barcelona WP 393.97 and 394.97, revised, Mathematics of Operations Research (in press). [36] A.M. Manelli, Core convergence without monotone preferences and free disposal, Journal of Economic Theory 55 (1991), 400415. [37] A.M. Manelli, Monotonic preferences and core equivalence, Econometrica 59 (1991b), 123138. [38] A. MasColell, A re¯nement of the core equivalence theorem, Economic Letters 3 (1979), 307310. [39] A. MasColell, E±ciency and decentralization in the pure theory of public goods, Quarterly Journal of Economics 94 (1980), 625641. [40] R. Myerson, Game Theory, Cambridge London: Harvard University Press, 1991. [41] J. Ostroy, A reformulation of the marginal productivity theory of distribution, Econometrica 52 (1984), 599630. [42] M. Pauly, Clubs, commonality and the core: An integration of game theory and the theory of public goods, Economica (1967), 314324. [43] M. Pauly, Cores and clubs, Public Choice 9 (1970), 5365. [44] A. Roth and M. Sotomayor, Twosided Matching; A Study in Gametheoretic Modeling and Analysis, Cambridge: Cambridge University Press, 1990. [45] H.E. Scarf, The core of an nperson game, Econometrica 35 (1967), 5067. [46] R. Selten, A noncooperative model of characteristic function bargaining, in \Essays in Game Theory and Mathematical Economics in Honor of O.Morgenstern," (V. BÄohm and M. Nachtkamp eds.), Manheim Wein ZÄurich: Bibliographisches Institut, 1981. [47] L.S. Shapley, On balanced sets and cores, Naval Research Logistics Quarterly 14 (1967), 453460. [48] L.S. Shapley and M. Shubik, Quasicores in a monetary economy with nonconvex preferences, Econometrica 34 (1966), 805827. [49] L.S. Shapley and M. Shubik, On market games, Journal of Economic Theory 1 (1969), 925. [50] M. Shubik, Edgeworth Market Games, in \Contributions to the Theory of Games IV, Annals of Mathematical Studies 40," (F.R. Luce, and A.W. Tucker, eds.), Princeton: Princeton University Press, 1959. [51] M. Shubik, The `Bridge Game' economy: An example of indivisibilities, Journal of Political Economy 79 (1971), 909912. [52] M. Shubik and M. Wooders, Nearmarkets and marketgames, Cowles Foundation Discussion Paper No. 657, 1982. [53] M. Shubik and M. Wooders, Clubs, nearmarkets and marketgames, in \Topics in Mathematical Economics and Game Theory; Essays in Honor of Robert J. Aumann," (M. Wooders ed.), Fields Institute Communication Volume, Providence: American Mathematical Society, 1999. [54] M. Shubik and M. Wooders, Approximate cores of replica games and economies: Part I. replica games, externalities, and approximate cores, Mathematical Social Sciences 6 (1983), 2748. [55] V. Vasil'ev, S. Weber and H. Wiesmeth, Core equivalence with congested public goods, Economic Theory 6 (1995), 373387. [56] S. Weber, On ²cores of balanced games, International Journal of Game Theory 8, 241250. [57] M.Wooders, Equilibria, the Core, and Jurisdiction Structures in Economies with a Local Public Good, Journal of Economic Theory 18 (1978), 328348. [58] Wooders, M.H. (1977) A characterization of approximate equilibria and cores in a class of coalition economies, Stony Brook Department of Economics Working Paper No. 184, Revised 1979, online at http://www.warwick.ac.uk/fac/soc/Economics/wooders/. [59] M. Wooders, Asymptotic cores and asymptotic balancedness of large replica games, Stony Brook Department of Economics Working Paper No. 215, 1979, revised 1980, online at http://www.warwick.ac.uk/fac/soc/Economics/wooders/. [60] M. Wooders, The epsilon core of a large replica game, Journal of Mathematical Economics 11 (1983), 277300. [61] M. Wooders, Stability of jurisdiction structures in economies with a local public good, Mathematical Social Sciences 15 (1988), 2429. [62] M. Wooders, The e±caciousness of small groups and the approximate core property in games without side payments, University of Bonn Sonderforschungsbereich 303 Discussion Paper No. B17 (1991). [63] M. Wooders, Inessentiality of large groups and the approximate core property; An equivalence theorem, Economic Theory 2 (1992), 129147. [64] M. Wooders, Large games and economies with e®ective small groups, in \Game Theoretic Aproaches to General Equilibrium Theory," (J.F.Mertens and S. Sorin eds.), Dordrecht Boston London: Kluwer Academic Publishers, 1994. [65] M. Wooders, Equivalence of games and markets, Econometrica 62 (1994), 11411160. [66] M.Wooders, Multijurisdictional economies, the Tiebout Hypothesis, and sorting, Proceedings of the National Academy of Sciences 96 (1999), 1058510587, online at http://www.pnas.org/cgi/content/full/96/19/10585. [67] M. Wooders, and W.R. Zame, Approximate cores of large games, Econometrica 52 (1984), 13271350. [68] M. Wooders and W.R. Zame, NTU values of large games, IMSSS Technical Report No. 503, 1987. [69] Wooders, M.H. and W.R. Zame (1989) \Approximate cores of large games without sidepayments," notes in manuscript. 
URI:  http://wrap.warwick.ac.uk/id/eprint/1640 
Actions (login required)
View Item 