Manipulability in Matching Markets: Conflict and Coincidence of Interests

We study comparative statics of manipulations by women in the men-proposing deferred acceptance mechanism in the two-sided one-to-one marriage market. We prove that if a group of women employs truncation strategies or weakly successfully manipulates, then all other women weakly benefit and all men are weakly harmed. We show that our results do not appropriately generalize to the many-to-one college admissions model.matching, deferred acceptance, manipulability, welfare

Matching with Couples Revisited

It is well known that a stable matching in a many-to-one matching market with couples need not exist. We introduce a new matching algorithm for such markets and show that for a general class of large random markets the algorithm will find a stable matching with high probability. In particular we allow the number of couples to grow at a near-linear rate. Furthermore, truth-telling is an approximated equilibrium in the game induced by the new matching algorithm. Our results are tight: for markets in which the number of couples grows at a linear rate, we show that with constant probability no stable matching exists

A Noncooperative Support for Equal Division in Estate Division Problems

We consider estate division problems, a generalization of bankruptcy problems. We show that in a direct revelation claim game, if the underlying division rule satisfies efficiency, equal treatment of equals, and weak order preservation, then all (pure strategy) Nash equilibria induce equal division. Next, we consider division rules satisfying efficiency, equal treatment of equals, and claims monotonicity. For claim games with at most three agents, again all Nash equilibria induce equal division. Surprisingly, this result does not extend to claim games with more than three agents. However, if nonbossiness is added, then equal division is restored.Bankruptcy/estate division problems, claims monotonicity, direct revelation claim game, equal division, equal treatment of equals, Nash equilibria, nonbossiness, (weak) order preservation.

Interviewing Matching in Random Markets

In many centralized labor markets candidates interview with potential employers before matches are formed through a clearinghouse One prominent example is the market for medical residencies and fellowships, which in recent years has had a large increase in the number of interviews. There have been numerous efforts to reduce the cost of interviewing in these markets using a variety of signalling mechanisms, however, the theoretical properties of these mechanisms have not been systematically studied in models with rich preferences. In this paper we give theoretical guarantees for a variety of mechanisms, finding that these mechanisms must properly balance competition. We consider a random market in which agents' latent preferences are based on observed qualities, personal taste and (ex post) interview shocks and assume that following an interview mechanism a final stable match is generated with respect to preferences over interview partners. We study a novel many-to-many interview match mechanism to coordinate interviews and that with relatively few interviews, when suitably designed, the interview match yields desirable properties. We find that under the interview matching mechanism with a limit of $k$ interviews per candidate and per position, the fraction of positions that are unfilled vanishes quickly with $k$. Moreover the ex post efficiency grows rapidly with $k$, and reporting sincere pre-interview preferences to this mechanism is an $\epsilon$-Bayes Nash equilibrium. Finally, we compare the performance of the interview match to other signalling and coordination mechanisms from the literature

New Challenges in Multihospital Kidney Exchange

The growth of kidney exchange presents new challenges for the design of kidney exchange clearinghouses. The players now include directors of transplant centers, who see sets of patient-donor pairs, and can choose to reveal only difficult-to-match pairs to the clearinghouse, while withholding easy-to-match pairs to transplant locally. This reduces the number of transplants. We discuss how the incentives for hospitals to enroll all pairs in kidney exchange can be achieved, and how the concentration of hard to match pairs increases the importance of long, non-simultaneous nondirected donor chains