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Eisenberg-Gale markets: Algorithms and game-theoretic properties

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  • Jain, Kamal
  • Vazirani, Vijay V.

Abstract

We define a new class of markets, the Eisenberg-Gale markets. This class contains Fisher's linear market, markets from the resource allocation framework of Kelly [Kelly, F.P., 1997. Charging and rate control for elastic traffic. Europ. Transactions Telecommunications 8, 33-37], as well as numerous interesting new markets. We obtain combinatorial, strongly polynomial algorithms for several markets in this class. Our algorithms have a simple description as ascending price auctions. Our algorithms lead to insights into game-theoretic properties of these markets, such as efficiency, fairness, and competition monotonicity. They also help determine if these markets always have rational equilibria. A classification of Eisenberg-Gale markets w.r.t. these properties reveals a surprisingly rich set of possibilities.

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  • Jain, Kamal & Vazirani, Vijay V., 2010. "Eisenberg-Gale markets: Algorithms and game-theoretic properties," Games and Economic Behavior, Elsevier, vol. 70(1), pages 84-106, September.
    • Handle: RePEc:eee:gamebe:v:70:y:2010:i:1:p:84-106
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    1. William C. Brainard & Herbert E. Scarf, 2005. "How to Compute Equilibrium Prices in 1891," American Journal of Economics and Sociology, Wiley Blackwell, vol. 64(1), pages 57-83, January.
    2. E. Eisenberg, 1961. "Aggregation of Utility Functions," Management Science, INFORMS, vol. 7(4), pages 337-350, July.
    3. Francisco Barahona, 1995. "Packing Spanning Trees," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 104-115, February.
    4. Groenevelt, H., 1991. "Two algorithms for maximizing a separable concave function over a polymatroid feasible region," European Journal of Operational Research, Elsevier, vol. 54(2), pages 227-236, September.
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    Cited by:

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    8. Gagan Goel & Vijay V. Vazirani, 2011. "A Perfect Price Discrimination Market Model with Production, and a Rational Convex Program for It," Mathematics of Operations Research, INFORMS, vol. 36(4), pages 762-782, November.
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    10. Kelli Francis-Staite, 2022. "Internal multi-portfolio rebalancing processes: Linking resource allocation models and biproportional matrix techniques to portfolio management," Papers 2201.06183, arXiv.org.
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    12. Martijn H. H. Schoot Uiterkamp & Marco E. T. Gerards & Johann L. Hurink, 2022. "On a Reduction for a Class of Resource Allocation Problems," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1387-1402, May.
    13. Anna Bogomolnaia & Herve Moulin & Fedor Sandomirskiy & Elena Yanovskaya, 2016. "Dividing Goods or Bads Under Additive Utilities," HSE Working papers WP BRP 147/EC/2016, National Research University Higher School of Economics.
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    17. Ashish Goel & Reyna Hulett & Benjamin Plaut, 2018. "Markets Beyond Nash Welfare for Leontief Utilities," Papers 1807.05293, arXiv.org, revised Dec 2019.

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