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Large Games and Economies with Effective Small Groups

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Game-Theoretic Methods in General Equilibrium Analysis

Part of the book series: NATO ASI Series ((ASID,volume 77))

Abstract

Our social and economic life is carried out within groups — firms, families, market-places, and clubs, for example. Individuals cooperate within groups to benefit from increasing returns to group size and coordination of activities. Individuals compete within groups for shares of the surplus generated by the activities of the group. There is competition between groups for scarce resources and for group members. Collective activities of groups of individuals are widespread in social and economic interaction.

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References

  1. Albers, W. (1979) ‘Core-and-Kernel Variants Based on Imputations and Demand Profiles’, in Game Theory and Related Topics, O. Moeschlin and D. Pallaschke, (eds.), North Holland, Amsterdam

    Google Scholar 

  2. Allen, B. (1992) ‘Incentives in Market Games with Asymmetric Information: The Core’, C. A. R. E. S. S. Working Paper # 91–38, Department of Economics, University of Pennsylvania.

    Google Scholar 

  3. Allen, B. (1992) ‘Incentives in Market Games with Asymmetric Information: Approximate (NTU) Cores in Large Economies’, C. A. R. E. S. S. Working Paper No. 92–05, Department of Economics, University of Pennsylvania, to appear.

    Google Scholar 

  4. Anderson, R. (1991) ‘Large Square Economies: An Asymptotic Interpretation’, University of California at Berkeley Working paper.

    Google Scholar 

  5. Atkinson, A. and Stiglitz, J. (1980) Lectures on Public Economics McGraw-Hill Co. New York.

    Google Scholar 

  6. Aumann R.J. (1964) ‘Markets with a Continuum of Traders’, Econometrica 32, 39–50.

    Article  Google Scholar 

  7. Aumann, R.J. (1987) Game Theory,The New Palgrave: A Dictionary of Economics, J. Eatwell, M. Milgate, and P. Newman, eds. The Macmillan Press.

    Google Scholar 

  8. Aumann, R.J. and Dreze, J. (1974) ‘Cooperative Games with Coalition Structures’, International Journal of Game Theory 3, 217–37.

    Article  Google Scholar 

  9. Aumann, R.J. and Shapley, L.S. (1974) Values of Nonatomic Economies, Princeton, New Jersey, Princeton University Press.

    Google Scholar 

  10. Barro, R. and Romer, P. (1987) ‘Ski-Lift Pricing, with Applications to Labor and Other Markets’, American Economic Review 77, 875–890.

    Google Scholar 

  11. Bennett, E. (1983) ‘The Aspiration Approach to Predicting Coalition Formation In Side payments Games’, International Journal of Game Theory 12, 1–28.

    Article  Google Scholar 

  12. Bennett, E. (1991) ‘Three Approaches to Bargaining in NTU Games’, Game Equilibrium Models III, Reinhard Selten ed., Springer-Verlag, Heidelberg.

    Google Scholar 

  13. Bennett, E. and Wooders, M.H. (1979) ‘Income Distribution and Firm Formation’, Journal of Comparative Economics 3, 304–317.

    Article  Google Scholar 

  14. Bewley, T. (1981) ‘A Critique of Tiebout’s Theory of Local Public Expenditure’ Econometrica 49, 713–740.

    Google Scholar 

  15. le Breton, M., Owen, G. and Weber, S. (1992) ‘Strongly Balanced Cooperative Games’ International Journal of Game Theory 20, 419–428.

    Google Scholar 

  16. Berglas, E. (1976) ‘Distribution of Tastes and Skills and the Provision of Local Public Goods’, Journal of Public Economics 6, 409–423.

    Article  Google Scholar 

  17. Böhm, V. (1974) ‘The Limit of the Core of an Economy with Production’ International Economic Review 15, 143–148.

    Google Scholar 

  18. Bondareva, O. (1962) ‘Theory of the Core in an n-Person Game’, Vestnik, LGU13, 141–142 (in Russian), ( Leningrad State University, Leningrad).

