Chapter 46 Non-cooperative games with many players

Handbook of Game Theory with Economic Applications

Volumn 3, Issue , 2002, Pages 1761-1808

  Khan, M Ali ^a   Sun, Yeneng ^b  

^a JOHNS HOPKINS UNIVERSITY   (United States)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

idiosyncratic shocks; large games; Lebesgue continuum; Loeb continuum; pure strategy Nash equilibria

Indexed keywords

EID: 67649306604     PISSN: 15740005     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1574-0005(02)03009-6     Document Type: Review

References (286)

1. Aiyagari R. Uninsured idiosyncratic risk and aggregate saving. Quarterly Journal of Economics 109 (1994) 659-684
2. Allen B. Randomization and the limit points of monopolistic competition. Journal of Mathematical Economics 23 (1994) 205-218
3. Allen B., and Hellwig M. Price-setting firms and the oligopolistic foundations of perfect competition. American Economic Review 76 (1986) 387-392
4. Allen B., and Hellwig M. Bertrand-Edgeworth oligopoly in large markets. Review of Economic Studies 53 (1986) 175-204
5. Allen B., and Hellwig M. The approximation of competitive equilibria by Bertrand-Edgeworth equilibria in large markets. Journal of Mathematical Economics 16 (1989) 387-392
6. Anderson R.M. A nonstandard representation for Brownian motion and Ito integration. Israel Journal of Mathematics 25 (1976) 15-46
7. Anderson R.M. Non-standard analysis with applications to economics. In: Hildenbrand W., and Sonnenschein H. (Eds). Handbook of Mathematical Economics Vol. 4 (1991), North-Holland, New York
8. Chapter 14. Anderson R.M. The core in perfectly competitive economies. In: Aumann R.J., and Hart S. (Eds). Handbook of Game Theory Vol. 1 (1994), North-Holland, New York 413-458
9. Arrow K.J., and Debreu G. Existence of an equilibrium for a competitive economy. Econometrica 22 (1954) 265-290
10. Arrow K.J., and Radner R. Allocation of resources in large teams. Econometrica 47 (1979) 361-392
11. Artstein Z. A note on Fatou's lemma in several dimensions. Journal of Mathematical Economics 6 (1979) 277-282
12. Artstein Z. Distributions of random sets and random selections. Israel Journal of Mathematics 46 (1983) 313-324
13. Artstein Z., and Hart S. Law of large numbers for random sets and allocation processes. Mathematics of Operations Research 6 (1981) 485-492
14. Artstein Z., and Prikry K. Caratheodory selections and the Scorza-Dragoni property. Journal of Mathematical Analysis and Applications 127 (1987) 540-547
15. Ash R.B. Real Analysis and Probability (1972), Academic Press, Amsterdam
16. Aumann R.J. Markets with a continuum of traders. Econometrica 32 (1964) 39-50
17. Aumann R.J. Integrals of set-valued functions. Journal of Mathematical Analysis and Applications 12 (1965) 1-12
18. Aumann R.J. Existence of competitive equilibria in markets with a continuum of traders. Econometrica 34 (1966) 1-17
19. Aumann R.J. An elementary proof that integration preserves uppersemicontinuity. Journal of Mathematical Economics 3 (1976) 15-18
20. Aumann R.J. Game theory. In: Eatwell J., Milgate M., and Newman P.K. (Eds). The New Palgrave (1987), The Macmillan Press, New York 460-482
21. Aumann R.J. Rationality and bounded rationality. Games and Economic Behavior 21 (1997) 2-14
22. Chapter 43. Aumann R.J., and Heifetz A. Incomplete information. In: Aumann R.J., and Hart S. (Eds). Handbook of Game Theory Vol. 3 (2002), North-Holland, London 1665-1686
23. Aumann R.J., Katznelson Y., Radner R., Rosenthal R.W., and Weiss B. Approximate purification of mixed strategies. Mathematics of Operations Research 8 (1983) 327-341
24. Balder E.J. On Cournot-Nash equilibrium distributions for games with differential information and discontinuous payoffs. Economic Theory 1 (1991) 339-354
25. Balder E.J. A unifying approach to Nash equilibria. International Journal of Game Theory 24 (1995) 79-94
26. to appear. Balder E.J. Lectures on Young measures. Cahiers de Mathématiques de la Décision (1995), CEREMADE, Amsterdam
27. Balder E.J. Comments on the existence of equilibrium distributions. Journal of Mathematical Economics 25 (1996) 307-323
28. Balder E.J. Remarks on Nash equilibria for games with additively coupled payoffs. Economic Theory 9 (1997) 161-167
29. Balder E.J. On the existence of Cournot-Nash equilibria in continuum games. Journal of Mathematical Economics 32 (1999) 207-223
30. Balder E.J. Young measure techniques for existence of Cournot-Nash-Walras equilibria. In: Wooders M.H. (Ed). Topics in Mathematical Economics and Game Theory: Essays in honor of R.J. Aumann (1999), American Mathematical Society 31-39
31. Balder E.J. Incompatibility of usual conditions for equilibrium existence in continuum economies without ordered preferences. Journal of Economic Theory 93 (2000) 110-117
32. Balder E.J., and Rustichini A. An equilibrium result for games with private information and infinitely many players. Journal of Economic Theory 62 (1994) 385-393
33. (1991). Balder E.J., and Yannelis N.C. Equilibria in random and Bayesian games with a continuum of players. In: Khan M.A., and Yannelis (Eds) (1991)
