Elena Grigorieva

The private value single item bisection auction

In this paper we present a new iterative auction, the bisection auction, that can be used for the sale of a single indivisible object. The bisection auction has fewer rounds than the classical English auction and causes less information to be revealed than the Vickrey auction. Still, it preserves all characteristics the English auction shares with the Vickrey auction: there exists an equilibrium in weakly dominant strategies in which everyone behaves truthfully, the object is allocated in accordance with efficiency requirements to the buyer who has the highest valuation, and the price paid by the winner of the object equals the second-highest valuation

The communication complexity of private value single-item auctions

This paper is concerned with information revelation in single-item auctions. We compute how much data needs to be transmitted in three strategically equivalent auctions-the Vickrey auction, the English auction and the recently proposed bisection auction-and show that in the truth-telling equilibrium the bisection auction is the best performer.

On the Fastest Vickrey Algorithm

We investigate the algorithmic performance of Vickrey-Clarke-Groves mechanisms in the single item case. We provide a formal definition of a Vickrey algorithm for this framework, and give a number of examples of Vickrey algorithms. We consider three performance criteria, one corresponding to a Pareto criterion, one to worst-case analysis, and one related to first-order stochastic dominance. We show that Pareto best Vickrey algorithms do not exist and that worst-case analysis is of no use in discriminating between Vickrey algorithms. For the case of two bidders, we show that the bisection auction stochastically dominates all Vickrey algorithms. We extend our analysis to the study of weak Vickrey algorithms and winner determination algorithms. For the case of two bidders, we show that the One-Search algorithm stochastically dominates all column monotonic weak Vickrey algorithms and that a suitably adjusted version of the bisection algorithm, the WD bisection algorithm, stochastically dominates all winner determination algorithms. The WD bisection algorithm Pareto dominates all column monotonic winner determination algorithms in the n bidder case.

Inefficiency of Equilibria in Query Auctions with Continuous Valuations

We show that, when bidders have continuous valuations, any ex post equilibrium in an ex post individually rational query auction can only be ex post efficient when the running timeof the auction is infinite for almost all realizations of valuations of the bidders. We also show that this result applies to the general class of bisection auctions. In contrast we show that, when we allow for inefficient allocations with arbitrarily small probability, there is a query auction (to be more specific, a bisection auction) that attains this level of approximate efficiency in equilibrium, while additionally the running time of the auction in equilibrium is finite for all realizations of valuations.

Fraction Auctions: The Tradeoff between Efficiency and Running Time

This paper studies the sales of a single indivisible object where bidders have continuous valuations. In Grigorieva et al. [14] it was shown that, in this setting, query auctions necessarily allocate inefficiently in equilibrium. In this paper we propose a new sequential auction, called the c-fraction auction. We show the existence of an ex-post equilibrium, called bluff equilibrium, in which bidders behave truthfully except for particular constellations of observed bids at which it is optimal to pretend a slightly higher valuation. We show c-fraction auctions guarantee approximate efficiency at any desired level of accuracy, independent of the number of bidders, when bidders choose to play the bluff equilibrium. We discuss the running time and the efficiency in the bluff equilibrium. We show that by changing the parameter c of the auction we can trade off efficiency against running time. (This abstract was borrowed from another version of this item.)

The Family of C-Bisection Auctions: Efficiency and Running Time

In this paper we analyze the performance of a recently proposed sequential auction, called the c-bisection auction, that can be used for a sale of a single indivisible object. We discuss the running time and the efficiency in the ex-post equilibrium of the auction. We show that by changing the parameter c of the auction we can trade off efficiency against running time. Moreover, we show that the auction that gives the desired level of efficiency in expectation takes the same number of rounds for any number of players.