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A Perfect Price Discrimination Market Model with Production, and a (Rational) Convex Program for It

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Algorithmic Game Theory (SAGT 2010)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 6386))

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Abstract

Recent results showed PPAD-completeness of the problem of computing an equilibrium for Fisher’s market model under additively separable, piecewise-linear, concave utilities. We show that introducing perfect price discrimination in this model renders its equilibrium polynomial time computable. Moreover, its set of equilibria are captured by a convex program that generalizes the classical Eisenberg-Gale program, and always admits a rational solution.

We also introduce production into our model; our goal is to carve out as big a piece of the general production model as possible while still maintaining the property that a single (rational) convex program captures its equilibria, i.e., the convex program must optimize individually for each buyer and each firm.

Research supported by NSF Grants CCF-0728640 and CCF-0914732, ONR Grant N000140910755, and a Google Research Grant.

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Author information

Authors and Affiliations

  1. Georgia Institute of Technology, Atlanta

    Gagan Goel & Vijay Vazirani

Authors
  1. Gagan Goel
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  2. Vijay Vazirani
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Editor information

Editors and Affiliations

  1. Lecturer, Department of Computer Science, University of Ioannina, Dourouti University Campus, 45110, Ioannina, Greece

    Spyros Kontogiannis

  2. Department of Informatics and Telecommunications Panepistimiopolis, Ilissia, Professor, National and Kapodistrian University of Athens, 15784, Athens, Greece

    Elias Koutsoupias

  3. Computer Engineering and Informatics Department (CEID), University of Patras, 26500, Patras, Greece

    Paul G. Spirakis

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Goel, G., Vazirani, V. (2010). A Perfect Price Discrimination Market Model with Production, and a (Rational) Convex Program for It. In: Kontogiannis, S., Koutsoupias, E., Spirakis, P.G. (eds) Algorithmic Game Theory. SAGT 2010. Lecture Notes in Computer Science, vol 6386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16170-4_17

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  • DOI: https://doi.org/10.1007/978-3-642-16170-4_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16169-8

  • Online ISBN: 978-3-642-16170-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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