34. mimeo. Barut Y. Existence and computation of a stationary equilibrium in a heterogeneous agent, dynamic economic model with incomplete markets (2000), Rice University, Providence
35. Başçi E., and Sertel M. Prakash and Sertel's theory of non-cooperative equilibria in social systems - twenty years later. Journal of Mathematical Economics 25 (1996) 1-18
36. Berge C. Topological Spaces (1959), Oliver and Boyd
37. Bergin J., and Bernhardt D. Anonymous sequential games with aggregate uncertainty. Journal of Mathematical Economics 21 (1992) 543-562
38. Bewley T.F. The equality of the core and the set of equilibria in economies with infinitely many commodities and a continuum of agents. International Economic Review 14 (1973) 383-393
39. Billingsley P. Convergence of Probability Measures (1968), Wiley, London
40. Bollobás B., and Varopoulos N.Th. Representation of systems of measurable sets. Mathematical Proceedings of the Cambridge Philosophical Society 78 (1974) 323-325
41. Chapter 30. Brams S.J. Voting procedures. In: Aumann R.J., and Hart S. (Eds). Handbook of Game Theory Vol. 2 (1994), North-Holland, New York 1055-1090
42. Castaing C., and Valadier M. Convex Analysis and Measurable Multifunctions. Lecture Notes in Mathematics Vol. 580 (1977), Springer-Verlag, Amsterdam
43. mimeo. Chakrabarti S.K. Pure strategy Markov equilibria in stochastic games with a continuum of players (2000), IUPUI, Berlin
44. Chakrabarti S.K., and Khan M.A. Equilibria of large games with imperfect observability. In: Aliprantis C.D., Border K.C., and Luxemburg W.A.J. (Eds). Positive Operators, Reisz Spaces and Economics (1991), Springer-Verlag
45. Chamberlin E. The Theory of Monopolistic Competition (1933), Harvard University Press, Berlin
46. Chamberlin E. Monopolistic or imperfect competition. Quarterly Journal of Economics LI (1937) 557
47. Champsaur P., and Laroque G. A note on incentives in large economies. Review of Economic Studies 49 (1982) 627-635
48. Chipman J.S. External economies of scale and competitive equilibrium. Quarterly Journal of Economics 84 (1970) 347-385
49. Constantinides G.M., and Rosenthal R.W. Strategic analysis of the competitive exercise of certain financial options. Journal of Economic Theory 32 (1984) 128-138
50. Cordoba J.M., and Hammond P.J. Asymptotically Walrasian strategy-proof exchange. Mathematical Social Sciences 36 (1998) 185-212
51. Also translation by N. Bacon (1897) (Macmillan, New York). Cournot A. Recherches sur les Principles Mathématiques de la Théorie des Richesses (1838), Librairie des Sciences Politiques et Sociales, Cambridge
52. Cutland N. Nonstandard measure theory and its applications. Bulletin of the London Mathematical Society 15 (1983) 529-589
53. In: Cutland N. (Ed). Nonstandard Analysis and its Applications (1988), Cambridge University Press, Paris
54. Dasgupta P., and Hammond P. Fully progressive taxation. Journal of Public Economics 13 (1980) 141-154
55. Debreu G. A social equilibrium existence theorem. Proceedings of the National Academy of Sciences U.S.A. 38 (1952) 386-393
56. Part 1. Debreu G. Integration of correspondences. Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability 2 (1967), University of California Press, New York 351-372
57. Dierker E., and Haller H. Tax systems and direct mechanisms in large finite economies. Journal of Economics 52 (1990) 99-116
58. Diestel J. Sequences and Series in Banach Spaces (1984), Springer-Verlag, Berkeley
59. Diestel J., and Uhl Jr. J.J. Vector Measures (1977), American Mathematical Society, Berlin
60. p-spaces. In: Tucker D.H., and Maynard H.B. (Eds). Vector and Operator Valued Measures and Applications (1973), Academic Press, Providence
61. Doob J.L. Stochastic processes depending on a continuous parameter. Transactions of the American Mathematical Society 42 (1937) 107-140
62. Doob J.L. Stochastic Processes (1953), Wiley, New York
63. Dubey P., Mas-Colell A., and Shubik M. Efficiency properties of strategic market games: an axiomatic approach. Journal of Economic Theory 22 (1980) 339-362
64. Dubey P., and Shapley L.S. Noncooperative exchange with a continuum of traders. Cowles Foundation Discussion Paper No. 447 (1977)
65. Dubey P., and Shapley L.S. Noncooperative general exchange with a continuum of traders: two models. Journal of Mathematical Economics 23 (1994) 253-293
66. Dvoretsky A., Wald A., and Wolfowitz J. Elimination of randomization in certain problems of statistics and of the theory of games. Proceedings of the National Academy of Sciences U.S.A. 36 (1950) 256-260
67. Dvoretsky A., Wald A., and Wolfowitz J. Elimination of randomization in certain statistical decision problems in certain statistical decision procedures and zero-sum two-person games. Annals of Mathematical Statistics 22 (1951) 1-21
68. Dvoretsky A., Wald A., and Wolfowitz J. Relations among certain ranges of vector measures. Pacific Journal of Mathematics 1 (1951) 59-74
69. Edgeworth F.Y. Mathematical Psychics (1881), Kegan Paul, New York
70. Fan K. Fixed points and minimax theorems in locally convex linear spaces. Proceedings of the National Academy of Sciences U.S.A. 38 (1952) 121-126