    Google Scholar 

  19. Conley J. (1991) ‘Convergence Theorems on the Core of a Public Goods Economy: Sufficient Conditions’, Journal of Economic Theory, (forthcoming)

    Google Scholar 

  20. Crawford, V.P. (1991) ‘Comparative Statics in Matching Markets’ Journal of Economic Theory 54, 389–400.

    Google Scholar 

  21. Crawford, V. and Knoer, E. (1981) ‘Job Matchings with Heterogeneous Firms and Workers’, Econometrica 49, 437–50.

    Article  Google Scholar 

  22. Demange G. (1990) ‘Intermediate Preferences and Stable Coalition Structure’, DELTA EHSS, Discussion Paper.

    Google Scholar 

  23. Demange, G. and Henriet, D. (1990) ‘Sustainable Oligopolies’ Journal of Economic Theory 54, 417–428.

    Google Scholar 

  24. Debreu G. and Scarf, H. (1963) “A Limit Theorem on the Core of an Economy” International Economic Review 4, 235–246.

    Google Scholar 

  25. Dreze, J. and Greenberg, J. (1980), ‘Hedonic Coalitions: Optimality and Stability’ Econometrica 48, 987–1004.

    Google Scholar 

  26. Edgeworth, F.Y. (1881) Mathematical PsychicsKegan Paul: London.

    Google Scholar 

  27. Ellickson, B. (1973) ‘A Generalization of the Pure Theory of Public Goods’ American Economic Review 63, 417–432.

    Google Scholar 

  28. Ellickson, B. (1979) “Competitive Equilibrium with Local Public Goods” Journal of Economic Theory 21, 46–61.

    Google Scholar 

  29. Elul, R. (1987) ‘A Comment on the Existence of Strong e-Cores of Large Games’, Weizmann Institute Department of Mathematics manuscript.

    Google Scholar 

  30. Engl, G. and Scotchmer, S. (1991) ‘The Core and Hedonic Core: Equivalence and Comparative Statics’, mimeo (Revised June 26, 1992 ).

    Google Scholar 

  31. Faulhaber, G.R. (1975), ‘Cross-Subsidization; Pricing in Public Enterprises’ American Economic Review 65, 966–977.

    Google Scholar 

  32. Florenzano, M. (1990) ‘Edgeworth Equilibria, Fuzzy Core, and Equilibria of a Production Economy without Ordered Preferences’, Journal of Mathematical Analysis and Applications 153, 18–36.

    Article  Google Scholar 

  33. Foley, D. (1970) ‘Lindahl’s Solution and the Core of an Economy with Public Goods’ Econometrica 38, 66–72.

    Google Scholar 

  34. Gale, D. (1986) ‘Bargaining and Competition Part 1: Characterization’ Econometrica 54, 807–818.

    Google Scholar 

  35. Gale, D. (1986) ‘Bargaining and Competition Part 2: Existence’, Econometrica 54, 807–818.

    Article  Google Scholar 

  36. Gale, D. and Shapley, L.S. (1962) ‘College Admissions and the Stability of Marriage’, American Mathematical Monthly 69, 9–15.

    Article  Google Scholar 

  37. Gilles, D.B. (1953) ‘Some Theorems on n-person games’ Ph.D. Dissertation, Department of Mathematics, Princeton University, Princeton.

    Google Scholar 

  38. Greenberg, J. and Weber, S. (1986) ‘Strong Tiebout Equilibrium with Restricted Preference Domain’, Journal of Economic Theory 38, 101–117.

    Article  Google Scholar 

  39. Greenberg, J. and Weber, S. (1991) ‘Stable Coalition Structures in Consecutive Games’, York University Discussion Paper.

    Google Scholar 

  40. Gretsky, N., Ostroy, J.M., and Zame, W.R. (1992) ‘The Nonatomic Assignment Model’ Economic Theory 2, 103–128.

    Google Scholar 

  41. Hammond, P. (1992) ‘The Power of Small Coalitions in Large Economies’, to appear in Mathematical Models in Economics, (eds). by Bacharach, M.O.L., Dempster, M.A.H. and Ernos, J.L., Oxford University Press, Oxford.

