Information Design of the Mounty Hall Problem

In this talk, I will introduce the following variant of the Monty Hall Problem. There are n doors, behind each of which hides an a priori random reward, independently distributed according to a common prior. A clue box is attached to each door, which, if inspected, yields a clue about the rewards behind possibly all doors. The game host designs what clues to be put in each box and announces at the beginning of the game what each clue reveals about the rewards. Given the design, the player decides sequentially which clue box to inspect by paying an inspection fee and when to stop inspecting the boxes. Upon stopping, the player can then utilize the clues collected so far to open a door whose attached box has already been inspected and take the reward behind it. The player wishes to maximize the reward obtained from the opened door, while the host maximizes the fees collected from inspections. Under specific designs, the player's problem can be reduced to several classic sequential information acquisition problems, such as the Pandora's box problem or the Wald's sequential sampling problem. I will discuss the optimal designs of the clue boxes when the host faces different informational constraints.  These informational constraints arise from the potential applications in different settings such as product-page design on online platforms, information design in delegated search, and reward design in video games.

Short Bio: Zhenyu Hu is a Dean’s Chair Associate Professor at the Department of Analytics & Operations at the National University of Singapore. He obtained his PhD in industrial engineering from the University of Illinois at Urbana-Champaign and a bachelor in mathematics from Sun Yat-sen University. His research focuses on dynamic pricing and revenue management, supply chain management, and mechanism and information design. He currently serves as an associate editor for M&SOM.