Supermodularity and complementarity

Supermodularity and Complementarity

Volumn , Issue , 2011, Pages 1-272

  Topkis, Donald M ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84890749086     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Book

References (122)

1. Ahuja, Ravindra K., Thomas L. Magnanti, and James B. Orlin. 1993. Network flows. Englewood Cliffs: Prentice Hall.
2. Akinc, Umit, and Basheer K. Khumawala. 1977. An efficient branch and bound algorithm for the capacitated warehouse location problem. Management Science 23:585-594.
3. Amir, Rabah. 1996. Sensitivity analysis of multisector optimal economic dynamics. Journal of Mathematical Economics 25:123-141.
4. Amir, Rabah, Leonard J. Mirman, and William R. Perkins. 1993. One-sector nonclassical optimal growth: Optimality conditions and comparative dynamics. International Economic Review 32:625-644.
5. Athey, Susan. 1995. Characterizing properties of stochastic objective functions. Working paper, Massachusetts Institute of Technology.
6. Bagwell, Kyle, and Garey Ramey. 1994. Coordination economies, advertising and search behavior in retail markets. American Economic Review 84:498-517.
7. Baker, Kirby A., and Alden F. Pixley. 1975. Polynomial interpolation and the Chinese remainder theorem. Mathematische Zeitschrift 143:165-174.
8. Balinski, M. L. 1970. On a selection problem. Management Science 17:230-231.
9. Becker, Gary S. 1973. A theory of marriage: Part I. Journal of Political Economy 81:813-846.
10. Bergman, George M. 1977. On the existence of subalgebras of direct products with prescribed d-fold projections. Algebra Universalis 7:341-356.
11. Billingsley, Patrick. 1979. Probability and measure. New York: Wiley.
12. Birkhoff, Garrett. 1967. Lattice theory. 3rd edition. American Mathematical Society Colloquium Publications. Volume 25. Providence: American Mathematical Society.
13. Bixby, Robert E., William H. Cunningham, and Donald M. Topkis. 1985. The partial order of a polymatroid extreme point. Mathematics of Operations Research 10:367-378.
14. Blackwell, D. 1965. Discounted dynamic programming. Annals of Mathematical Statistics 36:226-235.
15. Brown, George W. 1951. Iterative solution of games by fictitious play. In Activity analysis of production and allocation, edited by T. C. Koopmans. New York: Wiley.
16. Bulow, Jeremy I., John D. Geanakoplos, and Paul D. Klemperer. 1985. Multimarket oligopoly: Strategic substitutes and complements. Journal of Political Economy 93:488-511.
17. Bushnell, P. Timothy, and Allen D. Shepard. 1995. The economics of modern manufacturing: Comment. American Economic Review 85:987-990.
18. Cunningham, William H. 1984. Testing membership in matroid polyhedra. Journal of Combinatorial Theory, Series B 36:161-188.
19. Dantzig, George B. 1955. Linear programming under uncertainty. Management Science 1:197-206.
20. Dantzig, George B. 1963. Linear programming and extensions. Princeton: Princeton University Press.
21. Davis, Anne C. 1955. A characterization of complete lattices. Pacific Journal of Mathematics 5:311-319.
22. Debreu, Gerard. 1959. Theory of value. New Haven: Yale University Press.
23. Deng, Xiaotie, and Christos H. Papadimitriou. 1994. On the complexity of cooperative solution concepts. Mathematics of Operations Research 19:257-266.
24. Dunstan, F. D. J., and D. J. A. Welsh. 1973. A greedy algorithm for solving a certain class of linear programmes. Mathematical Programming 5:338-353.
25. Edgeworth, F. Y. 1925. The pure theory of monopoly. In Volume 1 of Papers relating to political economy, edited by F. Y. Edgeworth. New York: Burt Franklin.
26. Edlin, Aaron S., and Chris Shannon. 1996. Strict monotonicity in comparative statics. Working paper, University of California, Berkeley.
27. Edmonds, Jack. 1970. Submodular functions, matroids, and certain polyhedra. In Combinatorial structures and their applications, edited by Richard Guy, Haim Hanani, Norbert Sauer, and Johanan Schonheim. New York: Gordon and Breach.
28. Eppen, Gary D., F. J. Gould, and B. Peter Pashigian. 1969. Extensions of the planning horizon theorem in the dynamic economic lot size model. Management Science 15:268-277.
