OPTIMIZATION OF THE AUCTION DURATION IN THE PRESENSE OF TIME-DEPENDANT COSTS
DOI:
https://doi.org/10.20998/2079-0023.2023.02.05Keywords:
auction, duration, optimization, forecasting, bidding, ordinal statistics, Poisson processAbstract
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.
References
Pro publichni zakupivli: Zakon Ukrainy vid 25.12.2015 №922-VIII: stanom na 01.01.023 [On Public Procurement: Law of Ukraine dated 25.12.2015 №922-VIII: as of 01.01.023]. URL: https://
zakon.rada.gov.ua/laws/show/922-19 (accessed 29.11.2023).
Melnikov O. S. Porivnialnyi analiz isnuiuchykh orhanizatsiinykh mekhanizmiv provedennia torhiv [Comparative Analysis of Different Organizational Mechanisms for Competitive Bidding]. Publichne upravlinnya: teoriya ta praktyka [Public administration: theory and practice]. Kharkiv, DocNaukDerzhUpr Publ., 2012. Vol. 1 (9), pp.130134. URL: https://repository.kpi.kharkov.ua/bitstream/KhPI-Press/2897/
/Melnykov_2012_Porivnialnyi%20analiz.pdf (accessed 29.11.2023).
Myerson R. Optimal auction design. Math. Oper. Res. 1981, vol. 6 (1), pp. 58–73.
Riley J., Samuelson W. Optimal Auctions. Amer. Econ. Review. 1981, vol. 71, pp. 381392.
Bulow J., Roberts J. The simple economics of optimal auctions. J. Polit. Econ. 1989, Vol. 97 (5), pp. 1060–1090.
Zhang H. The optimal sequence of prices and auctions. European Economic Review. 2021, 133 (2021) 103681. URL: https://doi.org/
1016/ j.euroecorev.2021 (accessed 29.11.2023).
Jusselin P., Mastrolia T., Rosenbaum, M. Optimal Auction Duration: A Price Formation Viewpoint. Operations Research. 2021, vol. 69 (6), pp. 173445.
Melnikov, O. S. Optymizatsiia strokiv provedennia konkursnykh torhiv [Optimization of Deadlines for Competitive Bidding Procedures]. Zbirnyk materialiv IV Mizhnarodnoyi konferencii "Strategiya innovaciynogo rozvytku ekonomyki: biznes, nauka, osvita” [Proc. of the 4th Int. Conf. “Strategy of innovative development of the economy: business, science, education”]. Kharkiv, NTU KhPI Publ., 2012, pp. 184186. URL: https://repository.
kpi.kharkov.ua/bitstream/KhPI-Press/39777/1/
Melnykov_Optymizatsiia_strokiv_2012.pdf (accessed 29.11.2023).
Vickrey W. Counterspeculation, Auctions, and Competitive Sealed Tenders. Journal of Finance. 1961, vol. 16, pp. 837.
Klemperer, P. Auctions: Theory and Practice. Princeton: Princeton University Press Publ., 2004. 256 p.
Weisstein, E. W. Order Statistic. MathWorld A Wolfram Web Resource. URL: https://mathworld.wolfram.com/OrderStatistic.html (accessed 29.11.2023).
Tunuguntla S., Hoban P. R. A Near-Optimal Bidding Strategy for Real-Time Display Advertising Auctions. J. of Marketing Research. 2021, vol. 58(1), pp. 121. DOI: 10.1177/002224372096854.
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