Amortized Analysis of Asynchronous Price Dynamics

Authors Yun Kuen Cheung , Richard Cole

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Yun Kuen Cheung
  • Max Planck Institute for Informatics, Saarland Informatics Campus, Saarbrücken, Germany
Richard Cole
  • Courant Institute, NYU, New York, USA

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Yun Kuen Cheung and Richard Cole. Amortized Analysis of Asynchronous Price Dynamics. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 18:1-18:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


We extend a recently developed framework for analyzing asynchronous coordinate descent algorithms to show that an asynchronous version of tatonnement, a fundamental price dynamic widely studied in general equilibrium theory, converges toward a market equilibrium for Fisher markets with CES utilities or Leontief utilities, for which tatonnement is equivalent to coordinate descent.

Subject Classification

ACM Subject Classification
  • Theory of computation → Market equilibria
  • Asynchronous Tatonnement
  • Fisher Market
  • Market Equilibrium
  • Amortized Analysis


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  1. Carlos Alós-Ferrer and Nick Netzer. The logit-response dynamics. Games and Economic Behavior, 68(2):413-427, 2010. Google Scholar
  2. Kenneth J. Arrow, H. D. Block, and Leonid Hurwicz. On the stability of competitive equilibrium, ii. Econometrica, 27(1):82-109, 1959. Google Scholar
  3. Petra Berenbrink, Tom Friedetzky, Leslie Ann Goldberg, Paul W. Goldberg, Zengjian Hu, and Russell A. Martin. Distributed selfish load balancing. SIAM J. Comput., 37(4):1163-1181, 2007. URL:
  4. Benjamin Birnbaum, Nikhil R. Devanur, and Lin Xiao. Distributed algorithms via gradient descent for fisher markets. In Proceedings of the 12th ACM Conference on Electronic Commerce, EC '11, pages 127-136. ACM, 2011. URL:
  5. Lawrence E. Blume. The statistical mechanics of strategic interaction. Games and Economic Behavior, 5(3):387-424, 1993. Google Scholar
  6. Bernard Chazelle. Natural algorithms. In SODA, pages 422-431, 2009. Google Scholar
  7. Bernard Chazelle. The dynamics of influence systems. In FOCS, pages 311-320, 2012. Google Scholar
  8. X. Chen, D. Dai, Y. Du, and S. H. Teng. Settling the complexity of arrow-debreu equilibria in markets with additively separable utilities. In 2009 50th Annual IEEE Symposium on Foundations of Computer Science, pages 273-282, 2009. URL:
  9. Xi Chen, Xiaotie Deng, and Shang-Hua Teng. Settling the complexity of computing two-player nash equilibria. J. ACM, 56(3):14:1-14:57, may 2009. Google Scholar
  10. Xi Chen, Dimitris Paparas, and Mihalis Yannakakis. The complexity of non-monotone markets. J. ACM, 64(3):20:1-20:56, 2017. URL:
  11. Yun Kuen Cheung. Analyzing Tatonnement Dynamics in Economics Markets. PhD thesis, Courant Institute of Mathematical Sciences, New York University, Proquest Dissertations Publishing, 2014. Available at URL:
  12. Yun Kuen Cheung and Richard Cole. Amortized analysis on asynchronous gradient descent. CoRR, abs/1412.0159, 2014. Google Scholar
  13. Yun Kuen Cheung, Richard Cole, and Nikhil Devanur. Tatonnement beyond gross substitutes? Gradient descent to the rescue. In STOC, pages 191-200, 2013. Full version available at URL:
  14. Yun Kuen Cheung, Richard Cole, and Ashish Rastogi. Tatonnement in ongoing markets of complementary goods. In EC, pages 337-354, 2012. URL:
  15. Yun Kuen Cheung, Richard Cole, and Yixin Tao. Dynamics of distributed updating in fisher markets. In Proceedings of the 2018 ACM Conference on Economics and Computation, Ithaca, NY, USA, June 18-22, 2018, EC '18, pages 351-368, 2018. URL:
  16. Yun Kuen Cheung, Richard Cole, and Yixin Tao. A unified approach to analyzing asynchronous coordinate descent - standard and partitioned. Submitted, 2018. Google Scholar
  17. Bruno Codenotti, Benton McCune, and Kasturi Varadarajan. Market equilibrium via the excess demand function. In STOC, pages 74-83, 2005. URL:
  18. Bruno Codenotti, Amin Saberi, Kasturi Varadarajan, and Yinyu Ye. Leontief economies encode nonzero sum two-player games. In Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithm, SODA '06, pages 659-667. Society for Industrial and Applied Mathematics, 2006. Google Scholar
