When bidders are not substitutes, we show that there is no standard ascending auction that implements a bidder-optimal competitive equilibrium under truthful bidding. Such an impossibility holds also in environments where the Vickrey payoff vector is a competitive equilibrium payoff and is thus stronger than de Vries, Schummer and Vohra’s [On ascending Vickrey auctions for heterogeneous objects...

We cast the problem of combinatorial auction design in a Bayesian framework in order to incorporate prior information into the auction process and minimize the number of rounds to convergence. We first develop a generative model of agent valuations and market prices such that clearing prices become maximum a posteriori estimates given observed agent valuations. This generative model then forms ...

We introduce several notions of potentials for mechanism design problems with interdependent values, and relate them to implementation in ex-post equilibrium. Whereas ex-post implementation is closely linked to the ordinal concept of best-alternative potentials, the celebrated Vickrey-Clarke-Groves mechanism corresponds to the stronger notion of a cardinal potential: agents agree not only on th...

Auctions are useful mechanism for allocating items (goods, tasks, resources, etc.) in multiagent systems. The bulk of auction theory assumes that the bidders’ valuations for items are given a priori. In many applications, however, the bidders need to expend significant effort to determine their valuations. In this paper we analyze computational bidder agents that can refine their valuations (ow...

where A = {j : q(j) > p(j)} is the of items whose prices have increased (in q relative to p). That is, whenever a bidder loses the items of S ∩ A because of being outbid, it still wants to retain the items S \ A it has, at the original prices. We saw several examples of GS valuations, including k-unit demand valuations, downward-sloping valuations for identical items, and so on. In this lecture...