TL;DR#
Classic prophet inequalities assume passive reward distributions. However, in many real-world applications, rewards are associated with strategic players who can manipulate information revelation to maximize their chances of being selected. This paper investigates the robustness of simple threshold policies under such strategic manipulations. It focuses on how these players act and what is the impact on the searcher.
The paper provides a formal analysis of the optimal information revealing strategy for each strategic player, showing that they will use simple thresholding mechanisms. Then it demonstrates the intrinsic robustness of prophet inequalities to this strategic reward signaling, showing that simple threshold policies achieve a good approximation ratio, even in the strategic case. This is particularly true in cases like identical and log-concave reward distributions. The findings improve our understanding of how to design effective search policies in situations where players act strategically.
Key Takeaways#
Why does it matter?#
This paper is crucial for researchers in optimal stopping problems and mechanism design. It bridges the gap between theoretical models and real-world strategic interactions, addressing limitations of classic prophet inequalities. The findings highlight the robustness of simple threshold policies even under strategic reward signaling, opening avenues for more realistic and applicable models in economics, online advertising and more.
Visual Insights#
Full paper#
