OPTIMIZATION OF THE AUCTION DURATION IN THE PRESENSE OF TIME-DEPENDANT COSTS

Abstract

This paper examines the influence of the duration of auctions or tenders on the expected gain of their organizer. Extending the duration of bidding affects auction results in two ways. On the one hand, it allows attracting a larger number of participants to the auction, and the competition between them increases the chances of the auctioneer to get a better price. On the other hand, delaying bids delays the receipt of money (for auctions) or required goods or services (for tenders), and time has value in itself. The influence of these two factors, which act in opposite directions, suggests the existence of an optimal duration of the bidding process. The paper develops a mathematical model of bidding, which formalizes these considerations and provides an algorithm to determine their optimal duration. The arrival of bidders willing to participate in the auction is modeled as a Poisson process. Each participant is characterized by his own assessment of the value of the object put up for auction. These estimates are assumed to be independent identically distributed random variables drawn from some parametric distribution. Under these assumptions, Myerson's revenue equivalence theorem makes it possible to predict the expected results of the auction as a function of the number of bidders, regardless of the auction rules. On this basis, it is possible to compare the benefits and costs associated with changing the duration of time for accepting applications for participation in bidding, which makes it possible to determine its optimal value. The obtained optimality conditions have a meaningful and intuitive economic interpretation. For practical applications, the use of Monte Carlo methods based on the empirical distribution of bid and ask prices is proposed. The practical implementation of the proposed algorithm can improve the economic performance of the auctioneer, which is especially relevant for the public sector of the economy.