71. Fan K. Applications of a theorem concerning sets with convex sections. Mathematische Annalen 163 (1966) 189-203
72. Feldman M., and Gilles C. An expository note on individual risk without aggregate uncertainty. Journal of Economic Theory 35 (1985) 26-32
73. Fudenberg D., Levine D.K., and Pesendorfer W. When are non-anonymous players negligible. Journal of Economic Theory 79 (1998) 46-71
74. Fudenberg D., and Tirole J. Game Theory (1991), MIT Press, London
75. Gabszewicz J.J., and Vial J.P. Oligopoly á la Cournot in general equilibrium analysis. Journal of Economic Theory 4 (1972) 381-400
76. Gale D. Large economies with trading uncertainty. Review of Economic Studies 46 (1979) 319-338
77. A correction. Review of Economic Studies 48 (1980) 363-364
78. Glicksberg I. A further generalization of Kakutani's fixed point theorem with application to Nash equilibrium points. Proceedings of the American Mathematical Society 3 (1952) 170-174
79. Green E.J. Continuum and finite player non-cooperative models of competition. Econometrica 52 (1984) 975-993
80. Gresik T., and Satterthwaite M. The rate at which a simple market converges to efficiency as the number of traders increases: an asymptotic result for optimal trading mechanisms. Journal of Economic Theory 48 (1989) 304-322
81. Sonderforschungsberech 21. Guesnerie R. On taxation and incentives: further reflections on the limits of redistribution. Discussion Paper No. 89 (1981), University of Bonn, Cambridge
82. Guesnerie R. A Contribution to the Pure Theory of Taxation (1995), Cambridge University Press
83. Gul F., and Postlewaite A. Asymptotic efficiency in large exchange economies with asymmetric information. Econometrica 60 (1992) 1273-1292
84. mimeo. Haller H. Equilibria of a class of nonatomic generalized games (1988), Virginia Polytechnic Institute, Cambridge
85. Haller H. Competition in a stock market with small firms. Journal of Economics 3 (1988) 243-261
86. Halmos P.R., and Vaughan H.E. The marriage problem. American Journal of Mathematics 72 (1950) 214-215
87. Chapter 28. Hammerstein P., and Selten R. Game theory and evolutionary biology. In: Aumann R.J., and Hart S. (Eds). Handbook of Game Theory Vol. 2 (1994), North-Holland 929-994
88. Hammond P.J. Symposium on incentive compatibility: introduction. Review of Economic Studies 46 (1979) 181-184
89. Hammond P.J. Straightforward individual incentive compatibility in large economies. Review of Economic Studies 46 (1979) 263-282
90. Hammond P.J. Markets as constraints: multilateral incentive compatibility. Review of Economic Studies 54 (1987) 399-412
91. Hammond P.J. Four characterizations of constrained Pareto efficiency in continuum economies with widespread externalities. Japanese Economic Review 46 (1995) 103-124
92. Chapter 11. Hammond P.J. Rights, free exchange, and widespread externalities. In: Laslier J.-F., Fleurbaey M., Gravel N., and Trannoy A. (Eds). Freedom in Economics: New Perspectives in Normative Analysis (1998), Routledge, Amsterdam 139-157
93. Chapter 16. Hammond P.J. History as a widespread externality in some Arrow-Debreu market games. In: Chichilnisky G. (Ed). Markets, Information and Uncertainty: Essays in Economic Theory in Honor of Kenneth J. Arrow (1999), Cambridge University Press, London and New York 328-361
94. Hammond P.J., and Sun Y.N. Joint measurability and the one-way Fubini property for a continuum of independent variables. Working Paper No. 00-008 (2000), Department of Economics, Stanford University, Cambridge
95. Part I. Harsanyi J.C. Games with incomplete information played by Bayesian players. Management Science 14 (1967-1968) 159-183
96. Part II. Harsanyi J.C. Games with incomplete information played by Bayesian players. Management Science 14 (1967-1968) 320-334
97. Part III. Harsanyi J.C. Games with incomplete information played by Bayesian players. Management Science 14 (1967-1968) 486-502
98. Harsanyi J.C. Games with randomly disturbed payoffs. International Journal of Game Theory 2 (1973) 1-23
99. Hart O. Monopolistic competition in a large economy with differentiated commodities. Review of Economic Studies 46 (1979) 1-30
100. A correction. Review of Economic Studies 49 (1982) 313-314
101. Hart O. On stockholder unanimity in large stock market economies. Econometrica 47 (1979) 1057-1083
102. Hart O. Perfect competition and optimal product differentiation. Journal of Economic Theory 22 (1980) 279-312
103. Hart O. A model of imperfect competition with Keynesian features. Quarterly Journal of Economics 97 (1982) 109-138
104. Hart O. Imperfect competition in general equilibrium: an overview of recent work. In: Arrow K.J., and Honkapohja S. (Eds). Frontiers of Economics (1984), Blackwell
105. Hart O. Monopolistic competition in the spirit of Chamberlin: a general model. Review of Economic Studies 52 (1985) 529-546
106. Hart O. Monopolistic competition in the spirit of Chamberlin: special results. Economic Journal 95 (1985) 889-908
107. Hart S., Hildenbrand W., and Kohlberg E. On equilibrium allocations as distributions on the commodity space. Journal of Mathematical Economics 1 (1974) 159-166
