A Strongly Polynomial Algorithm for Linear Exchange Markets

Published Online:https://doi.org/10.1287/opre.2021.2258

References

  • Adler I, Cosares S (1991) A strongly polynomial algorithm for a special class of linear programs. Oper. Res. 39(6):955–960.LinkGoogle Scholar
  • Arrow KJ, Debreu G (1954) Existence of an equilibrium for a competitive economy. Econometrica 22(3):265–290.CrossrefGoogle Scholar
  • Brainard W, Scarf H (2000) How to compute equilibrium prices in 1891. Cowles Foundation Discussion Paper 1270, Cowles Foundation, New Haven, CT.Google Scholar
  • Codenotti B, Pemmaraju S, Varadarajan K (2004) The computation of market equilibria. ACM SIGACT News 35(4):23–37.CrossrefGoogle Scholar
  • Cohen E, Megiddo N (1994) Improved algorithms for linear inequalities with two variables per inequality. SIAM J. Comput. 23(6):1313–1347.CrossrefGoogle Scholar
  • Cornet B (1989) Linear exchange economies. Technical report, Cahier Eco-Math, Université de Paris, Paris.Google Scholar
  • Cottle RW, Veinott AF (1972) Polyhedral sets having a least element. Math. Program. 3(1):238–249.CrossrefGoogle Scholar
  • Darwish O, Mehlhorn K (2016) Improved balanced flow computation using parametric flow. Inform. Process. Lett. 116(9):560–563.CrossrefGoogle Scholar
  • Devanur NR, Vazirani VV (2003) An improved approximation scheme for computing Arrow-Debreu prices for the linear case. Pandya PK, Radhakrishnan J, eds. FST TCS 2003 Foundation Software Tech. Theoret. Comput. Sci., Lecture Notes in Computer Science, vol. 2914 (Springer, Berlin), 149–155.Google Scholar
  • Devanur NR, Garg J, Végh LA (2016) A rational convex program for linear Arrow-Debreu markets. ACM Trans. Econom. Comput. 5(1):6.Google Scholar
  • Devanur NR, Papadimitriou CH, Saberi A, Vazirani VV (2008) Market equilibrium via a primal–dual algorithm for a convex program. J. ACM 55(5):22.CrossrefGoogle Scholar
  • Duan R, Mehlhorn K (2015) A combinatorial polynomial algorithm for the linear Arrow–Debreu market. Inform. Comput. 243:112–132.CrossrefGoogle Scholar
  • Duan R, Garg J, Mehlhorn K (2016) An improved combinatorial polynomial algorithm for the linear Arrow-Debreu market. Kraughgamer R, ed. SODA’16 Proc. 27th Annu. ACM-SIAM Sympos. Discrete Algorithms (Society for Industrial and Applied Mathematics, Philadelphia), 90–106.Google Scholar
  • Eaves BC (1976) A finite algorithm for the linear exchange model. J. Math. Econom. 3:197–203.CrossrefGoogle Scholar
  • Edmonds J (1967) Systems of distinct representatives and linear algebra. J. Res. National Bureau Standards B 71:241–245.CrossrefGoogle Scholar
  • Eisenberg E, Gale D (1959) Consensus of subjective probabilities: The Pari-Mutuel method. Ann. Math. Statist. 30(1):165–168.CrossrefGoogle Scholar
  • Gale D (1976) The linear exchange model. J. Math. Econom. 3(2):205–209.CrossrefGoogle Scholar
  • Garg R, Kapoor S (2006) Auction algorithms for market equilibrium. Math. Oper. Res. 31(4):714–729.LinkGoogle Scholar
  • Garg J, Végh LA (2019) A strongly polynomial algorithm for linear exchange markets. STOC 2019 Proc. 51st Annu. ACM SIGACT Sympos. Theory Comput. (Association for Computing Machinery, New York), 54–65.Google Scholar
  • Garg J, Mehta R, Vazirani VV, Yazdanbod S (2017) Settling the complexity of Leontief and PLC exchange markets under exact and approximate equilibria. STOC 2017 Proc. 49th Annu. ACM SIGACT Sympos. Theory Comput. (Association for Computing Machinery, New York), 890–901.Google Scholar
  • Ghiyasvand M, Orlin JB (2012) A simple approximation algorithm for computing Arrow-Debreu prices. Oper. Res. 60(5):1245–1248.LinkGoogle Scholar
  • Goel G, Vazirani V (2011) A perfect price discrimination market model with production, and a rational convex program for it. Math. Oper. Res. 36(4):762–782.LinkGoogle Scholar
  • Goldberg AV, Tarjan RE (1989) Finding minimum-cost circulations by canceling negative cycles. J. ACM. 36(4):873–886.CrossrefGoogle Scholar
  • Grötschel M, Lovász L, Schrijver A (1988) Geometric Algorithms and Combinatorial Optimization, Algorithms and Combinatorics, vol. 2 (Springer Verlag, Berlin).CrossrefGoogle Scholar
