A primal-dual algorithm for computing Fisher equilibrium in the absence of gross substitutability property

We provide the first strongly polynomial time exact combinatorial algorithm to compute Fisher equilibrium for the case when utility functions do not satisfy the Gross substitutability property. The motivation for this comes from the work of Kelly, Maulloo, and Tan [F.P. Kelly, A.K. Maulloo, D.K.H. T...

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Vydané v:	Theoretical computer science Ročník 378; číslo 2; s. 143 - 152
Hlavní autori:	Garg, Dinesh, Jain, Kamal, Talwar, Kunal, Vazirani, Vijay V.
Médium:	Journal Article Konferenčný príspevok..
Jazyk:	English
Vydavateľské údaje:	Amsterdam Elsevier B.V 06.06.2007 Elsevier
Predmet:	Algorithmics. Computability. Computer arithmetics Applied sciences Combinatorial algorithm Combinatorics Combinatorics. Ordered structures Computer science; control theory; systems Computing market equilibria Exact sciences and technology Fisher equilibrium Graph theory Gross substitutability property Mathematics Miscellaneous Primal-dual algorithm Programming theory Sciences and techniques of general use Strongly polynomial time exact algorithm Theoretical computing Computing market equilibria Primal-dual algorithm Strongly polynomial time exact algorithm Gross substitutability property Fisher equilibrium Combinatorial algorithm Polynomial Computer theory Node Research Computing Communication network Knowledge Equilibrium Convex programming Flow Polynomial time Maximum Tree Numerical stability Communication
ISSN:	0304-3975, 1879-2294
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Abstract	We provide the first strongly polynomial time exact combinatorial algorithm to compute Fisher equilibrium for the case when utility functions do not satisfy the Gross substitutability property. The motivation for this comes from the work of Kelly, Maulloo, and Tan [F.P. Kelly, A.K. Maulloo, D.K.H. Tan, Rate control for communication networks: Shadow prices, proportional fairness and stability, Journal of Operational Research (1998)] and Kelly and Vazirani [F.P. Kelly, Vijay V. Vazirani, Rate control as a market equilibrium (2003) (in preparation)] on rate control in communication networks. We consider a tree like network in which root is the source and all the leaf nodes are the sinks. Each sink has got a fixed amount of money which it can use to buy the capacities of the edges in the network. The edges of the network sell their capacities at certain prices. The objective of each edge is to fix a price that can fetch the maximum money for it, and the objective of each sink is to buy capacities on edges in such a way that it can facilitate the sink to pull maximum flow from the source. In this problem, the edges and the sinks play precisely the role of sellers and buyers, respectively, in Fisher’s market model. The utility of a buyer (or sink) takes the form of a Leontief function which is known for not satisfying Gross substitutability property. We develop an O ( m 3 ) exact combinatorial algorithm for computing equilibrium prices of the edges. The time taken by our algorithm is independent of the values of sink money and edge capacities. A corollary of our algorithm is that equilibrium prices and flows are rational numbers. Although there are algorithms to solve this problem they are all based on convex programming techniques. To the best of our knowledge, ours is the first strongly polynomial time exact combinatorial algorithm for computing equilibrium prices of Fisher’s model under the case when buyers’ utility functions do not satisfy gross substitutability property.
