Approximately Stable, School Optimal, and Student-Truthful Many-to-One Matchings (via Differential Privacy)

We present a mechanism for computing asymptotically stable school optimal matchings, while guaranteeing that it is an asymptotic dominant strategy for every student to report their true preferences to the mechanism. Our main tool in this endeavor is differential privacy: we give an algorithm that coordinates a stable matching using differentially private signals, which lead to our truthfulness guarantee. This is the first setting in which it is known how to achieve nontrivial truthfulness guarantees for students when computing school optimal matchings, assuming worst- case preferences (for schools and students) in large markets

Game Changers: Rewriting the Playbook A Sports and Entertainment Law Symposium

Attorney Steven Howard Roth participated in the following fireside chat with Akron Law Review Associate Editor Andrew Fleming as part of the Akron Law Review 2023 Symposium at The University of Akron School of Law in April 2023. Some content may be modified and/or abbreviated from its original transcript for purposes of flow and brevity. Attorney Roth is the Founder and a Principal of Roth Firm, LLC, a law firm that represents individuals and domestic and international companies within the middle and upper middle market in business and transactional matters. Attorney Roth’s practice focuses on the areas of mergers and acquisitions, corporate transactions and governance, sports, media and entertainment, intellectual property law, securities, and commercial real estate. Leveraging his unique skill set and experience, Attorney Roth has successfully negotiated and closed over $850 million in transactions for his clients. Since 2020, Attorney Roth has been recognized each year as a Best Lawyers: Ones to Watch and an Ohio Super Lawyers Rising Star. Prior to starting Roth Firm, Attorney Roth worked for several private businesses and organizations, including a regional law firm, as counsel for a private equity company, and as a legal consultant for a multi-billion dollar steel company. Attorney Roth has also worked for multiple professional sports teams, including NFL and NBA franchise teams, governing bodies, and sports agencies. Attorney Roth holds a JD and MBA, with a concentration in banking and finance, from Case Western Reserve University

Private Matchings and Allocations

We consider a private variant of the classical allocation problem: given k goods and n agents with individual, private valuation functions over bundles of goods, how can we partition the goods amongst the agents to maximize social welfare? An important special case is when each agent desires at most one good, and specifies her (private) value for each good: in this case, the problem is exactly the maximum-weight matching problem in a bipartite graph. Private matching and allocation problems have not been considered in the differential privacy literature, and for good reason: they are plainly impossible to solve under differential privacy. Informally, the allocation must match agents to their preferred goods in order to maximize social welfare, but this preference is exactly what agents wish to hide. Therefore, we consider the problem under the relaxed constraint of joint differential privacy: for any agent i, no coalition of agents excluding i should be able to learn about the valuation function of agent i. In this setting, the full allocation is no longer published---instead, each agent is told what good to get. We first show that with a small number of identical copies of each good, it is possible to efficiently and accurately solve the maximum weight matching problem while guaranteeing joint differential privacy. We then consider the more general allocation problem, when bidder valuations satisfy the gross substitutes condition. Finally, we prove that the allocation problem cannot be solved to non-trivial accuracy under joint differential privacy without requiring multiple copies of each type of good.Comment: Journal version published in SIAM Journal on Computation; an extended abstract appeared in STOC 201