Optimal Stopping with Interdependent Values

TL;DR

This paper develops the first constant factor approximation algorithms for online prophet and secretary problems with interdependent values, bridging economic and algorithmic approaches for strategic and non-strategic agents.

Contribution

It introduces novel algorithms with simple stopping rules for interdependent values in prophet and secretary models, achieving constant factor approximations.

Findings

First constant factor approximation for prophet problems with interdependent values.

First constant factor approximation for secretary problems with interdependent values.

Applicable to both strategic and non-strategic agent settings.

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.