Dynamics of distributed updating in fisher markets

Yun Kuen Cheung, Richard Cole, Yixin Tao

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

A major goal in Algorithmic Game Theory is to justify equilibrium concepts from an algorithmic and complexity perspective. One appealing approach is to identify natural distributed algorithms that converge quickly to an equilibrium. This paper established new convergence results for two generalizations of proportional response in Fisher markets with buyers having CES utility functions. The starting points are respectively a new convex and a new convex-concave formulation of such markets. The two generalizations correspond to suitable mirror descent algorithms applied to these formulations. Several of our new results are a consequence of new notions of strong Bregman convexity and of strong Bregman convex-concave functions, and associated linear rates of convergence, which may be of independent interest. Among other results, we analyze a damped generalized proportional response and show a linear rate of convergence in a Fisher market with buyers whose utility functions cover the full spectrum of CES utilities aside the extremes of linear and Leontief utilities; when these utilities are included, we obtain an empirical O(1/T) rate of convergence.

Original languageEnglish (US)
Title of host publicationACM EC 2018 - Proceedings of the 2018 ACM Conference on Economics and Computation
PublisherAssociation for Computing Machinery, Inc
Pages351-368
Number of pages18
ISBN (Electronic)9781450358293
DOIs
StatePublished - Jun 11 2018
Event19th ACM Conference on Economics and Computation, EC 2018 - Ithaca, United States
Duration: Jun 18 2018Jun 22 2018

Other

Other19th ACM Conference on Economics and Computation, EC 2018
CountryUnited States
CityIthaca
Period6/18/186/22/18

Fingerprint

Updating
Rate of Convergence
Utility Function
Game theory
Algorithmic Game Theory
Directly proportional
Parallel algorithms
Mirrors
Descent Algorithm
Formulation
Concave function
Distributed Algorithms
Damped
Convergence Results
Justify
Convex function
Convexity
Mirror
Extremes
Cover

Keywords

  • Bregman divergence
  • Fisher market
  • Mirror descent
  • Proportional response

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Statistics and Probability
  • Computational Mathematics
  • Economics and Econometrics

Cite this

Cheung, Y. K., Cole, R., & Tao, Y. (2018). Dynamics of distributed updating in fisher markets. In ACM EC 2018 - Proceedings of the 2018 ACM Conference on Economics and Computation (pp. 351-368). Association for Computing Machinery, Inc. https://doi.org/10.1145/3219166.3219189

Dynamics of distributed updating in fisher markets. / Cheung, Yun Kuen; Cole, Richard; Tao, Yixin.

ACM EC 2018 - Proceedings of the 2018 ACM Conference on Economics and Computation. Association for Computing Machinery, Inc, 2018. p. 351-368.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Cheung, YK, Cole, R & Tao, Y 2018, Dynamics of distributed updating in fisher markets. in ACM EC 2018 - Proceedings of the 2018 ACM Conference on Economics and Computation. Association for Computing Machinery, Inc, pp. 351-368, 19th ACM Conference on Economics and Computation, EC 2018, Ithaca, United States, 6/18/18. https://doi.org/10.1145/3219166.3219189
Cheung YK, Cole R, Tao Y. Dynamics of distributed updating in fisher markets. In ACM EC 2018 - Proceedings of the 2018 ACM Conference on Economics and Computation. Association for Computing Machinery, Inc. 2018. p. 351-368 https://doi.org/10.1145/3219166.3219189
Cheung, Yun Kuen ; Cole, Richard ; Tao, Yixin. / Dynamics of distributed updating in fisher markets. ACM EC 2018 - Proceedings of the 2018 ACM Conference on Economics and Computation. Association for Computing Machinery, Inc, 2018. pp. 351-368
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