  19. Richard Cole and Lisa Fleischer. Fast-converging tatonnement algorithms for one-time and ongoing market problems. In STOC, pages 315-324, 2008. URL:
  20. Richard Cole, Lisa Fleischer, and Ashish Rastogi. Discrete price updates yield fast convergence in ongoing markets with finite warehouses. CoRR, 2010. Google Scholar
  21. Constantinos Daskalakis, Paul W. Goldberg, and Christos H. Papadimitriou. The complexity of computing a nash equilibrium. SIAM J. Comput., 39(1):195-259, 2009. Google Scholar
  22. Nikhil R. Devanur, Christos H. Papadimitriou, Amin Saberi, and Vijay V. Vazirani. Market equilibrium via a primal-dual algorithm for a convex program. J. ACM, 55(5):22:1-22:18, 2008. Google Scholar
  23. Akitaka Dohtani. Global stability of the competitive economy involving complementary relations among commodities. Journal of Mathematical Economics, 22(1):73-83, 1993. Google Scholar
  24. Ran Duan and Kurt Mehlhorn. A combinatorial polynomial algorithm for the linear arrow-debreu market. Inf. Comput., 243:112-132, 2015. URL:
  25. Krishnamurthy Dvijotham, Yuval Rabani, and Leonard J. Schulman. Convergence of incentive-driven dynamics in fisher markets. In Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA '17, pages 554-567. Society for Industrial and Applied Mathematics, 2017. Google Scholar
  26. Eyal Even-Dar, Alexander Kesselman, and Yishay Mansour. Convergence time to nash equilibrium in load balancing. ACM Trans. Algorithms, 3(3):32, 2007. URL:
  27. K. Jain. A polynomial time algorithm for computing the arrow-debreu market equilibrium for linear utilities. In Forty Fifth Annual IEEE Symposium on Foundations of Computer Science, FOCS'04, pages pp. 286-294, Rome, Italy, 2004. Google Scholar
  28. Jonathan A. Kelner, Lorenzo Orecchia, Aaron Sidford, and Zeyuan Allen Zhu. A simple, combinatorial algorithm for solving SDD systems in nearly-linear time. In STOC, pages 911-920, 2013. Google Scholar
  29. Yin Tat Lee and Aaron Sidford. Efficient accelerated coordinate descent methods and faster algorithms for solving linear systems. In FOCS, pages 147-156, 2013. Google Scholar
  30. C. E. Lemke and J. T. Howson Jr. Equilibrium points of bimatrix games. Journal of the Society for Industrial and Applied Mathematics, 12(2):413-423, 1964. Google Scholar
  31. Jure Leskovec, Lars Backstrom, and Jon M. Kleinberg. Meme-tracking and the dynamics of the news cycle. In KDD, pages 497-506, 2009. Google Scholar
  32. Jason R. Marden and Jeff S. Shamma. Revisiting log-linear learning: Asynchrony, completeness and payoff-based implementation. Games and Economic Behavior, 75(2):788-808, 2012. Google Scholar
  33. James B. Orlin. Improved algorithms for computing Fisher’s market clearing prices. In Proceedings of the Forty Second Annual ACM Symposium on Theory of Computing, STOC'10, pages 291-300, 2010. Google Scholar
  34. Siddharth Pal and Richard J. La. Simple learning in weakly acyclic games and convergence to Nash equilibria, 2015. URL:
  35. Christos H. Papadimitriou and Mihalis Yannakakis. An impossibility theorem for price-adjustment mechanisms. PNAS, 5(107):1854-1859, 2010. Google Scholar
  36. Hirofumi Uzawa. Walras' tatonnement in the theory of exchange. Review of Economic Studies, 27(3):182-194, 1960. Google Scholar
  37. Vijay V. Vazirani and Mihalis Yannakakis. Market equilibrium under separable, piecewise-linear, concave utilities. J. ACM, 58(3):10:1-10:25, 2011. Google Scholar
  38. Léon Walras. Eléments d' Economie Politique Pure. Corbaz, 1874. (Translated as: Elements of Pure Economics. Homewood, IL: Irwin, 1954.). Google Scholar
  39. Fang Wu and Li Zhang. Proportional response dynamics leads to market equilibrium. In Proceedings of the Thirty-ninth Annual ACM Symposium on Theory of Computing, STOC '07, pages 354-363. ACM, 2007. URL:
  40. Yinyu Ye. A path to the arrow-debreu competitive market equilibrium. Math. Program., 111(1-2):315-348, 2008. URL:
  41. Li Zhang. Proportional response dynamics in the fisher market. Theor. Comput. Sci., 412(24):2691-2698, 2011. Google Scholar
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