Speaker: Halil İbrahim Bayrak, Bilkent University
Date & Time: February 18, 2022, Friday 17:00
Title: Distributionally Robust Optimal Allocation with Costly Verification
Abstract: A principal wants to allocate an object to a set of agents in a way that generates the highest payoff for himself. Each agent privately knows the payoff of the principal when he receives the object.
No monetary transfers are allowed due to efficiency concerns, but the principal can verify each agent’s type (private information) at a cost.
We assume that the agents’ types are distributed according to a probability distribution belonging to a commonly known ambiguity set.
When there is no ambiguity and the types are independent, optimal mechanisms are known to be favored-agent mechanisms, characterized by a favored agent and a threshold. If all agents other than the favored report a net payoff (type minus verification cost) under the threshold, the favored agent receives the good without being verified. Otherwise, the agent with the highest net payoff receives the object only after successful verification. We consider support-only and Markov ambiguity sets and show that there are infinitely many favored-agent mechanisms that maximize the principal’s worst-case payoff. Furthermore, we identify a Pareto robustly optimal favored-agent mechanism that is not out-performed by any other optimal mechanism. We see that the (Pareto
robustly) optimal choices of favored agents and thresholds do not depend on the verification costs. We also show that optimal mechanisms cannot be restricted to the set of favored-agent mechanisms under support-only ambiguity sets.
Bio: Halil İbrahim Bayrak is currently a visiting Ph.D. student in the Department of Electrical and Systems Engineering at the University of Pennsylvania, thanks to the Bideb grant 2214-A received from Tubitak. He received his B.S. and M.S. degrees in Industrial Engineering from Bilkent University in 2013 and 2015. At the time being, he is a Ph.D.
candidate in Industrial Engineering at Bilkent University. His research interests include mechanism design and robust optimization.