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WINE
2005
Springer

Walrasian Equilibrium: Hardness, Approximations and Tractable Instances

14 years 4 months ago
Walrasian Equilibrium: Hardness, Approximations and Tractable Instances
We study the complexity issues for Walrasian equilibrium in a special case of combinatorial auction, called single-minded auction, in which every participant is interested in only one subset of commodities. Chen et al. [5] showed that it is NP-hard to decide the existence of a Walrasian equilibrium for a single-minded auction and proposed a notion of approximate Walrasian equilibrium called relaxed Walrasian equilibrium. We show that every single-minded auction has a relaxed Walrasian equilibrium that satisfies at least two-thirds of the participants, proving a conjecture posed in [5]. Motivated by practical considerations, we introduce another concept of approximate Walrasian equilibrium called weak Walrasian equilibrium. We show NP-completeness and hardness of approximation results for weak Walrasian equilibria. In search of positive results, we restrict our attention to the tollbooth problem [19], where every participant is interested in a single path in some underlying graph. We g...
Ning Chen, Atri Rudra
Added 28 Jun 2010
Updated 28 Jun 2010
Type Conference
Year 2005
Where WINE
Authors Ning Chen, Atri Rudra
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