A perfect price discrimination market model with production, and a rational convex program for it

Mathematics of Operations Research

Volumn 36, Issue 4, 2011, Pages 762-782

  Goel, Gagan ^a   Vazirani, Vijay V ^b  

^a GOOGLE INC   (United States)

^b Georgia Institute of Technology   (United States)

Author keywords

Combinatorial algorithm; Convex program; Fisher's market model; Market equilibrium; Perfect price discrimination; Piecewise linear concave utilities; Production

Indexed keywords

COMBINATORIAL ALGORITHM; CONVEX PROGRAMS; MARKET EQUILIBRIA; MARKET MODEL; PIECEWISE-LINEAR; PRICE DISCRIMINATION;

ALGORITHMS; COMPUTATIONAL EFFICIENCY; COSTS; PIECEWISE LINEAR TECHNIQUES; POLYNOMIAL APPROXIMATION; PRODUCTION;

COMMERCE;

EID: 81855211855     PISSN: 0364765X     EISSN: 15265471     Source Type: Journal    
DOI: 10.1287/moor.1110.0517     Document Type: Article

References (27)

1. Anderson, S. P., A. de Palma. 1988. Spatial price discrimination with heterogeneous products. Rev. Econom. Stud. 55(4) 573-592.
2. Arrow, K., G. Debreu. 1954. Existence of an equilibrium for a competitive economy. Econometrica 22(3) 265-290.
3. Bhaskar, V., T. To. 2004. Is perfect price discrimination really efficient? An analysis of free entry. RAND J. Econom. 35(4) 762-776.
4. Birnbaum, B., N. R. Devanur, L. Xiao. 2010. New convex programs and distributed algorithms for Fisher markets with linear and spending constraint utilities. Proc. ACM EC 2011, ACM, New York.
5. Chakrabarty, D., N. Devanur, V. V. Vazirani. 2010. Rationality and strongly polynomial solvability of Eisenberg-Gale markets with two agents. SIAM J. Discrete Math. 24(3) 1117-1136.
6. Chen, X., S.-H. Teng. 2009. Spending is not easier than trading: On the computational equivalence of Fisher and Arrow-Debreu equilibria. Y. Dong, D.-Z. Du, O. Ibarra, eds. Algorithms and Computation, Vol. 5878. Lecture Notes in Computer Science, Springer, Berlin/Heidelberg, 647-656.
7. Chen, X., D. Dai, Y. Du, S.-H. Teng. 2009. Settling the complexity of Arrow-Debreu equilibria in markets with additively separable utilities. IEEE 50th Annual Sympos. Foundations Comput. Sci., Atlanta, IEEE Computer Society, Washington, DC, 273-282.
8. Codenotti, B., K. Varadarajan. 2004. Efficient computation of equilibrium prices for markets with Leontief utilities. Proc. 31st Internat. Colloquim Automata, Languages, and Programming (ICALP), Springer, Berlin/Heidelberg, 371-382.
9. Devanur, N., C. H. Papadimitriou, A. Saberi, V. V. Vazirani. 2008. Market equilibrium via a primal-dual-type algorithm. J. ACM 55(5) Article 22.
10. Edlin, A., M. Epelbaum, W. Heller. 1994. Surplus maximization and price discrimination in general equilibrium: Part I. Working Papers 9405, Centro de Investigacion Economica, ITAM, Tizapán, Mexico.
11. Eisenberg, E., D. Gale. 1959. Consensus of subjective probabilities: The pari-mutuel method. Ann. Math. Statist. 30(1) 165-168.
12. Grötschel, M., L. Lovasz, A. Schrijver. 1988. Geometric Algorithms and Combinatorial Optimization. Springer-Verlag, Heidelberg, Germany.
13. Heller, M., W. P Edlin, A. S. Epelbaum. 1998. Is perfect price discrimination really efficient?: Welfare and existence in general equilibrium. Econometrica 66(4) 897-922.
14. Jain, K. 2007. A polynomial time algorithm for computing the Arrow-Debreu market equilibrium for linear utilities. SIAM J. Comput. 37(1) 303-318. (Pubitemid 351321998)
15. Jain, K., V. V. Vazirani. 2010. Eisenberg-Gale markets: Algorithms and game-theoretic properties. Games Econom. Behavior 70(1) 84-106.
16. Jain, K., V. V. Vazirani, Y. Ye. 2005. Market equilibrium for homothetic, quasi-concave utilities and economies of scale in production. Proc. 16th Ann. ACM-SIAM Sympos. Discrete Algorithms (SODA '05), SIAM, Philadelphia, 63-71. (Pubitemid 40851358)
17. Kelly, F. P. 1997. Charging and rate control for elastic traffic. Eur. Trans. Telecomm. 8 33-37.
18. Liu, Q., K. Serfes. 2005. Imperfect price discrimination, market structure, and efficiency. Canadian J. Econom. 38(4) 1191-1203. (Pubitemid 41825301)
19. Norman, G., W. B. MacLeod, J.-F. Thisse. 1988. Price discrimination and equilibrium in monopolistic competition. Internat. J. Indust. Organ. 6(4) 429-446.
20. Pigou, A. C. 1900. The Economics of Welfare. MacMillan and Company, London.
21. Varian, H. 1996. Differential pricing and efficiency. First Monday 1(2). http://firstmonday.org/htbin/cgiwrap/bin/ojs/index.php/fm/rt/printerFriendly/ 473/394.
22. Varian, H. R. 1985. Price discrimination and social welfare. Amer. Econom. Rev. 75(4) 870-875.
23. Vazirani, V. V. 2009. Rational convex programs and efficient algorithms for 2-player Nash and nonsymmetric bargaining games. Proc. 2nd Internat. Sympos. Game Theory, Paphos, Cyprus.
24. Vazirani, V. V. 2010. Spending constraint utilities, with applications to the Adwords market. Math. Oper. Res. 35(2) 458-478.
25. Vazirani, V. V. 2012. The notion of a rational convex program, and an algorithm for the Arrow-Debreu Nash bargaining game. ACM-SIAM Sympos. Discrete Algorithms, Kyoto, Japan. Forthcoming.
26. Vazirani, V. V., M. Yannakakis. 2011. Market equilibrium under separable, piecewise-linear, concave utilities. J. ACM 58(3) Article 10.
27. Ye, Y. 2007. Exchange market equilibria with Leontief's utility: Freedom of pricing leads to rationality. Theoret. Comput. Sci. 378(2) 134-142. (Pubitemid 46719675)