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Approximation of Walrasian equilibrium in single-minded auctions

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Abstract

We consider a social optimization model of pricing scheme in single-minded auctions, in cases where Walrasian equilibrium does not exist. We are interested in the maximization of the ratio, R, of happy bidders over all agents, in a feasible allocation-pricing scheme. We show NP-hardness of the optimization problem, establish lower and upper bounds of R, as well as develop greedy algorithms to approximate the optimal value of R.

Keywords

Combinatorial auction
Walrasian equilibrium

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This work was supported by the National Natural Science Foundation of China (60135010, 60321002) and the Chinese National Key Foundation Research and Development Plan (2004CB318108).