108. Hart S., and Kohlberg E. Equally distributed correspondences. Journal of Mathematical Economics 1 (1974) 167-174
109. Hart S., and Schmeidler D. Existence of correlated equilibria. Mathematics of Operations Research 14 (1989) 18-25
110. Hervés-Beloso C., Moreno-Garcia E., and Pascoa M.R. Manipulation-proof equilibrium in atomless economies with commodity differentiation. Economic Theory 14 (1999) 545-563
111. Hiai F., and Umegaki H. Integrals, conditional expectations and martingales of multivalued functions. Journal of Multivariate Analysis 7 (1977) 167-174
112. Hildenbrand W. Core and Equilibria of a Large Economy (1974), Princeton University Press, Oxford
113. Hildenbrand W. Distributions of agents' characteristics. Journal of Mathematical Economics 2 (1975) 129-138
114. mimeo. Housman D. Equilibria in nonatomic strategic form games (1987), Worcester Polytechnique Institute, Princeton
115. Housman D. Infinite player noncooperative games and the continuity of the Nash equilibrium correspondence. Mathematics of Operations Research 13 (1988) 488-496
116. Hurd A.E., and Loeb P.A. An Introduction to Nonstandard Real Analysis (1985), Academic Press
117. Hurwicz L. On informationally decentralized systems. In: McGuire C.B., and Radner R. (Eds). Decision and Organization (1972), North-Holland, Orlando
118. Jamison R.E. A quick proof for a one-dimensional version of Liapunov's theorem. American Mathematical Monthly 81 (1974) 507-508
119. Jaynes G., Okuno M., and Schmeidler D. Efficiency in an atomless economy with fiat money. International Economic Review 19 (1978) 149-157
120. Jovanovic B., and Rosenthal R.W. Anonymous sequential games. Journal of Mathematical Economics 17 (1988) 77-87
121. Judd K.L. The law of large numbers with a continuum of iid random variables. Journal of Economic Theory 35 (1985) 19-25
122. Kaneko M., and Wooders M.H. The core of a game with a continuum of players and finite coalitions: the model and some results. Mathematical Social Sciences 12 (1986) 105-137
123. Kaneko M., and Wooders M.H. The core of a continuum economy with widespread externalities and finite coalitions: from finite to continuum economies. Journal of Economic Theory 49 (1989) 135-168
124. Kaneko M., and Wooders M.H. Widespread externalities and perfectly competitive markets: examples. In: Gilles R.P., and Ruys P.H.M. (Eds). Imperfections and Behavior in Economic Organizations (1994), Kluwer Academic, Amsterdam
125. Kannai Y. Continuity properties of the core of a market. Econometrica 38 (1970) 791-815
126. Karni E., and Levin D. Social attributes and strategic equilibrium: a restaurant pricing game. Journal of Political Economy 102 (1994) 822-840
127. Karni E., and Schmeidler D. Fixed preferences and changing tastes. American Economic Review 80 (1990) 262-267
128. Keisler H.J. Hyperfinite model theory. In: Gandy R.O., and Hyland J.M.E. (Eds). Logic Colloquium 76 (1977), North-Holland, Boston
129. Keisler H.J. An infinitesimal approach to stochastic analysis. Memoirs of the American Mathematical Society 48 (1984) 1-184
130. (1988). Keisler H.J. Infinitesimals in probability theory. Cutland (1988)
131. Kelsey D., and Milne F. The existence of equilibrium in incomplete markets and the objective function of the firm. Journal of Mathematical Economics 25 (1996) 229-246
132. Khan M.A. An alternative proof of Diestel's theorem. Glasgow Math. Journal 25 (1984) 45-46
133. Khan M.A. On the integration of set-valued mappings in a non-reflexive Banach space. Simon Stevin 59 (1985) 257-267
134. Khan M.A. Equilibrium points of non-atomic games over a non-reflexive Banach space. Journal of Approximation Theory 43 (1985) 370-376
135. Khan M.A. Equilibrium points of nonatomic games over a Banach space. Transactions of the American Mathematical Society 293 (1986) 737-749
136. Khan M.A. On the extensions of the Cournot-Nash theorem. In: Aliprantis C.D., Burkinshaw O.L., and Rothman N. (Eds). Advances in Equilibrium Theory (1986), Springer-Verlag, Amsterdam
137. Khan M.A. On Cournot-Nash equilibrium distributions for games with a nonmetrizable action space and upper semicontinuous payoffs. Transactions of the American Mathematical Society 315 (1989) 127-146
138. Khan M.A. A result on large anonymous games: an elementary and self-contained exposition. In: Moore J., Reizman R., and Melvin J. (Eds). Trade, Theory, and Econometrics: Essays in Honour of John S. Chipman (1998), Routledge, Berlin 206-236
139. 1(μ, X) and an approximate version of Fatou's lemma. Journal of Mathematical Analysis and Applications 114 (1986) 569-573
140. Khan M.A., and Papageorgiou N. On Cournot-Nash equilibrium in generalized qulitative games with a continuum of players. Nonlinear Analysis 11 (1987) 741-755
141. Khan M.A., and Papageorgiou N. On Cournot-Nash equilibrium in generalized qualitative games with an atomless measure space of players. Proceedings of the American Mathematical Society 100 (1987) 505-510
142. Khan M.A., Rath K.P., and Sun Y.N. On the existence of pure strategy equilibria in games with a continuum of players. Journal of Economic Theory 76 (1997) 13-46
