Delegated online search

In a delegation problem, a principal Ƥ with commitment power tries to pick one out of n options. Each option is drawn independently from a known distribution. Instead of inspecting the options herself, Ƥ delegates the information acquisition to a rational and self-interested agent A . After inspection, A proposes one of the options, and Ƥ can accept or reject. In this paper, we study a natural online variant of delegation, in which the agent searches through the options in an online fashion. How can we design algorithms for Ƥ that approximate the utility of her best option in hindsight? We show that Ƥ can obtain a Θ(1/ n )-approximation and provide more fine-grained bounds independent of n based on two parameters. If the ratio of maximum and minimum utility for A is bounded by a factor α, we obtain an Ω(log log α/ log α)- approximation algorithm, and we show that this is best possible. If Ƥ cannot distinguish options with the same value for herself, we show that ratios polynomial in 1/α cannot be avoided. If the utilities of Ƥ and A for each option are related by a factor β, we obtain an Ω(1/ log β)-approximation, and Ω(log log β/ log β) is best possible.