Posted Pricing and Dynamic Prior-independent Mechanisms with Value Maximizers

We study posted price auctions and dynamic prior-independent mechanisms for (ROI-constrained) value maximizers. In contrast to classic (quasi-linear) utility maximizers, these agents aim to maximize their total value subject to a minimum ratio of value per unit of payment made. When personalized posted prices are allowed, posted price auctions for value maximizers can be reduced to posted price auctions for utility maximizers. However, for anonymous posted prices, the well-known 12 approximation for utility maximizers is impossible for value maxi-mizers and we provide a posted price mechanism with 12 (1 − 1 /e ) approximation. Moreover, we demonstrate how to apply our results to design prior-independent mechanisms in a dynamic environment; and to the best of our knowledge, this gives the first constant revenue approximation with multiple value maximizers. Finally, we provide an extension to combinatorial auctions with submodular / XOS agents.