    Google Scholar 

  42. Hammond, P., Kaneko, M. and Wooders M.H. (1989) ‘Continuum Economies with Finite Coalitions: Core, Equilibria, and Widespread Externalities’, Journal of Economic Theory 49, 113–134.

    Article  Google Scholar 

  43. Hildenbrand, W. (1974) Core and Equilibria of a Large Economy, Princeton University Press, Princeton, New Jersey.

    Google Scholar 

  44. Hildenbrand, W. (1992) Market Demand: Theory and Empirical Evidence,University of Bonn Sonderforschingsbereich 303 Discussion Paper No. A-359.

    Google Scholar 

  45. Hildenbrand, W. and Kirman A. (1974) Introduction to Equilibrium Analysis, North Holland Publishing Co. Amsterdam and Oxford, and American Elsevier Publishing Co. Inc. New York.

    Google Scholar 

  46. Ichiishi, T. (1977) ‘Coalition Structure in a Labor Managed Economy’ Econometrica 45, 341–360.

    Google Scholar 

  47. Ichiishi, T. (1981) ‘A Social Coalitional Equilibrium Existence Lemma’ Econometrica 49, 369–377.

    Google Scholar 

  48. Kaneko, M. (1983) ‘Housing Markets with Indivisibilities’ Journal of Urban Economics 13, 22–50.

    Google Scholar 

  49. Kaneko, M. and Wooders, M.H. (1989) ‘The Core of a Continuum Economy with Widespread Externalities and Finite Coalitions: From Finite to Continuum Economics’, Journal of Economic Theory 49, 135–168.

    Article  Google Scholar 

  50. Kaneko, M. and Wooders, M.H. (1986) ‘The Core of a Game with a Continuum of Players and Finite Coalitions: The Model and some Results’, Mathematical Social Sciences 12, 105–137.

    Article  Google Scholar 

  51. Kaneko, M. and Wooders, M.H. (1984) ‘The Core of a Game with a Continuum of Players and Finite Coalitions; Non-emptiness with Bounded Sizes of Coalitions’, IMA Preprint Series No. 126, Institute of Mathematics and Its Applications, University of Minnesota.

    Google Scholar 

  52. Kaneko, M. and Wooders, M.H. (1982) ‘Cores of Partitioning Games’ Mathematical Social Sciences 3, 313–327.

    Google Scholar 

  53. Khan, M. Ali (1974) ‘Some Remarks on the Core of a “Large” Economy’ Econometrica 42, 633–642.

    Google Scholar 

  54. Koutsougeras, L. and Yannelis, N. (1993) ‘Incentive Compatibility and Information Superiority of the Core of an Economy with Differential Information’, Economic Theory 3, 195–216.

    Article  Google Scholar 

  55. Mas-Colell, A. (1975) ‘A Model of Equilibrium with Differentiated Commodities’ Journal of Mathematical Economics 2, 263–295.

    Google Scholar 

  56. Mas-Colell, A. (1979) ‘A Refinement of the Core Equivalence Theorem’ Economic Letters307–310.

    Google Scholar 

  57. McGuire, M.C. (1991) ‘Group Composition, Collective Consumption, and Collaborative Production’, American Economic Review 81, 1391–1407.

    Google Scholar 

  58. Moldovanu, B. and Winter, E. (1992) ‘Consistent Demands for Coalition Formation’, University of Bonn Sonderforschungsbereich Discussion Paper No B-147 (Revised).

    Google Scholar 

  59. Moulin, M. (1988) Axioms of Cooperative Decision Making, Econometric Society Monograph No. 15, Cambridge Press, Cambridge.

