The final step in getting an Israeli M.D. is performing a year-long internship in one of the hospitals in Israel. Internships are decided upon by a lottery, which is known as “The Internship Lottery”. In 2014 we redesigned the lottery, replacing it with a more efficient one. This paper presents the market, the redesign process and the new mechanism which is now in use. There are two main lessons that we have learned from this market. The first is the “Do No Harm” principle, which states that (almost) all participants should prefer the new mechanism to the old one. The second is that new approaches need to be used when dealing with two-body problems in object assignment. We focus on the second lesson, and study two-body problems in the context of the assignment problem. We show that decomposing stochastic assignment matrices to deterministic allocations is NP-hard in the presence of couples, and present a polynomial time algorithm with the optimal worst case guarantee. We also study the performance of our algorithm on real-world and on simulated data.

Assignment games represent a tractable model of two-sided markets with transfers. We study the likely properties of the core of randomly generated assignment games. When the joint productivity of every firm and worker has a noise element with a bounded distribution, with high probability all workers who have approximately the same human capital level are paid roughly equal wages, and all firms of similar quality make similar profits. This implies that core allocations vary significantly in balanced markets, but that there is core convergence in even slightly unbalanced markets. The same phenomenon occurs when firms' quality and workers' human capital level are complementary factors in productivity. When the noise element is unbounded, there may be a large variation in payoffs.

School choice districts that implement stable matchings face various design issues that impact students’ assignments to schools. We study properties of the rank distribution of students with random preferences, when schools use different tiebreaking rules to rank equivalent students. We find that under a multiple tiebreaking rule a vanishing fraction of students match to one of their top choices, in contrast to a single tiebreaking rule under which a constant fraction of students are assigned to one of their top choices. We find that when students can submit only a relatively short preference list, the multiple tiebreaking rule allows a constant fraction of students to match to one of their top choices, with only a “small” fraction of students remaining unmatched.

Upon completion of the medical studies, and before getting the diploma, doctors in Israel are required to do an internship in a hospital. For most students, the assignment is determined by a lottery, which takes into consideration the preferences of these students. We propose a novel way to perform this lottery, in which (on average) a larger number of students gets one of their top choices. We report about implementing this method in the 2014 Internship Lottery in Israel.

We present a bargaining model with incomplete information and players who repeatedly revise their actions over a finite period of time. For an open set of parameters, one-sided reputation-building leads to a deadline effect in the form of last-minute strategic interaction, and is linked with a non-negligible risk of reaching an inefficient outcome. Two-sided reputation-formation necessarily induces substantial delay and inefficiency with positive probability.