29. Erlenkotter, Donald. 1969. Preinvestment planning for capacity expansion: A multilocation dynamic model. Ph.D. dissertation, Stanford University.
30. Ford, L. R., Jr., and D. R. Fulkerson. 1962. Flows in networks. Princeton: Princeton University Press.
31. Frink, Orrin, Jr., 1942. Topology in lattices. Transactions of the American Mathematical Society 51:569-582.
32. Fudenberg, Drew, and Jean Tirole. 1991. Game theory. Cambridge: MIT Press.
33. Fujimoto, Takao. 1984. An extension of Tarski's fixed point theorem and its application to isotone complementarity problems. Mathematical Programming 28:116-118.
34. Gale, David, and Themistocles Politof. 1981. Substitutes and complements in network flow problems. Discrete Applied Mathematics 3:175-186.
35. Garey, Michael R., and David S. Johnson. 1979. Computers and intractability: A guide to the theory of NP-completeness. San Francisco: W. H. Freeman.
36. Glasserman, Paul, and David D. Yao. 1994. Monotone structure in discrete-event systems. New York: Wiley.
37. Grötschel, M., L. Lovász, and A. Schrijver. 1981. The ellipsoid method and its consequences in combinatorial optimization. Combinatorica 1:169-197.
38. Gusfield, Dan, and Robert W. Irving. 1989. The stable marriage problem. Cambridge: MIT Press.
39. Hardy, G. H., J. E. Littlewood, and G. Pólya. 1934. Inequalities. Cambridge: Cambridge University Press.
40. Heyman, Daniel P., and Matthew J. Sobel. 1984. Stochastic models in operations research. Volume 2. New York: McGraw-Hill.
41. Ichiishi, Tatsuro. 1981. Super-modularity: Applications to convex games and to the greedy algorithm for LP. Journal of Economic Theory 25:283-286.
42. Ichiishi, Tatsuro. 1990. Comparative cooperative game theory. International Journal of Game Theory 19:139-152.
43. Ichiishi, Tatsuro. 1993. The cooperative nature of the firm. Cambridge: Cambridge University Press.
44. Jorgenson, D. W., J. J. McCall, and R. Radner. 1967. Optimal replacement policy. Amsterdam: North-Holland.
45. Kandori, Michihiro, and Rafael Rob. 1995. Evolution of equilibria in the long run: A general theory and applications. Journal of Economic Theory 65:383-414.
46. Karlin, Samuel. 1960. Dynamic inventory policy with varying stochastic demands. Management Science 6:231-258.
47. Klee, Victor, and Peter Kleinschmidt. 1987. The d-step conjecture and its relatives. Mathematics of Operations Research 12:718-755.
48. Klee, Victor, and George J. Minty. 1972. How good is the simplex method? In Inequalities III, edited by Oved Shisha. New York: Academic Press.
49. Kremer, Michael. 1993. The O-ring theory of economic development. Quarterly Journal of Economics 108:551-575.
50. Lehmann, E. L. 1955. Ordered families of distributions. Annals of Mathematical Statistics 26:399-419.
51. Levitan, R. E., and M. Shubik. 1971. Noncooperative equilibria and strategy spaces in an oligopolistic market. In Differential games and related topics, edited by H. W. Kuhn and G. P. Szegö. Amsterdam: North-Holland.
52. Lin, Y. Joseph. 1992. The Becker-Brock efficient matching theorem with a supermodular technology defined on an n-lattice. Mathematical Social Sciences 24:105-109.
53. Lippman, Steven A., John W. Mamer, and Kevin F. McCardle. 1987. Comparative statics in noncooperative games. Journal of Economic Theory 41:288-303.
54. Littlechild, S. C., and G. Owen. 1973. A simple expression for the Shapley value in a special case. Management Science 20:370-372.
55. Littlechild, S. C., and G. F. Thompson, 1977. Aircraft landing fees: A game theory approach. Bell Journal of Economics 8:186-204.
56. Milgrom, Paul, Yingyi Qian, and John Roberts. 1991. Complementarities, momentum, and the evolution of modern manufacturing. American Economic Review 81:84-88.
57. Milgrom, Paul, and John Roberts. 1990a. Rationalizability, learning, and equilibrium in games with strategic complementarities. Econometrica 58:1255-1277.
