Approximation of Walrasian equilibrium in single-minded auctions

Approximation of Walrasian equilibrium in single-minded auctions

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 a...

Ascending auctions and Walrasian equilibrium

We present a family of submodular valuation classes that generalizes gross substitute. We show that Walrasian equilibrium always exist for one class in this family, and there is a natural ascending auction which finds it. We prove some new structural properties on gross-substitute auctions which, in turn, show that the known ascending auctions for this class (Gul-Stacchetti and Ausbel) are, in ...

Efficient Interdependent Value Combinatorial Auctions with Single Minded Bidders

We study the problem of designing efficient auctions where bidders have interdependent values; i.e., values that depend on the signals of other agents. We consider a contingent bid model in which agents can explicitly condition the value of their bids on the bids submitted by others. In particular, we adopt a linear contingent bidding model for single minded combinatorial auctions (CAs), in whi...

Walrasian Price Equilibrium

Walrasian Equilibrium with Gross Substitutes

Sloan Foundation for their support. We are grateful to Vincent Crawford who provided valuable comments and pointed out to us the connection between Kelso and Crawford [5] and our work, to John Geanakoplos for suggesting a weakening of our main assumption, and to Don Brown for valuable comments.