  • Hochbaum DS, Naor J (1994) Simple and fast algorithms for linear and integer programs with two variables per inequality. SIAM J. Comput. 23(6):1179–1192.CrossrefGoogle Scholar
  • Jain K (2007) A polynomial time algorithm for computing an Arrow-Debreu market equilibrium for linear utilities. SIAM J. Comput. 37(1):303–318.CrossrefGoogle Scholar
  • Jain K, Mahdian M, Saberi A (2003) Approximating market equilibria. Arora S, Jansen K, Rolim JDP, Sahai A, eds. RANDOM 2003 APPROX 2003 Approximation Randomization Combinatorial Optimization Algorithms Techniques, Lecture Notes in Computer Science, vol. 2764 (Springer, Berlin), 98–108.Google Scholar
  • Kamiyama N (2019) A note on balanced flows in equality networks. Inform. Process. Lett. 145:74–76.CrossrefGoogle Scholar
  • Lemke CE (1965) Bimatrix equilibrium points and mathematical programming. Management Sci. 11(7):681–689.LinkGoogle Scholar
  • Megiddo N (1983) Toward a genuinely polynomial algorithm for linear programming. SIAM J. Comput. 12(2):347–353.CrossrefGoogle Scholar
  • Nenakov EI, Primak ME (1983) One algorithm for finding solutions of the Arrow-Debreu model. Kibernetica 3:127–128.Google Scholar
  • Olver N, Végh LA (2017) A simpler and faster strongly polynomial algorithm for generalized flow maximization. STOC 2017 Proc. 49th Annu. ACM SIGACT Sympos. Theory Comput. (Association for Computing Machinery, New York), 100–111.Google Scholar
  • Orlin JB (1993) A faster strongly polynomial minimum cost flow algorithm. Oper. Res. 41(2):338–350.LinkGoogle Scholar
  • Orlin JB (2010) Improved algorithms for computing Fisher’s market clearing prices. STOC’10 Proc. 42nd ACM Sympos. Theory Comput. (Association for Computing Machinery, New York), 291–300.Google Scholar
  • Orlin JB (2013) Max flows in O(nm) time, or better. STOC’13 Proc. 45th Annu. ACM Sympos. Theory Comput. (Association for Computing Machinery, New York), 765–774.Google Scholar
  • Shmyrev VI (2009) An algorithm for finding equilibrium in the linear exchange model with fixed budgets. J. Appl. Indust. Math. 3(4):505–518.CrossrefGoogle Scholar
  • Tardos É (1985) A strongly polynomial minimum cost circulation algorithm. Combinatorica 5(3):247–255.CrossrefGoogle Scholar
  • Tardos É (1986) A strongly polynomial algorithm to solve combinatorial linear programs. Oper. Res. 34(2):250–256.LinkGoogle Scholar
  • Varian H (1974) Equity, envy and efficiency. J. Econom. Theory 29(2):217–244.Google Scholar
  • Vavasis SA, Ye Y (1996) A primal-dual interior point method whose running time depends only on the constraint matrix. Math. Program. 74(1):79–120.CrossrefGoogle Scholar
  • Vazirani V (2010) Spending constraint utilities with applications to the adwords market. Math. Oper. Res. 35(2):458–478.LinkGoogle Scholar
  • Vazirani VV (2012) The notion of a rational convex program, and an algorithm for the Arrow-Debreu Nash bargaining game. J. ACM 59(2):7.CrossrefGoogle Scholar
  • Végh LA (2013) Concave generalized flows with applications to market equilibria. Math. Oper. Res. 39(2):573–596.LinkGoogle Scholar
  • Végh LA (2016) A strongly polynomial algorithm for a class of minimum-cost flow problems with separable convex objectives. SIAM J. Comput. 45(5):1729–1761.CrossrefGoogle Scholar
  • Végh LA (2017) A strongly polynomial algorithm for generalized flow maximization. Math. Oper. Res. 42(2):179–211.LinkGoogle Scholar
  • Walras L (1874) Eléments d’Economie Politique Pure, ou Théorie de la Richesse Sociale (in French). [English translation: Elements of Pure Economics; or, the Theory of Social Wealth] (American Economic Association and the Royal Economic Society, Corbaz & Cie, Lausanne).Google Scholar
  • Ye Y (2005) A new complexity result on solving the Markov decision problem. Math. Oper. Res. 30(3):733–749.LinkGoogle Scholar
  • Ye Y (2008) A path to the Arrow–Debreu competitive market equilibrium. Math. Program. 111(1–2):315–348.CrossrefGoogle Scholar
  • Ye Y (2011) The simplex and policy-iteration methods are strongly polynomial for the Markov decision problem with a fixed discount rate. Math. Oper. Res. 36(4):593–603.LinkGoogle Scholar
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