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News

June 18 at 4.40 pm - Research seminar by Dmitry Livdan (University of California, Berkeley) «Optimal Double Auction» joint with Alex Boulatov and Terrence Hendershott

Venue: Shabolovka st. 26, Room 3402

On Thursday, June 18 at 4.40 pm International College of Economics and Finance will hold the Research Seminar.
Speaker: Dmitry Livdan (University of California, Berkeley) <Curriculum Vitae>
Theme: «Optimal Double Auction» joint with Alex Boulatov and Terrence Hendershott
Venue: Shabolovka st. 26, Room 3402

Abstract: We consider a private value double-auction model which can be viewed as an extension of the model of Riley and Samuelson (1981) to the case of multiple sellers. Each seller has one unit of the same asset for sale and buyers compete to purchase one unit of the asset from one of the sellers. In the model sellers costlessly adjust their reserve prices, while sequentially moving buyers optimally choose between sellers to maximize their respective expected payoffs. The reserve price plays the role of a choice variable in the model, for both types of players. The refinement we propose in this paper is based on the following trade-off. From the sellers' perspective the probability of selling the good is increasing in the number of buyers bidding for it and, therefore, sellers have the incentive to decrease their reserve price to attract more buyers. From buyers' perspective, the probability of winning the auction decreases in the number of buyers and therefore buyers with higher private valuations are better off choosing sellers with slightly higher reserve price but fewer number of buyers. We exploit this trade-off to construct the symmetric Nash equilibrium in pure strategies in this double auction. Our first result is that such equilibrium exists and it is unique in the case of two sellers and the even number of buyers and it does not exist when the number of buyers is odd. The equilibrium reserve price is lower than the reserve price set by the monopolist (Riley and Samuelson (1981)) and each seller is visited by the same number of buyers. This is in contrast to the result of Burguet and Sakovics (1999) that there are no symmetric pure-strategy equilibria in the case of two competing sellers when buyers move simultaneously. Our second result is for the case of the number of buyers equal to the integer fraction m of the number of sellers. We show that the symmetric pure-strategy Nash equilibrium exists when m is below an endogenous cut-off m* which we fully characterize. This equilibrium is not unique as it is supported on the interval of the reserve prices.

Everyone interested is welcome to attend!

See the web-page of the seminar < http://icef.hse.ru/en/announcements/148649729.html >
Pass can be ordered by:
tel. +7 (495) 772-95-90 ext. 26090
e-mail: vzheleznov@hse.ru
contact: Slava Zheleznov