58. Milgrom, Paul, and John Roberts. 1990b. The economics of modern manufacturing: Technology, strategy, and organization. American Economic Review 80:511-528.
59. Milgrom, Paul, and John Roberts. 1991. Adaptive and sophisticated learning in normal form games. Games and Economic Behavior 3:82-100.
60. Milgrom, Paul, and John Roberts. 1994. Comparing equilibria. American Economic Review 84:441-459.
61. Milgrom, Paul, and John Roberts. 1995. The economics of modern manufacturing: Reply. American Economic Review 85:997-999.
62. Milgrom, Paul, and John Roberts. 1996. The LeChatelier principle. American Economic Review 86:173-179.
63. Milgrom, Paul, and Christina Shannon. 1994. Monotone comparative statics. Econometrica 62:157-180.
64. Monma, C. L., and D. M. Topkis. 1982. Minimum cuts and equivalent combinatorial structures. Working paper, Bell Laboratories.
65. Moulin, Hervé. 1988. Axioms of cooperative decision making. Cambridge: Cambridge University Press.
66. Moulin, Hervé. 1989. Monotonic surplus sharing: Characterization results. Games and Economic Behavior 1:250-274.
67. Moulin, Hervé. 1990. Cores and large cores when population varies. International Journal of Game Theory 19:219-232.
68. Nagelhout, Robert V., and Gerald L. Thompson. 1981. A cost operator approach to multistage location-allocation. European Journal of Operational Research 6:149-161.
69. Ore, Oystein. 1962. Theory of graphs. American Mathematical Society Colloquium Publications. Volume 38. Providence: American Mathematical Society.
70. Panzar, John C., and Robert D. Willig. 1977. Free entry and the sustainability of natural monopoly. Bell Journal of Economics 8:1-22.
71. Papadimitriou, Christos H. 1994. Computational complexity. Reading, Mass.: Addison-Wesley.
72. Picard, Jean-Claude. 1976. Maximal closure of a graph and applications to combinatorial problems. Management Science 22:1268-1272.
73. Picard, Jean-Claude, and H. Donald Ratliff. 1978. A cut approach to the rectilinear distance facility location problem. Operations Research 26:422-433.
74. Rhys, J. M. W. 1970. A selection problem of shared fixed costs and network flows. Management Science 17:200-207.
75. Robinson, Julia. 1951. An iterative method of solving a game. Annals of Mathematics 54:296-301.
76. Rockafellar, R. Tyrrell. 1970. Convex analysis. Princeton: Princeton University Press.
77. Rosenthal, Edward C. 1988. Communication and its cost in graph-restricted games. Theory and Decision 25:275-286.
78. Rosenthal, Edward C. 1990. Monotonicity of the core and value in dynamic cooperative games. International Journal of Game Theory 19:45-57.
79. Samuelson, Paul A. 1947. Foundations of economic analysis. Harvard Economic Studies. Volume 80. Cambridge: Harvard University Press.
80. Samuelson, Paul A. 1952. Spatial price equilibrium and linear programming. American Economic Review 42:283-303.
81. Samuelson, Paul A. 1974. Complementarity. Journal of Economic Literature 12:1255-1289.
82. Serfozo, Richard F. 1976. Monotone optimal policies for Markov decision processes. Mathematical Programming Study 6:202-215.
83. Shaked, Moshe, and J. George Shanthikumar. 1994. Stochastic orders and their applications. Boston: Academic Press.
84. Shannon, Chris. 1995. Weak and strong monotone comparative statics. Economic Theory 5:209-227.
85. Shapley, Lloyd S. 1953. A value for n-person games. In Volume 2 of Contributions to the Theory of Games, edited by H. W. Kuhn and A. W. Tucker. Annals of Mathematics Studies. Number 28. Princeton: Princeton University Press.
86. Shapley, Lloyd S. 1961. On network flow functions. Naval Research Logistics Quarterly 8:151-158.
87. Shapley, Lloyd S. 1962. Complements and substitutes in the optimal assignment problem. Naval Research Logistics Quarterly 9:45-48.
88. Shapley, Lloyd S. 1971. Cores of convex games. International Journal of Game Theory 1:11-26.
89. Shapley, Lloyd S., and Martin Shubik. 1969. On the core of an economic system with externalities. American Economic Review 59:678-684.