143. Khan M.A., Rath K.P., and Sun Y.N. Pure-strategy Nash equilibrium points in large non-anonymous games. In: Dutta B., Parthasarathy T., Potters J., Raghavan T.E.S., Ray D., and Sen A. (Eds). Game Theoretical Applications to Economics and Operations Research (1997), Kluwer Academic, New York
144. Khan M.A., Rath K.P., and Sun Y.N. On private information games without pure strategy equilibria. Journal of Mathematical Economics 31 (1999) 341-359
145. No. 252. Khan M.A., and Rustichini A. Differential information and a reformulation of Cournot-Nash equilibria. In: Théra M.A., and Baillon J.B. (Eds). Fixed Point Theory and Applications. Pitman Research Notes in Mathematics (1991), Longman, Amsterdam
146. Khan M.A., and Rustichini A. On Cournot-Nash equilibrium distributions for games with uncertainty and imperfect information. Journal of Mathematical Economics 22 (1993) 35-59
147. Khan M.A., and Sun Y.N. On symmetric Cournot-Nash equilibrium distributions in a finite-action, atomless game. In: Ali Khan M., and Yannelis (Eds) (1987-1991)
148. Khan M.A., and Sun Y.N. On a reformulation of Cournot-Nash equilibria. Journal of Mathematical Analysis and Applications 146 (1990) 442-460
149. (in Japanese). English original in: T. Maruyama and W. Takahashi, eds., Nonlinear and Convex Analysis in Economic Theory (Springer-Verlag, Berlin). Khan M.A., and Sun Y.N. On large games with finite actions: a synthetic treatment. Mita Journal of Economics 87 (1994) 73-84
150. Khan M.A., and Sun Y.N. Extremal structures and symmetric equilibria with countable actions. Journal of Mathematical Economics 24 (1995) 239-248
151. Khan M.A., and Sun Y.N. Pure strategies in games with private information. Journal of Mathematical Economics 24 (1995) 633-653
152. Khan M.A., and Sun Y.N. The marriage lemma and large anonymous games with countable actions. Mathematical Proceedings of the Cambridge Philosophical Society 117 (1995) 385-387
153. Khan M.A., and Sun Y.N. On integrals of set-valued functions with a countable range. Mathematics of Operations Research 21 (1996) 946-954
154. Khan M.A., and Sun Y.N. Nonatomic games on Loeb spaces. Proceedings of the National Academy of Sciences U.S.A. 93 (1996) 15518-15521
155. Khan M.A., and Sun Y.N. On Loeb measure spaces and their significance for non-cooperative game theory. In: Albers M., Hu B., and Rosenthal J. (Eds). Current and Future Directions in Applied Mathematics (1997), Birkhäuser, London 183-218
156. Khan M.A., and Sun Y.N. Non-cooperative games on hyperfinite Loeb spaces. Journal of Mathematical Economics 31 (1999) 455-492
157. Khan M.A., and Vohra R. Equilibrium in abstract economies without ordered preferences and with a measure space of agents. Journal of Mathematical Economics 13 (1984) 133-142
158. Khan M.A., and Vohra R. On the existence of Lindahl equilibria in economies with a measure space of non-transitive consumers. Journal of Economic Theory 36 (1985) 319-332
159. In: Khan M.A., and Yannelis N.C. (Eds). Equilibrium Theory in Infinite Dimensional Spaces (1991), Springer-Verlag, Berlin
160. Kihlstrom R.E., and Laffont J.J. A general equilibrium entrepreneural theory of firm foundation based on risk aversion. Journal of Political Economy 87 (1979) 719-748
161. Kihlstrom R.E., and Laffont J.J. A competitive entrepreneural model of a stock market. In: McCall J.J. (Ed). The Economics of Information and Uncertainty (1982), The University of Chicago Press, Berlin
162. Kim S.H. Continuous Nash equilibria. Journal of Mathematical Economics 28 (1997) 69-84
163. Kim T., Prikry K., and Yannelis N.C. Carathéodory-type selections and random fixed point theorems. Journal of Mathematical Analysis and Applications 122 (1987) 393-407
164. Kim T., Prikry K., and Yannelis N.C. On a Carathéodory-type selection theorem. Journal of Mathematical Analysis and Applications 135 (1988) 664-670
165. Kim T., Prikry K., and Yannelis N.C. Equilibrium in abstract economies with a measure space and with an infinite dimensional strategy space. Journal of Approximation Theory 56 (1989) 256-266
166. Kim T., and Yannelis N.C. Existence of equilibrium in Bayesian games with infinitely many players. Journal of Economic Theory 77 (1997) 330-353
167. In: Kuhn H.W., and Tucker A.W. (Eds). Contributions to the Theory of Games, Vol. 1. Annals of Mathematics Studies (1950), Princeton University Press, Chicago
168. Kumar K., and Satterthwaite M. Monopolistic competition, aggregation of competitive information and the amount of product differentiation. Journal of Economic Theory 37 (1985) 32-54
169. Levine D.K., and Pesendorfer W. When are agents negligible?. American Economic Review 85 (1995) 1160-1170
170. (1988). Lindstrom T. An invitation to nonstandard analysis. Cutland (1988)
171. Loeb P.A. Conversion from nonstandard to standard measure spaces and applications in probability theory. Transactions of the American Mathematical Society 211 (1975) 113-122
172. Loeb P.A., and Rashid S. Lyapunov's theorem. In: Eatwell J., Milgate M., and Newman P.K. (Eds). The New Palgrave (1987), The Macmillan Press, Princeton
