The assignment problem with initial endowments (the "housing market") is a cornerstone of mechanism design. In the deterministic setting, Ma (1994) famously characterized the Top Trading Cycles (TTC) rule as the unique mechanism that satisfies strategy-proofness, Pareto efficiency, and individual rationality.

In this talk, I explore whether expanding the domain to probabilistic assignments allows for new, perhaps fairer, mechanisms. While randomization often bypasses impossibility results in mechanism design, we show a striking "collapse" in the housing market. We prove that if agents have deterministic initial endowments, TTC remains the only admissible rule, even under the weakest notions of strategy-proofness and efficiency extended to lotteries. I will detail this characterization, discuss some known impossibility results for probabilistic endowments for more than three agents, and conclude with some open problems in the design of exchange mechanisms.

Short Bio:

Dr. Soumyarup Sadhukhan is an Assistant Professor in the Department of Mathematics and Statistics at the Indian Institute of Technology (IIT) Kanpur. His primary research interests lie at the intersection of mathematics and economics, specifically in Game Theory, Mechanism Design, and Choice Theory.

Dr. Sadhukhan earned his PhD from the Economic Research Unit of the Indian Statistical Institute (ISI), Kolkata, where his thesis focused on probabilistic mechanism design. Prior to joining IIT Kanpur, he served as a C.V. Raman Post-doctoral Fellow at the Department of Computer Science and Automation, Indian Institute of Science (IISc), Bangalore.

His current work explores the axiomatic foundations of resource allocation, with a focus on probabilistic assignment problems and fair division. His research has been published in reputable journals, including the Journal of Economic Theory, Journal of Mathematical Economics, and Mathematics of Operations Research.