    Book  Google Scholar 

  60. Moulin, H. (1990) ‘Cores and Large Cores When Population Varies’ International Journal of Game Theory 19, 219–232.

    Google Scholar 

  61. Myerson, R.B. (1977) ‘Graphs and Cooperation in Games’ Mathematics of Operations Research 2, 225–229.

    Google Scholar 

  62. von Neumann. J. and Morgenstern, O. (1953) Theory of Games and Economic BehaviorPrinceton University Press, Princeton New Jersey.

    Google Scholar 

  63. Novshek, W. and Sonnenschein, H. (1978) ‘Cournot and Walras Equilibrium’, Journal of Economic Theory 19, 223–266.

    Article  Google Scholar 

  64. Oddou, C. (1982) ‘The Core of a Coalition Production Economy’ Journal of Mathematical Economics 9, 1–21.

    Google Scholar 

  65. Ostroy, J. (1980) ‘The No-Surplus Condition as a Characterization of Perfectly Competitive Equilibrium’, Journal of Economic Theory 222, 65–91.

    Google Scholar 

  66. Ostroy, J. (1984) ‘A Reformulation of the Marginal Productivity Theory of Distribution’, Econometrica 52, 599–630.

    Article  Google Scholar 

  67. Pauly, M. (1970) ‘Cores and Clubs’ Public Choice 9, 53–65.

    Google Scholar 

  68. 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.

    Article  Google Scholar 

  69. Roth, A. and Sotomayer, M. (1990) Two-sided Matching; A Study in Game-theoretic Modeling and AnalysisCambridge University Press, Cambridge.

    Google Scholar 

  70. Samuelson, P. (1954) ‘The Pure Theory of Public Expenditures’ Review of Economics and Statistics 36, 387–389.

    Google Scholar 

  71. Scarf, H. (1967) ‘The Core of an n-person Game’ Econometrica 35, 50–69.

    Google Scholar 

  72. Schweizer, U. (1983) ‘Efficient Exchange with a Variable Number of Consumers’ Econometrica 51, 575–585.

    Google Scholar 

  73. Schotter, A. and Schwödiauer, G. (1980), ‘Economics and Game Theory: A Survey’ Journal of Economic Literature 58, 479–527.

    Google Scholar 

  74. Scotchmer, S. and Wooders, M.H. (1987) ‘Competitive Equilibrium and the Core in Economies with Anonymous Crowding’, Journal of Public Economics 34, 159–174.

    Article  Google Scholar 

  75. Scotchmer, S. and Wooders, M.H. (1988) ‘Monotonicity in Games that Exhaust Gains to Scale’, IMSSS Technical Report No. 525, Stanford University.

    Google Scholar 

  76. Selten, R. (1981) ‘A Non-Cooperative Model of Characteristic Function Bargaining’, in Essays in Game Theory and Mathematical Economic in Honor of O. Morgenstern, V. Böhm, H. Nachtkamp (eds.), Bibliographisches Institut Mannheim, Wein -Zürich.

    Google Scholar 

  77. Shapley, L.S. (1967) ‘On Balanced Sets and Cores’, Navel Research Logistics Quarterly 9, 45–48.

    Article  Google Scholar 

  78. Shapley, L.S. and Shubik, M. (1966) ‘Quasi-Cores in a Monetary Economy with Non-convex Preferences’, Econometrica 34, 805–827.

    Article  Google Scholar 

  79. Shapley, L.S. and Shubik, M. (1969) ‘On Market Games’ Journal of Economic Theory 1, 9–25.

    Google Scholar 

  80. Shapley, L.S. and Shubik, M. (1969) ‘Pure Competition, Coalitional Power, and Fair Division’, International Economic Review 10, 337–362.

    Article  Google Scholar 

  81. Shapley, L.S. and Shubik, M. (1972) ‘The Assignment Game 1; The Core’ International Journal of Game Theory 1, 11–30.

    Google Scholar 

  82. Shapley, L.S. and Shubik, M. (1975) ‘Competitive Outcomes in the Cores of Market Games’, International Journal of Game Theory 4, 229–237.

    Article  Google Scholar 

  83. Sharkey, W.W. and Telser, L.G. (1978) ‘Supportable Cost Functions for the Multiproduct Firm’, Journal of Economic Theory 18, 23–37.