173. Loéve M. Probability Theory. 4th edn. Vols. I & II (1977), Springer-Verlag, London
174. Lucas Jr. R.E. On the size distribution of business firms. Bell Journal of Economics 9 (1978) 508-523
175. Lucas Jr. R.E., and Prescott E.C. Equilibrium search and unemployment. Journal of Economic Theory 7 (1974) 188-209
176. Lyapunov A. Sur les fonctions-vecteurs complètements additives. Bulletin Academic Sciences URSS Sér. Math. 4 (1940) 465-478
177. Ma T.W. On sets with convex sections. Journal of Mathematical Analysis and Applications 27 (1969) 413-416
178. Mailath G., and Postlewaite A. Asymmetric information bargaining problems with many agents. Review of Economic Studies 57 (1990) 351-368
179. Makowski L., and Ostroy J. The Vickrey-Clarke-Groves mechanism and perfect competition. Journal of Economic Theory 42 (1987) 244-261
180. Makowski L., and Ostroy J. The Vickrey-Clarke-Groves mechanism in continuum economies: characterization and existence. Journal of Mathematical Economics 21 (1992) 1-35
181. Mas-Colell A. Efficiency of non-cooperative equilibrium in economies with a continuum of traders. In: Ali Khan M., and Yannelis N.C. (Eds) (1978-1991)
182. Mas-Colell A. Non-cooperative approaches to the theory of perfect competition. Journal of Economic Theory 22 (1980) 121-135
183. Mas-Colell A. Perfect competition and the core. Review of Economic Studies 69 (1982) 15-30
184. Mas-Colell A. Cournotian foundations of Walrasian equilibrium theory. In: Hildenbrand W. (Ed). Advances in Economic Theory (1982), Cambridge University Press, New York
185. Mas-Colell A. Walrasian equilibria as limits of nonooperative equilibria, Part I: Mixed strategies. Journal of Economic Theory 30 (1983) 153-170
186. Mas-Colell A. On a theorem of Schmeidler. Journal of Mathematical Economics 13 (1984) 206-210
187. Mas-Colell A. The profit motive in the theory of monopolistic competition. Journal of Economics, Supplementum 4 (1984) 111-116
188. Mas-Colell A. On the second welfare theorem for anonymous net trades in exchange economies with many agents. In: Groves T., Radner R., and Reiter S. (Eds). Information, Incentives and Economic Mechanisms (1987), University of Minnesota Press, Cambridge
189. Mas-Colell A. On the theory of perfect competition. In: Jacobs D.P., Kalai E., and Kamien M.I. (Eds). Frontiers of Research in Economic Theory: The Nancy L. Schwartz Memorial Lectures, 1983-1997 (1998), Cambridge University Press, Minneapolis
190. Mas-Colell A., and Vives X. Implementation in economies with a continuum of agents. Review of Economic Studies 60 (1993) 613-630
191. Massó J. Undiscounted equilibrium payoffs of repeated games with a continuum of players. Journal of Mathematical Economics 22 (1993) 243-264
192. Massó J., and Rosenthal R.W. More on the 'anti-folk theorem'. Journal of Mathematical Economics 18 (1989) 281-290
193. McKenzie L.W. Competitive equilibrium with dependent consumer preferences. In: Antosiewicz H.A. (Ed). Proceedings of the Second Symposium in Linear Programming (1955) 277-294
194. Chapter 27. McMillan J., and Rothschild M. Search. In: Aumann R.J., and Hart S. (Eds). Handbook of Game Theory Vol. 2 (1994), North-Holland, Cambridge 905-928
195. Milgrom P.R., and Weber R.J. Topologies on information and strategies in games with incomplete information. In: Moeschlin O., and Pallashke D. (Eds). Game Theory and Mathematical Economics (1981), North-Holland, Amsterdam
196. Milgrom P.R., and Weber R.J. Distributional strategies for games with incomplete information. Mathematics of Operations Research 10 (1985) 619-632
197. Milnor J.W., and Shapley L.S. Values of large games, II: oceanic games. Mathematics of Operations Research 3 (1978) 290-307
198. Mirrlees J.A. An exploration in the theory of optimum income taxation. Review of Economics Studies 38 (1971) 175-208
199. Chapter 24. Myerson R.B. Communication, correlated equilibria and incentive compatibility. In: Aumann R.J., and Hart S. (Eds). Handbook of Game Theory Vol. 2 (1994), North-Holland, Amsterdam 827-848
200. Nash J.F. Equilibrium points in N-person games. Proceedings of the National Academy of Sciences U.S.A. 36 (1950) 48-49
201. Nash J.F. Noncooperative games. Annals of Mathematics 54 (1951) 286-295
202. Novshek W. Cournot equilibrium and free entry. Review of Economic Studies 47 (1980) 473-486
203. Novshek W., and Sonnenschein H. Cournot and Walras equilibrium. Journal of Economic Theory 19 (1978) 223-266
204. Novshek W., and Sonnenschein H. Small efficient scale as a foundation for Walrasian equilibrium. Journal of Economic Theory 22 (1980) 243-256
205. Novshek W., and Sonnenschein H. Walrasian equilibria as limits of noncooperative equilibria, Part II: Pure strategies. Journal of Economic Theory 30 (1983) 171-187
206. Nti K. Capital asset prices in an oligopolistic market. Journal of Economics 48 (1988) 35-57
207. Chapter 29. O'Neil B. Game theory models of peace and war. In: Aumann R.J., and Hart S. (Eds). Handbook of Game Theory Vol. 2 (1994), North-Holland, Amsterdam 995-1054
208. Palfrey T., and Srivastava S. Private information in large economies. Journal of Economic Theory 39 (1986) 34-58
