Optimal Stopping with Interdependent Values
Simon Mauras, Divyarthi Mohan, Rebecca Reiffenhäuser
TL;DR
The paper investigates online single-item selection under interdependent values in both prophet and secretary settings, connecting online stopping to Milgrom–Weber interdependent valuations. It introduces simple stopping rules that work with subadditive (and, in SOS cases, submodular-over-signals) valuation functions, yielding constant-factor welfare guarantees in both algorithmic and EPIC mechanism forms. Key results include a $4$-approximation for myopic prophet and an $8$-approximation mechanism, plus a $2e$-approximation algorithm and a $4e$-approximation truthful mechanism for secretary with farsighted or myopic agents, with improvements to $4$ for submodular-over-signals secretary valuations. The work thus bridges online decision theory and interdependent-valuation economics, providing constructive, implementable rules that degrade from the independent-values baselines by a factor of at most two (or four with incentives) and highlighting rich future research directions, including private valuations and combinatorial constraints.
Abstract
We study online selection problems in both the prophet and secretary settings, when arriving agents have interdependent values. In the interdependent values model, introduced in the seminal work of Milgrom and Weber [1982], each agent has a private signal and the value of an agent is a function of the signals held by all agents. Results in online selection crucially rely on some degree of independence of values, which is conceptually at odds with the interdependent values model. For prophet and secretary models under the standard independent values assumption, prior works provide constant factor approximations to the welfare. On the other hand, when agents have interdependent values, prior works in Economics and Computer Science provide truthful mechanisms that obtain optimal and approximately optimal welfare under certain assumptions on the valuation functions. We bring together these two important lines of work and provide the first constant factor approximations for prophet and secretary problems with interdependent values. We consider both the algorithmic setting, where agents are non-strategic (but have interdependent values), and the mechanism design setting with strategic agents. All our results are constructive and use simple stopping rules.