    Article  Google Scholar 

  84. Shubik, M. (1959) ‘Edgeworth Market Games’, in Luce, F.R. and Tucker, A.W. (eds.), Contributions to the Theory of Games IV, Annals of Mathematical Studies 40, Princeton: Princeton University Press, 277–278.

    Google Scholar 

  85. Shubik, M. (1973) ‘Commodity Money, Oligopoly, Credit and Bankruptcy in a General Equilibrium Model’, Western Economic Journal 11, 24–28.

    Google Scholar 

  86. Shubik, M. and Wooders, M.H. (1983) ‘Approximate Cores of Replica Games and Economies: Part I. Replica Games, Externalities, and Approximate Cores’, Mathematical Social Sciences 6, 27–48.

    Article  Google Scholar 

  87. Shubik, M. and Wooders, M.H. (1983) ‘Approximate Cores of Replica Games and Economies: Part II. Set-up Costs and Firm Formation in Coalition Production Economies’, Mathematical Social Sciences 6, 285–306.

    Article  Google Scholar 

  88. Shubik, M. and Wooders, M.H. (1986) ‘Near-Markets and Market-Games’ Economic Studies Quarterly 37, 289–299.

    Google Scholar 

  89. Silva, E.C.D. and Kahn, C.M. (1991) ‘Exclusion and Moral Hazard; the Case of Identical Demand’, Journal of Public Economics, (forthcoming).

    Google Scholar 

  90. Smith, A. (1776) An Inquiry Into the Nature and Causes of the Wealth of NationsLondon: W. Strahan.

    Google Scholar 

  91. Sondermann, D. (1974) ‘Economies of Scale and Equilibria in Coalition Production Economies’, Journal of Economic Theory 8, 259–271.

    Article  Google Scholar 

  92. Stigler, G. (1965) ‘Perfect Competition Historically Contemplated’ in Essays in The History of EconomicsChapter 8, Chicago: University of Chicago Press.

    Google Scholar 

  93. Tauman, Y. (1987) ‘The Aumann-Shapley Prices: A Survey’, in The Shapley Value: Essays in Honor of Lloyd S. Shapley, ed. A. Roth, Cambridge University, Cambridge, MA.

    Google Scholar 

  94. Tiebout, C. (1956) ‘A Pure Theory of Local Expenditures’ Journal of Political Economy 64, 416–424.

    Google Scholar 

  95. Thomson, W. and Lensberg, T. (1989) Axiomatic Theory of Bargaining with a Variable Number of Agents, Cambridge University Press, Cambridge, New York, New Rochelle, Melbourne, and Sydney.

    Book  Google Scholar 

  96. Winter, E. and Wooders, M.H. (1990) ‘On Large Games with Bounded Essential Coalition Sizes’, University of Bonn Sonderforschungsbereich 303 Discussion Paper B-149.

    Google Scholar 

  97. Winter, E. and Wooders, M.H. (1990) ‘An Axiomatization of the Core for Finite and Continuum Games’, Social Choice and Welfare, (to appear).

    Google Scholar 

  98. Wooders M.H. (1978) ‘Equilibria, the Core, and Jurisdiction Structures in Economies with a Local Public Good’, Journal of Economic Theory 18, 328–348.

    Article  Google Scholar 

  99. Wooders, M.H. (1979) ‘A Characterization of Approximate Equilibria and Cores in a Class of Coalition Economies’, (A revision of Stony Brook Department of Economics Working Paper No. 184).

    Google Scholar 

  100. Wooders, M.H. (1979) ‘Asymptotic Cores and Asymptotic Balancedness of Large Replica Games’ (Stony Brook Working Paper No. 215, Revised July 1980).

    Google Scholar 

  101. Wooders, M.H. (1980) ‘The Tiebout Hypothesis: Near Optimality in Local Public Good Economies’, Econometrica 48, 1467–1486.

