Computational optimization of auctioneer revenue in modified discrete Dutch auctions with cara risk preferences

Abstract

This research presents a computational optimization framework designed to maximize auctioneer revenue in modified discrete Dutch auctions by explicitly incorporating bidders’ risk preferences---modeled independently of wealth through the Constant Absolute Risk Aversion (CARA) utility function---thus enabling the analysis of risk-averse, risk-neutral, and risk-loving behaviors within the auction context. The study models bidders with three distinct risk profiles--risk-loving, risk-neutral, and risk-averse--employing nonlinear programming techniques to optimize expected revenues for the discrete bid levels. Discrete optimization methods are applied to analyze the impact of varying risk preferences, revealing that auctioneer revenue grows nonlinearly with bidder participation. For risk-neutral bidders (\alpha -> 0), revenue increases sharply from \mathscr{R}^* = 0.3849 for n=2 to \mathscr{R}^* = 0.8179 for n = 20 (a 112.5% increase), but the rate of growth declines significantly beyond n=30, with revenue plateauing near \mathscr{R}^* = 0.9454 for n = 100 (a mere 9.5\% increase from n = 30 to n = 100). Similar patterns hold for risk-averse (\alpha > 0) and risk-loving (\alpha < 0) bidders, though the magnitudes differ. Moreover, risk-loving bidders (for \alpha = -0.5) yield \mathscr{R}^* = 1.2122 for n = 100, a 28\% higher revenue than risk-neutral case with \mathscr{R}^*= 0.9454 and a 61% higher than risk-averse case (for \alpha = 0.5) with  \mathscr{R}^*=0.7519. This nonlinearity suggests diminishing marginal returns to additional bidders, a critical insight for auction design. The findings suggest that for larger bidder groups, fewer bid levels are sufficient for revenue maximization, with risk-averse behavior decreasing expected returns and risk-loving behavior amplifying them. This computational approach highlights the critical role of risk preferences in auction design, offering a robust mathematical model that can be adapted for broader applications in algorithmic auction mechanisms.