AbstractList	We provide the first strongly polynomial time exact combinatorial algorithm to compute Fisher equilibrium for the case when utility functions do not satisfy the Gross substitutability property. The motivation for this comes from the work of Kelly, Maulloo, and Tan [F.P. Kelly, A.K. Maulloo, D.K.H. Tan, Rate control for communication networks: Shadow prices, proportional fairness and stability, Journal of Operational Research (1998)] and Kelly and Vazirani [F.P. Kelly, Vijay V. Vazirani, Rate control as a market equilibrium (2003) (in preparation)] on rate control in communication networks. We consider a tree like network in which root is the source and all the leaf nodes are the sinks. Each sink has got a fixed amount of money which it can use to buy the capacities of the edges in the network. The edges of the network sell their capacities at certain prices. The objective of each edge is to fix a price that can fetch the maximum money for it, and the objective of each sink is to buy capacities on edges in such a way that it can facilitate the sink to pull maximum flow from the source. In this problem, the edges and the sinks play precisely the role of sellers and buyers, respectively, in Fisher’s market model. The utility of a buyer (or sink) takes the form of a Leontief function which is known for not satisfying Gross substitutability property. We develop an O ( m 3 ) exact combinatorial algorithm for computing equilibrium prices of the edges. The time taken by our algorithm is independent of the values of sink money and edge capacities. A corollary of our algorithm is that equilibrium prices and flows are rational numbers. Although there are algorithms to solve this problem they are all based on convex programming techniques. To the best of our knowledge, ours is the first strongly polynomial time exact combinatorial algorithm for computing equilibrium prices of Fisher’s model under the case when buyers’ utility functions do not satisfy gross substitutability property.
Author	Jain, Kamal Vazirani, Vijay V. Garg, Dinesh Talwar, Kunal
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Keywords	Computing market equilibria Primal-dual algorithm Strongly polynomial time exact algorithm Gross substitutability property Fisher equilibrium Combinatorial algorithm Polynomial Computer theory Node Research Computing Communication network Knowledge Equilibrium Convex programming Flow Polynomial time Maximum Tree Numerical stability Communication
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References	Rahul Garg, Sanjiv Kapoor, Auction algorithms for market equilibrium, in: Proceedings of the 36th Annual ACM Symposium on the Theory of Computing, 2004 X. Deng, C.H. Papadimitriou, S. Safra, On the complexity of equilibria, in: STOC 2002, 2002 B. Codenotti, S. Pemmaraju, K. Varadarajan, On the polynomial time computation of equilibria for certain exchange economies, in: Proceedings of SODA, 2004 Eisenberg, Gale (b8) 1959; 30 Rahul Garg, Sanjiv Kapoor, Vijay Vazirani, An auction-based market equilibrium algorithms for the separable gross substitutability case, in: APPROX-RANDOM 2004, 2004, pp. 128–138 Scarf (b22) 1973; no. 24 B. Codenotti, K. Varadarajan, Efficient computation of equilibrium prices for markets with leontief utilities, in: Proceedings of ICALP, 2004 Kelly, Maulloo, Tan (b17) 1998 F.P. Kelly, Vijay V. Vazirani, Rate control as a market equilibrium (2003) (in preparation) Newman, Primak (b20) 1992; 52 Yinyu Ye, Exchange market equilibria with leontief’s utility: Freedom of pricing leads to rationality, in: Proceedings of 1st Workshop on Internet and Network