    Article  Google Scholar 

  102. Wooders, M.H. (1981) ‘A Limit Theorem on the c-Core of an Economy with Public Goods’, National Tax Institute of Japan Paper No. 20.

    Google Scholar 

  103. Wooders, M.H. (1983) ‘The Epsilon Core of a Large Replica Game’, Journal of Mathematical Economics 11, 277–300.

    Article  Google Scholar 

  104. Wooders, M.H. (1988) ‘Stability of Jurisdiction Structures in Economies with a Local Public Good’, Mathematical Social Sciences 15, 24–29.

    Article  Google Scholar 

  105. Wooders, M.H. (1988) ‘Large Games are Market Games 1. Large Finite Games’, C.O.R. E. Discussion Paper No. 8842 (Revised June 1989).

    Google Scholar 

  106. Wooders, M.H. (1989) ‘A Tiebout Theorem’, Mathematical Social Sciences 18, 33–55.

    Article  Google Scholar 

  107. Wooders, M.H. (1991) ‘On Large Games and Competitive Markets 1: Theory’ University of Bonn Sonderforschungsbereich 303 Discussion Paper No. B-195 (Revised August 1992 ).

    Google Scholar 

  108. Wooders, M.H. (1991) ‘On Large Games and Competitive Markets 2: Applications’ University of Bonn Sonderforschungsbereich 303 Discussion Paper No. B-196 (Revised August 1992 ).

    Google Scholar 

  109. Wooders, M.H. (1992) ‘Inessentiality of Large Groups and the Approximate Core Property; An Equivalence Theorem’, Economic Theory 2, 129–147.

    Article  Google Scholar 

  110. Wooders, M.H. (1992) ‘The Attribute Core, Core Convergence, and Small Group Effectiveness; The Effects of Property Rights Assignments on Attribute Games’, to appear in Essays in Honor of Martin Shubik, Dubey, P. and Geanakoplos, J. eds.

    Google Scholar 

  111. Wooders, M.H. (1992) ‘Approximating Games by Markets’, Econometrica (to appear).

    Google Scholar 

  112. Wooders, M.H. (1993) ‘Convergence of the Core to Competitive Outcomes in Economies with Public Goods’, University of Toronto, Department of Economics, Discussion Paper No. 9301.

    Google Scholar 

  113. Wooders, M.H. and Zame, W.R. (1984) ‘Approximate Cores of Large Games’, Econometrica.

    Google Scholar 

  114. Wooders, M.H. and Zame, W.R. (1987) ‘Large Games; Fair and Stable Outcomes’, Journal of Economic Theory 42, 59–93.

    Article  Google Scholar 

  115. Wooders, M.H. and Zame, W.R. (1987) ‘NTU Values of Large Games’, IMSSS Technical Report No. 503.

    Google Scholar 

  116. Wooders, M.H. and Zame, W.R. (1988) ‘Values of Large Finite Games’, in The Shapley Value; Essays in Honor of Lloyd S. Shapley, ed. A. Roth, Cambridge University Press, Cambridge.

    Google Scholar 

  117. Yannelis, N. (1991) ‘The Core of an Economy with Differential Information’, Economic Theory 1, 183–198.

    Article  Google Scholar 

  118. Zajac, E. (1972) ‘Some Preliminary Thoughts on Subsidization’, presented at the Conference on Telecommunications Research, Washington. 7–278.

    Google Scholar 

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  1. Myrna H. Wooders
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Editors and Affiliations

  1. Center for Operations Research & Econometrics, Université Catholique de Louvain, Louvain-la-Neuve, Belgium

    Jean-François Mertens

  2. Ecole Normale Supérieure, Paris, France

    Sylvain Sorin

  3. Université Paris X, Nanterre, France

    Sylvain Sorin

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Wooders, M.H. (1994). Large Games and Economies with Effective Small Groups. In: Mertens, JF., Sorin, S. (eds) Game-Theoretic Methods in General Equilibrium Analysis. NATO ASI Series, vol 77. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1656-7_14

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  • DOI: https://doi.org/10.1007/978-94-017-1656-7_14

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