Nonlinear optimization of revenue per unit of time in discrete Dutch auctions with risk-aware bidders

Document Type : Research Article

Authors

• R.A. Shamim ^{1, 2}
• M.K. Majahar Ali ³

¹ School of Mathematical Sciences, Universiti Sains Malaysia, 11800, Pulau Penang, Malaysia.

² Department of Mathematics, University of Kotli, 11100, Azad Jammu and Kashmir, Pakistan.

³ School of Mathematical Sciences, Universiti Sains Malaysia, 11800, Pulau Pinang, Malaysia.

10.22067/ijnao.2025.93750.1656

Abstract

This study develops a computational framework to optimize the auctioneer’s revenue per unit of time in modified discrete Dutch auction by incorporating bidders’ risk preferences through the constant absolute risk aversion utility function. Bidders are categorized into three distinct risk profiles—risk-loving, risk-neutral, and risk-averse—allowing for a comprehensive analysis of how risk attitudes influence auction outcomes. A nonlinear programming methodology is utilized to ascertain the optimal revenue per unit time while incorporating discrete bid levels. The findings demonstrate that, at the outset, an increase in the number of bidders substantially boosts the revenue per unit time; nevertheless, after reaching a specific point, the incremental benefits decrease, resulting in a plateau. Additionally, the analysis suggests that, in auctions featuring larger pools of bidders, achieving maximum revenue per unit time necessitates fewer bid levels, as surplus bid levels do not yield further revenue improvements. Bidders exhibiting risk-averse tendencies tend to generate lower returns due to their cautious bidding patterns, whereas risk-seeking participants contribute to higher revenue per unit time by engaging in more assertive bidding. Collectively, these results highlight the significant influence of bidders’ risk preferences on auction design and establish a comprehensive mathematical framework that can be readily adapted to various algorithmic auction mechanisms. Behavioral interpretation via the prospect theory and alignment with published field evidence support the model’s external validity.

Keywords

• Auctions
• Constant absolute risk aversion
• Discrete Dutch auction
• Nonlinear programming
• Revenue per unit of time

Main Subjects

• Modeling and Simulation

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