Nash equilibria in fisher market

Bharat Adsul, Ch Sobhan Babu, Jugal Garg, Ruta Mehta, Milind Sohoni

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

Abstract

Much work has been done on the computation of market equilibria. However due to strategic play by buyers, it is not clear whether these are actually observed in the market. Motivated by the observation that a buyer may derive a better payoff by feigning a different utility function and thereby manipulating the Fisher market equilibrium, we formulate the Fisher market game in which buyers strategize by posing different utility functions. We show that existence of a conflict-free allocation is a necessary condition for the Nash equilibria (NE) and also sufficient for the symmetric NE in this game. There are many NE with very different payoffs, and the Fisher equilibrium payoff is captured at a symmetric NE. We provide a complete polyhedral characterization of all the NE for the two-buyer market game. Surprisingly, all the NE of this game turn out to be symmetric and the corresponding payoffs constitute a piecewise linear concave curve. We also study the correlated equilibria of this game and show that third-party mediation does not help to achieve a better payoff than NE payoffs.

Original languageEnglish (US)
Title of host publicationAlgorithmic Game Theory - Third International Symposium, SAGT 2010, Proceedings
Pages30-41
Number of pages12
EditionM4D
DOIs
StatePublished - Dec 6 2010
Externally publishedYes
Event3rd International Symposium on Algorithmic Game Theory, SAGT 2010 - Athens, Greece
Duration: Oct 18 2010Oct 20 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberM4D
Volume6386 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other3rd International Symposium on Algorithmic Game Theory, SAGT 2010
CountryGreece
CityAthens
Period10/18/1010/20/10

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Adsul, B., Babu, C. S., Garg, J., Mehta, R., & Sohoni, M. (2010). Nash equilibria in fisher market. In Algorithmic Game Theory - Third International Symposium, SAGT 2010, Proceedings (M4D ed., pp. 30-41). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6386 LNCS, No. M4D). https://doi.org/10.1007/978-3-642-16170-4_4