90. Sharkey, William W. 1982a. Cooperative games with large cores. International Journal of Game Theory 11:175-182.
91. Sharkey, William W. 1982b. Suggestions for a game-theoretic approach to public utility pricing and cost allocation. Bell Journal of Economics 13:57-68.
92. Sharkey, William W. 1982c. The theory of natural monopoly. Cambridge: Cambridge University Press.
93. Sharkey, William W., and Lester G. Telser. 1978. Supportable cost functions for the multiproduct firm. Journal of Economic Theory 18:23-37.
94. Shubik, Martin. 1981. Game theory models and methods in political economy. In Volume 1 of Handbook of mathematical economics, edited by Kenneth J. Arrow and Michael D. Intriligator. Amsterdam: North-Holland.
95. Sobel, Matthew J. 1988. Isotone comparative statics in supermodular games. Working paper. SUNY at Stony Brook.
96. Sprumont, Yves. 1990. Population monotonic allocation schemes for cooperative games with transferable utility. Games and Economic Behavior 2:378-394.
97. Tamir, A. 1991. On the core of network synthesis games. Mathematical Programming 50:123-135.
98. Tarski, Alfred. 1955. A lattice-theoretical fixpoint theorem and its applications. Pacific Journal of Mathematics 5:285-309.
99. Topkis, Donald M. 1968. Ordered optimal solutions. Ph.D. dissertation, Stanford University.
100. Topkis, Donald M. 1976. The structure of sublattices of the product of n lattices. Pacific Journal of Mathematics 65:525-532.
101. Topkis, Donald M. 1977. Topology and subcomplete sublattices. Working paper.
102. Topkis, Donald M. 1978. Minimizing a submodular function on a lattice. Operations Research 26:305-321.
103. Topkis, Donald M. 1979. Equilibrium points in nonzero-sum n-person submodular games. SIAM Journal on Control and Optimization 17:773-787.
104. Topkis, Donald M. 1980. Supermodular optimization games. Working paper. Bell Laboratories.
105. Topkis, Donald M. 1983. Activity selection games and the minimum-cut problem. Networks 13:93-105.
106. Topkis, Donald M. 1984a. Adjacency on polymatroids. Mathematical Programming 30:229-237.
107. Topkis, Donald M. 1984b. Complements and substitutes among locations in the two-stage transshipment problem. European Journal of Operational Research 15:89-92.
108. Topkis, Donald M. 1987. Activity optimization games with complementarity. European Journal of Operational Research 28:358-368.
109. Topkis, Donald M. 1992. Paths on polymatroids. Mathematical Programming 54:335-351.
110. Topkis, Donald M. 1995a. Comparative statics of the firm. Journal of Economic Theory 67:370-401.
111. Topkis, Donald M. 1995b. The economics of modern manufacturing: Comment. American Economic Review 85:991-996.
112. Veinott, Arthur F., Jr. 1964. Production planning with convex costs: A parametric study. Management Science 10:441-460.
113. Veinott, Arthur F., Jr. 1965. Optimal policy for a multiproduct, dynamic, nonstationary inventory problem. Management Science 12:206-222.
114. Veinott, Arthur F., Jr. 1970. A correction for "Optimal policy for a multiproduct dynamic, nonstationary inventory problem." Management Science 16:518
115. Vives, Xavier. 1990. Nash equilibrium with strategic complementarities. Journal of Mathematical Economics 19:305-321.
116. Von Neumann, John, and Oskar Morgenstern. 1944. Theory of games and economic behavior. Princeton: Princeton University Press.
117. Wagner, Harvey M., and Thomson M. Whitin. 1958. Dynamic version of the economic lot size model. Management Science 5:89-96.
118. White, Chelsea C., III. 1980. Monotone control laws for noisy, countable-state Markov chains. European Journal of Operational Research 5:124-132.
119. White, John A. 1971. A quadratic facility location problem. AIIE Transactions 3:156-157.
120. Whitney, Hassler. 1935. On the abstract properties of linear dependence. American Journal of Mathematics 57:509-533.
121. Zangwill, Willard I. 1969. A backlogging model and a multi-echelon model of a dynamic economic lot size production system-A network approach. Management Science 15:506-527.
122. Zhou, Lin. 1994. The set of Nash equilibria of a supermodular game is a complete lattice. Games and Economic Behavior 7:295-300.