209. Papageorgiou N.S. Representation of set-valued operators. Transactions of the American Mathematical Society 292 (1985) 557-572
210. Papageorgiou N.S. Contributions to the theory of set-valued functions and set-valued measures. Transactions of the American Mathematical Society 304 (1987) 245-265
211. Papageorgiou N.S. On a paper by Khan and Majumdar. Journal of Mathematical Analysis and Applications 150 (1990) 574-578
212. Parthasarathy K.R. Probability Measures on Metric Spaces (1967), Academic Press, Amsterdam
213. Pascoa M.R. Approximate purification of Nash equilibrium in nonatomic games. CARESS Working Paper No. 88-21 (1988), University of Pennsylvania, New York
214. Pascoa M.R. Noncooperative equilibrium and Chamberlinian monopolistic competition. Journal of Economic Theory 60 (1993) 335-353
215. Pascoa M.R. Approximate equilibrium in pure strategies for non-atomic games. Journal of Mathematical Economics 22 (1993) 223-241
216. Pascoa M.R. Monopolistic competition and non-neighboring goods. Economic Theory 9 (1997) 129-142
217. Pascoa M.R. Nash equilibrium and the law of larger numbers. International Journal of Game Theory 27 (1998) 83-92
218. Peleg B. Equilibrium points for games with infinitely many players. Journal of the London Mathematical Society 44 (1969) 292-294
219. Postlewaite A.W., and Schmeidler D. Approximate efficiency of non-Walrasian Nash equilibria. Econometrica 40 (1978) 127-135
220. Prakash P., and Sertel M.R. Existence of non-cooperative equilibria in social systems. Journal of Mathematical Economics 25 (1996) 19-32
221. Radner R., and Rosenthal R.W. Private information and pure-strategy equilibria. Mathematics of Operations Research 7 (1982) 401-409
222. Rashid S. Equilibrium points of non-atomic games: asymptotic results. Economics Letters 12 (1983) 7-10
223. Rashid S. The approximate purification of mixed strategies with finite observation sets. Economics Letters 19 (1985) 133-135
224. Rashid S. Economies with Many Agents (1987), The Johns Hopkins University Press
225. Rashid S. A direct proof of purification for Schmeidler's theorem. Applied Mathematics Letters 5 (1992) 23-24
226. Rath K.P. A direct proof of the existence of pure strategy equilibria in games with a continuum of players. Economic Theory 2 (1992) 427-433
227. Rath K.P. Some refinements of Nash equilibria of large games. Games and Economic Behavior 7 (1994) 92-103
228. Rath K.P. Representation of finite action large games. International Journal of Game Theory 24 (1995) 23-35
229. Rath K.P. On the representation of sets in finite measure spaces. Journal of Mathematical Analysis and Applications 200 (1996) 506-510
230. Rath K.P. Existence and upper hemicontinuity of equilibrium distributions of anonymous games with discontinuous payoffs. Journal of Mathematical Economics 26 (1996) 305-324
231. Rath K.P. Perfect and proper equilibria of large games. Games and Economic Behavior 22 (1998) 331-342
232. Rath K.P., Sun Y.N., and Yamashige S. The nonexistence of symmetric equilibria in anonymous games with compact action spaces. Journal of Mathematical Economics 24 (1995) 331-346
233. Rauh M.T. A model of temporary search market equilibrium. Journal of Economic Theory 77 (1997) 128-153
234. Rauh M.T. Heterogeneous beliefs, price dispersion and welfare-improving price controls. Economic Theory 18 (2001) 577-603
235. Rob R. Entry, fixed costs and the aggregation of private information. Review of Economic Studies 54 (1987) 619-630
236. Roberts D.J. The incentives for correct revelation of preferences and the number of consumers. Journal of Public Economics 6 (1976) 359-374
237. Roberts D.J. Large economies" and "Perfectly and imperfectly competitive market. In: Eatwell J., Milgate M., and Newman P.K. (Eds). The New Palgrave (1987), The Macmillan Press, Baltimore
238. Roberts D.J., and Postlewaite A. The incentives for price-taking behavior in large exchange economies. Econometrica 44 (1976) 115-127
239. Roberts K. The limit points of monopolistic competition. Journal of Economic Theory 22 (1980) 256-278
240. Roberts K. The theoretical limits to redistribution. Review of Economic Studies 51 (1984) 177-186
241. Robinson J. Economics of Imperfect Competition (1933), Macmillan, London
242. Royden H.L. Real Analysis (1968), Macmillan, London
243. Rudin W. Functional Analysis (1973), McGraw-Hill, New York
244. Rudin W. Real and Complex Analysis (1974), McGraw-Hill, New York
245. Rustichini A. A counterexample and an exact version of Fatou's lemma in infinite dimensions. Archiv der Mathematik 52 (1989) 357-362
246. Rustichini A. Mixing on function spaces. Economic Theory 3 (1993) 183-190
247. Rustichini A., Satterthwaite M.A., and Williams S.R. Convergence to efficiency in a simple market with incomplete information. Econometrica 62 (1994) 1041-1063
248. (1991). Rustichini A., and Yannelis N.C. What is perfect competition?. In: Ali Khan M., and Yannelis N.C. (Eds) (1991)
249. Samuelson P.A. The pure theory of public expenditure. Review of Economics and Statistics 36 (1954) 387-389
