Existence of 2-Competitive Pricing Beyond Utility Maximizers

Investigate whether a 2-competitive pricing rule exists for online auction agents with objectives beyond utility maximization.

Background

The paper develops prophet-inequality guarantees for online auctions in which agents may have stochastic price sensitivities, budgets, and objectives ranging from value maximization to utility maximization. For XOS combinatorial auctions, the half-pricing rule achieves competitive ratios that depend on the least price sensitivity, and the paper establishes tight bounds for the pricing rules it analyzes. However, the conclusion leaves unresolved whether the optimal 2-competitive guarantee known for utility-maximizing agents can be achieved by any pricing rule when agents have other objectives, including intermediate or mixed price sensitivities.