Economics, WINE, Hong Kong, December 2005 Wald (b23) 1936; 7 Kamal Jain, V.V. Vazirani, Yinyu Ye, Market equilibria for homothetic, quasi-concave utilities and economies of scale in production, in: Proceedings, 16th Annual ACM-SIAM Symposium on Discrete Algorithms, 2005 Kamal Jain, A polynomial time algorithm for computing the Arrow–Debreu market equilibrium for linear utilities, in: FOCS, 2004 Kamal Jain, Mohammad Taghi Hajiaghayi, The prize-collecting generalized steiner tree problem via a new approach of primal-dual schema, in: Manuscript, 2004 K. Jain, M. Mahdian, A. Saberi, Approximating market equilibrium, in: Workshop on Approximation Algorithms for Combinatorial Optimization, APPROX 2003, 2003 Nikhil R. Devanur, Vijay V. Vazirani, An improved approximation scheme for the computing Arrow–Debreu prices in the linear case, in: Proceedings of Foundations of Software Technology and Theoretical Computer Science, 2003, 2002 Deng, Papadimitriou, Safra (b4) 2003; 67 Gale (b9) 1960 Kelly (b19) 1997; 8 Yinyu Ye, A path to Arrow–Debreu competitive market equilibrium, Working Paper, Department of Management Science and Engineering, Stanford University, Stanford, CA 94305, 2004, Mathematical Programming (2004) (in press) Nikhil R. Devanur, Christos H. Papadimitriou, Amin Saberi, Vijay V. Vazirani, Market equilibrium via a primal-dual-type algorithm, in: 43rd Symposium on Foundations of Computer Science, FOCS 2002, November 2002, pp. 389–395 Arrow, Debreu (b1) 1954; 22 Christos H. Papadimitriou, Algorithms, games, and the internet, in: ACM STOC’01, Hersonissos, Crete, Greece, 6–8 July 2001 L. Walras, Éléments d’économie politique pure ou théorie de la richesse sociale (Elements of Pure Economics, or The Theory of Social Wealth), Lausanne, Paris, 1874 (1899, 4th Ed., 1926, Rev. Ed., 1954, Engl. Transl.) Goemans, Williamson (b12) 1995; 42 10.1016/j.tcs.2007.02.017_b21 10.1016/j.tcs.2007.02.017_b25 Goemans (10.1016/j.tcs.2007.02.017_b12) 1995; 42 Kelly (10.1016/j.tcs.2007.02.017_b19) 1997; 8 10.1016/j.tcs.2007.02.017_b24 Newman (10.1016/j.tcs.2007.02.017_b20) 1992; 52 Scarf (10.1016/j.tcs.2007.02.017_b22) 1973; no. 24 Eisenberg (10.1016/j.tcs.2007.02.017_b8) 1959; 30 10.1016/j.tcs.2007.02.017_b6 Arrow (10.1016/j.tcs.2007.02.017_b1) 1954; 22 10.1016/j.tcs.2007.02.017_b7 10.1016/j.tcs.2007.02.017_b5 10.1016/j.tcs.2007.02.017_b2 10.1016/j.tcs.2007.02.017_b3 10.1016/j.tcs.2007.02.017_b26 10.1016/j.tcs.2007.02.017_b10 10.1016/j.tcs.2007.02.017_b14 Wald (10.1016/j.tcs.2007.02.017_b23) 1936; 7 10.1016/j.tcs.2007.02.017_b13 10.1016/j.tcs.2007.02.017_b11 Gale (10.1016/j.tcs.2007.02.017_b9) 1960 Deng (10.1016/j.tcs.2007.02.017_b4) 2003; 67 10.1016/j.tcs.2007.02.017_b18 Kelly (10.1016/j.tcs.2007.02.017_b17) 1998 10.1016/j.tcs.2007.02.017_b16 10.1016/j.tcs.2007.02.017_b15
References_xml	– volume: 52 start-page: 223 year: 1992 end-page: 231 ident: b20 article-title: Complexity of circumscribed and inscribed ellipsoid methods for solving equilibrium models publication-title: Applied Mathematics and Computation – volume: 42 start-page: 1115 year: 1995 end-page: 1145 ident: b12 article-title: Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming publication-title: Journal of ACM – year: 1998 ident: b17 article-title: Rate control for communication networks: Shadow prices, proportional fairness and stability publication-title: Journal of Operational Research – reference: Christos H. Papadimitriou, Algorithms, games, and the internet, in: ACM STOC’01, Hersonissos, Crete, Greece, 6–8 July 2001 – reference: Rahul Garg, Sanjiv Kapoor, Vijay Vazirani, An auction-based market equilibrium algorithms for the separable