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Competitive Equilibria for Non-quasilinear Bidders in Combinatorial Auctions

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 10123)

Abstract

quasilinearity is a ubiquitous and questionable assumption in the standard study of Walrasian equilibria. Quasilinearity implies that a buyer’s value for goods purchased in a Walrasian equilibrium is always additive with goods purchased with unspent money. It is a particularly suspect assumption in combinatorial auctions, where buyers’ complex preferences over goods would naturally extend beyond the items obtained in the Walrasian equilibrium.

We study Walrasian equilibria in combinatorial auctions when quasilinearity is not assumed. We show that existence can be reduced to an Arrow-Debreu style market with one divisible good and many indivisible goods, and that a “fractional” Walrasian equilibrium always exists. We also show that standard integral Walrasian equilibria are related to integral solutions of an induced configuration LP associated with a fractional Walrasian equilibrium, generalizing known results for both quasilinear and non-quasilnear settings.

Keywords

  • Competitive Equilibrium
  • Price Vector
  • Combinatorial Auction
  • Assignment Game
  • Complementary Slackness

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

R. Niazadeh—Supported by Google PhD Fellowship. This research was mostly done when the first author was doing an internship at Yahoo Research.

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Notes

  1. 1.

    We know that she chose a cup of coffee over a movie ticket initially, so that implies her value for a cup of coffee is less than her value for a movie ticket. On the other hand, there might also be complementarities here if the student is unable to enjoy the movie without first having a cup of coffee...

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Correspondence to Rad Niazadeh .

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Niazadeh, R., Wilkens, C.A. (2016). Competitive Equilibria for Non-quasilinear Bidders in Combinatorial Auctions. In: Cai, Y., Vetta, A. (eds) Web and Internet Economics. WINE 2016. Lecture Notes in Computer Science(), vol 10123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-54110-4_9

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  • DOI: https://doi.org/10.1007/978-3-662-54110-4_9

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