250. Samuelson P.A. The monopolistic competition revolution. In: Kuenne R.E. (Ed). Monopolistic Competition Theory: Studies in Impact (1967), Wiley, New York
251. Satterthwaite M., and Williams S. The rate of convergence to efficiency in the buyer's bid double auction as the market becomes large. Review of Economic Studies 56 (1989) 477-498
252. Schmeidler D. Equilibrium points of non-atomic games. Journal of Statistical Physics 7 (1973) 295-300
253. Chapter 21. Schwarz G. Game theory and statistics. In: Aumann R.J., and Hart S. (Eds). Handbook of Game Theory Vol. 2 (1994), North-Holland, New York 769-779
254. Seccia G., and Rauh M. Mean-variance analysis in temporary equilibrium. Research in Economics 55 (2001) 331-345
255. Shafer W., and Sonnenschein H. Equilibrium in abstract economies without ordered preferences. Journal of Mathematical Economics 2 (1975) 345-348
256. Shafer W., and Sonnenschein H. Equilibrium with externalities, commodity taxation and lump-sum transfers preferences. International Economic Review 17 (1976) 601-611
257. Shapiro N.Z., and Shapley L.S. Values of large games, I: A limit theorem. Mathematics of Operations Research 3 (1978) 1-9
258. Shapley L. Noncooperative general exchange. In: Lin S.A.Y. (Ed). Theory and Measurement of Economic Externalities (1976), Academic Press, Amsterdam
259. Unpublished Ph.D. dissertation. Shieh J. Static and dynamic large games with application to warrant pricing (1992), The Johns Hopkins University, New York
260. Sonnenschein H. The economics of incentives: an introductory account. In: Jacobs D.P., Kalai E., and Kamien M.I. (Eds). Frontiers of Research in Economic Theory: The Nancy L. Schwartz Memorial Lectures, 1983-1997 (1998), Cambridge University Press
261. Sun Y.N. Hyperfinite law of large numbers. Bulletin of Symbolic Logic 2 (1996) 189-198
262. Sun Y.N. Distributional properties of correspondences on Loeb spaces. Journal of Functional Analysis 139 (1996) 68-93
263. Sun Y.N. Integration of correspondences on Loeb spaces. Transactions of the American Mathematical Society 349 (1997) 129-153
264. Sun Y.N. A theory of hyperfinite processes: the complete removal of individual uncertainty via exact LLN. Journal of Mathematical Economics 29 (1998) 419-503
265. Sun Y.N. The almost equivalence of pairwise and mutual independence and the duality with exchangeability. Probability Theory and Related Fields 112 (1998) 425-456
266. Sun Y.N. The complete removal of individual uncertainty: multiple optimal choices and random economies. Economic Theory 14 (1999) 507-544
267. Sun Y.N. On the sample measurability problem in modeling individual risks. Research Paper No. 99-225 (1999), Center for Financial Engineering, National University of Singapore, Cambridge
268. Sun Y.N. Nonstandard analysis in mathematical economics. In: Loeb P.A., and Wolff M. (Eds). Mathematics and its Applications Vol. 510 (2000), Kluwer Academic 261-305
269. Talagrand M. Pettis integral and measure theory. Memoirs of the American Mathematical Society 51 (1984) 307
270. Tian G. Equilibrium in abstract economies with a non-compact infinite dimensional strategy space, an infinite number of agents and without ordered preferences. Economics Letters 33 (1992) 203-206
271. Tian G. On the existence of equilibria in generalized games. International Journal of Game Theory 20 (1992) 247-254
272. Toussaint S. On the existence of equilibrium with infinitely many commodities. Journal of Economic Theory 33 (1984) 98-115
273. Uhl Jr. J.J. The range of a vector-valued measure. Proceedings of the American Mathematical Society 23 (1969) 158-163
274. Uhl Jr. J.J. Pettis's measurability theorem. Contemporary Mathematics 2 (1980) 135-144
275. Valadier M. Young measures. In: Cellina A. (Ed). Methods of Nonconvex Analysis, Lecture Notes in Mathematics Vol. 1446 (1993), Springer-Verlag, Dordrecht
276. Vickrey W. Measuring marginal utility by reactions to risk. Econometrica 13 (1945) 319-333
277. Vives X. Aggregation of information in large Cournot markets. Econometrica 56 (1988) 851-876
278. von Neumann J. Einige Sätze über messbare Abbildungen. Annals of Mathematics 33 (1932) 574-586
279. von Neumann J., and Morgenstern O. Theory of Games and Economic Behavior. 3rd edn. (1953), Princeton University Press, Berlin
280. Wald A., and Wolfowitz J. Two methods of randomization in statistics and the theory of games. Annals of Mathematics 53 (1951) 581-586
281. Weinrich G. On the theory of effective demand under stochastic rationing. Journal of Economic Theory 34 (1984) 95-115
282. mimeo. Wieczorek A. Elementary large games and an application to economies with many agents (1996), Polish Academy of Sciences, Princeton
283. Unpublished Ph.D. dissertation. Yamashige S. Large games and large economies with incomplete information (1992), The Johns Hopkins University
284. Yannelis N.C. Equilibria in noncooperative models of competition. Journal of Economic Theory 41 (1987) 96-111
285. (1991). Yannelis N.C. Integration of Banach-valued correspondences. In: Ali Khan M., and Yannelis N.C. (Eds) (1991)
286. (1991). Yannelis N.C. Set-valued functions of two variables. In: Ali Khan M., and Yannelis N.C. (Eds) (1991)