gross substitutability case, in: APPROX-RANDOM 2004, 2004, pp. 128–138 – reference: K. Jain, M. Mahdian, A. Saberi, Approximating market equilibrium, in: Workshop on Approximation Algorithms for Combinatorial Optimization, APPROX 2003, 2003 – volume: 8 start-page: 33 year: 1997 end-page: 37 ident: b19 article-title: Charging and rate control for elastic traffic publication-title: European Transactions on Telecom – reference: Kamal Jain, A polynomial time algorithm for computing the Arrow–Debreu market equilibrium for linear utilities, in: FOCS, 2004 – reference: F.P. Kelly, Vijay V. Vazirani, Rate control as a market equilibrium (2003) (in preparation) – volume: 30 start-page: 165 year: 1959 end-page: 168 ident: b8 article-title: Consensus of subjective probabilities: The Pari–Mutuel method publication-title: Annals of Mathematical Statistics – reference: Yinyu Ye, Exchange market equilibria with leontief’s utility: Freedom of pricing leads to rationality, in: Proceedings of 1st Workshop on Internet and Network Economics, WINE, Hong Kong, December 2005 – reference: L. Walras, Éléments d’économie politique pure ou théorie de la richesse sociale (Elements of Pure Economics, or The Theory of Social Wealth), Lausanne, Paris, 1874 (1899, 4th Ed., 1926, Rev. Ed., 1954, Engl. Transl.) – volume: 22 start-page: 265 year: 1954 end-page: 290 ident: b1 article-title: Existence of an equilibrium for a competitive economy publication-title: Econometrica – reference: B. Codenotti, K. Varadarajan, Efficient computation of equilibrium prices for markets with leontief utilities, in: Proceedings of ICALP, 2004 – reference: Nikhil R. Devanur, Vijay V. Vazirani, An improved approximation scheme for the computing Arrow–Debreu prices in the linear case, in: Proceedings of Foundations of Software Technology and Theoretical Computer Science, 2003, 2002 – reference: Kamal Jain, Mohammad Taghi Hajiaghayi, The prize-collecting generalized steiner tree problem via a new approach of primal-dual schema, in: Manuscript, 2004 – reference: Yinyu Ye, A path to Arrow–Debreu competitive market equilibrium, Working Paper, Department of Management Science and Engineering, Stanford University, Stanford, CA 94305, 2004, Mathematical Programming (2004) (in press) – reference: Nikhil R. Devanur, Christos H. Papadimitriou, Amin Saberi, Vijay V. Vazirani, Market equilibrium via a primal-dual-type algorithm, in: 43rd Symposium on Foundations of Computer Science, FOCS 2002, November 2002, pp. 389–395 – reference: Kamal Jain, V.V. Vazirani, Yinyu Ye, Market equilibria for homothetic, quasi-concave utilities and economies of scale in production, in: Proceedings, 16th Annual ACM-SIAM Symposium on Discrete Algorithms, 2005 – reference: X. Deng, C.H. Papadimitriou, S. Safra, On the complexity of equilibria, in: STOC 2002, 2002 – year: 1960 ident: b9 article-title: Theory of Linear Economic Models – reference: B. Codenotti, S. Pemmaraju, K. Varadarajan, On the polynomial time computation of equilibria for certain exchange economies, in: Proceedings of SODA, 2004 – volume: 67 start-page: 311 year: 2003 end-page: 324 ident: b4 article-title: On the complexity of price equilibria publication-title: Journal of Computer and System Sciences – volume: 7 start-page: 637 year: 1936 end-page: 670 ident: b23 article-title: Über einige gleichungssysteme der mathematischen Ökonomie publication-title: Zeitschrift fur Nationalokonomie – reference: Rahul Garg, Sanjiv Kapoor, Auction algorithms for market equilibrium, in: Proceedings of the 36th Annual ACM Symposium on the Theory of Computing, 2004 – volume: no. 24 year: 1973 ident: b22 