Optimizing discrete dutch auctions with time considerations: a strategic approach for lognormal valuation distributions

Raja Aqib Shamim; Majid Khan Majahar Ali

doi:10.46481/jnsps.2025.2291

Authors

Raja Aqib Shamim School of Mathematical Sciences, Universiti Sains Malaysia, 11800, Pulau Penang, Malaysia | Department of Mathematics, University of Kotli, 11100, Azad Jammu and Kashmir, Pakistan https://orcid.org/0000-0002-2531-1249
Majid Khan Majahar Ali
majidkhanmajaharali@usm.my
School of Mathematical Sciences, Universiti Sains Malaysia, 11800, Pulau Penang, Malaysia https://orcid.org/0000-0002-5558-5929

Keywords:

Auctions, Lognormal distribution, Nonlinear programming, Discrete Dutch auction, Revenue optimization

Abstract

This research deviates from usual studies in auction literature primarily focused on maximizing expected revenue. Instead, we concentrate on the strategic design of discrete Dutch auctions in the context of bidder emotional attachment, wherein valuations follow a lognormal distribution. Our objective is to attain an optimal balance between the auctioned object’s selling price and the auction duration, ultimately maximizing the auctioneer’s expected revenue per unit of time. Our proposed models exhibit significantly higher average revenues per unit of time than counterparts neglecting time considerations and emotional attachment of the bidders. This achievement results from strategically reducing auction durations, enabling more auctions within the allotted time. This intentional trade-off ensures the marginal revenue decrease in shorter auctions is surpassed by the substantial increase in overall revenues from heightened auction frequency. Numerical results emphasize the utility of our modified discrete Dutch auction design, particularly in scenarios with a large number of bidders. Furthermore, increasing skewness in valuation distributions correlates with higher revenue per unit of time. Complete knowledge of the number of participating bidders is crucial, leading to a noticeable elevation in the auctioneer’s expected revenue per unit of time. However, the predictability of auction outcomes may be challenging, underscoring the nuanced nature of auction dynamics.

Dimensions

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