publication-title: The Computation of Economic Equilibria (With Collaboration of T. Hansen) – ident: 10.1016/j.tcs.2007.02.017_b25 – volume: 22 start-page: 265 year: 1954 ident: 10.1016/j.tcs.2007.02.017_b1 article-title: Existence of an equilibrium for a competitive economy publication-title: Econometrica doi: 10.2307/1907353 – volume: 52 start-page: 223 year: 1992 ident: 10.1016/j.tcs.2007.02.017_b20 article-title: Complexity of circumscribed and inscribed ellipsoid methods for solving equilibrium models publication-title: Applied Mathematics and Computation doi: 10.1016/0096-3003(92)90079-G – ident: 10.1016/j.tcs.2007.02.017_b11 doi: 10.1007/978-3-540-27821-4_12 – volume: 8 start-page: 33 year: 1997 ident: 10.1016/j.tcs.2007.02.017_b19 article-title: Charging and rate control for elastic traffic publication-title: European Transactions on Telecom doi: 10.1002/ett.4460080106 – ident: 10.1016/j.tcs.2007.02.017_b7 doi: 10.1007/978-3-540-24597-1_13 – ident: 10.1016/j.tcs.2007.02.017_b2 doi: 10.1145/1054916.1054927 – ident: 10.1016/j.tcs.2007.02.017_b16 – volume: 42 start-page: 1115 year: 1995 ident: 10.1016/j.tcs.2007.02.017_b12 article-title: Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming publication-title: Journal of ACM doi: 10.1145/227683.227684 – ident: 10.1016/j.tcs.2007.02.017_b18 – ident: 10.1016/j.tcs.2007.02.017_b13 doi: 10.1007/978-3-540-45198-3_9 – volume: 67 start-page: 311 year: 2003 ident: 10.1016/j.tcs.2007.02.017_b4 article-title: On the complexity of price equilibria publication-title: Journal of Computer and System Sciences doi: 10.1016/S0022-0000(03)00011-4 – ident: 10.1016/j.tcs.2007.02.017_b10 doi: 10.1145/1007352.1007430 – year: 1960 ident: 10.1016/j.tcs.2007.02.017_b9 – ident: 10.1016/j.tcs.2007.02.017_b21 doi: 10.1145/380752.380883 – volume: no. 24 year: 1973 ident: 10.1016/j.tcs.2007.02.017_b22 – ident: 10.1016/j.tcs.2007.02.017_b26 – ident: 10.1016/j.tcs.2007.02.017_b24 – ident: 10.1016/j.tcs.2007.02.017_b6 doi: 10.1109/SFCS.2002.1181963 – ident: 10.1016/j.tcs.2007.02.017_b3 doi: 10.1007/978-3-540-27836-8_33 – ident: 10.1016/j.tcs.2007.02.017_b14 doi: 10.1109/FOCS.2004.6 – year: 1998 ident: 10.1016/j.tcs.2007.02.017_b17 article-title: Rate control for communication networks: Shadow prices, proportional fairness and stability publication-title: Journal of Operational Research doi: 10.1057/palgrave.jors.2600523 – ident: 10.1016/j.tcs.2007.02.017_b5 doi: 10.1145/509919.509920 – ident: 10.1016/j.tcs.2007.02.017_b15 – volume: 7 start-page: 637 year: 1936 ident: 10.1016/j.tcs.2007.02.017_b23 article-title: Über einige gleichungssysteme der mathematischen Ökonomie publication-title: Zeitschrift fur Nationalokonomie doi: 10.1007/BF01316644 – volume: 30 start-page: 165 year: 1959 ident: 10.1016/j.tcs.2007.02.017_b8 article-title: Consensus of subjective probabilities: The Pari–Mutuel method publication-title: Annals of Mathematical Statistics doi: 10.1214/aoms/1177706369
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SubjectTerms	Algorithmics. Computability. Computer arithmetics Applied sciences Combinatorial algorithm Combinatorics Combinatorics. Ordered structures Computer science; control theory; systems Computing market equilibria Exact sciences and technology Fisher equilibrium Graph theory Gross substitutability property Mathematics Miscellaneous Primal-dual algorithm Programming theory Sciences and techniques of general use Strongly polynomial time exact algorithm Theoretical computing
Title	A primal-dual algorithm for computing Fisher equilibrium in the absence of gross substitutability property
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