Guillaume Haeringer

Constrained School Choice

Recently, several school districts in the US have adopted or consider adopting the Student-Optimal Stable mechanism or the Top Trading Cycles mechanism to assign children to public schools. There is evidence that for school districts that employ (variants of) the so-called Boston mechanism the transition would lead to efficiency gains. The first two mechanisms are strategy-proof, but in practice student assignment procedures typically impede a student to submit a preference list that contains all his acceptable schools. We study the preference revelation game where students can only declare up to a fixed number of schools to be acceptable. We focus on the stability and efficiency of the Nash equilibrium outcomes. Our main results identify rather stringent necessary and sufficient conditions on the priorities to guarantee stability or efficiency of either of the two mechanisms. This stands in sharp contrast with the Boston mechanism which has been abandoned in many US school districts but nevertheless yields stable Nash equilibrium outcomes.

A characterization of the single-peaked domain

We provide in this paper two properties that are both necessary and sufficient to characterize the domain of single-peaked preference profiles. This characterization allows for a definition of single-peaked preference profiles without using an ad hoc underlying order of the alternatives and also sheds light on the structure of single-peaked profiles. Considering the larger domain of value-restricted preference profiles (Sen, Econometrica 34:491–499, 1966) we also provide necessary and sufficient conditions for a preference profile to be single-caved or group-separable. Our results show that for single-peaked, single-caved and group-separable profiles it is sufficient to restrict to profiles containing of either three individuals and three alternatives or two individuals and four alternatives.

Decentralized job matching

This paper studies a multi-stage decentralized matching model where firms sequentially propose their (unique) positions to workers. At each stage workers sequentially decide which offer to accept (if any). A firm whose offer has been declined may make an offer to another worker in the next stage. The game stops when all firms either have been matched to a worker or have already made unsuccessful offers to any worker remaining in the market. We show that there is a unique subgame-perfect equilibrium outcome, the worker-optimal matching. Firms in this game have a weakly dominant strategy, which consists of making offers in the same order as given by their preferences. When workers play simultaneously any stable matching can be obtained as an equilibrium outcome, but an unstable matching can obtain in equilibrium.

More Strategies, More Nash Equilibria

This short paper isolates a non-trivial class of games for which there exists a monotone relation between the size of pure strategy spaces and the number of pure Nash equilibria (Theorem). This class is that of two- player nice games, i.e., games with compact real intervals as strategy spaces and continuous and strictly quasi-concave payoff functions, assumptions met by many economic models. We then show that the sufficient conditions for Theorem to hold are tight.

Equilibrium binding agreements: a comment

Abstract To construct their Equilibrium Binding Agreements, Ray and Vohra (J. Econ. Theory, 73 (1997) 30–78) define a concept of an equilibrium between coalitions and prove its existence for any coalition structure. We show that this result crucially depends on the quasi-concavity of the utility functions, which in turn depends on the type of mixed strategies used by the coalitions. When coalitions use uncorrelated mixed strategies utility functions may not be quasi-concave and an equilibrium may not exist. However, if coalitions use correlated strategies, an equilibrium always exist.

A comment on “School choice: An experimental study” [J. Econ. Theory 127 (1) (2006) 202–231]☆

We show that one of the main results in Chen and Sonmez (2006, 2008) [6] and [7] does no longer hold when the number of recombinations is sufficiently increased to obtain reliable conclusions. No school choice mechanism is significantly superior in terms of efficiency.

Better-reply Dynamics in Deferred Acceptance Games

In this paper we address the question of learning in a two-sided matching mechanism that utilizes the deferred acceptance algorithm. We consider a repeated matching game where at each period agents observe their match and have the opportunity to revise their strategy (i.e., the preference list they will submit to the mechanism). We focus in this paper on better-reply dynamics. To this end, we rst provide a characterization of better-replies and a comprehensive description of the dominance relation between strategies. Better-replies are shown to have a simple structure and can be decomposed into four types of changes. We then present a simple better-reply dynamics with myopic and boundedly rational agents and identify conditions that ensure that limit outcomes are outcome equivalent to the outcome obtained when agents play their dominant strategies. Better-reply dynamics may not converge, but if they do converge, then the limit strategy proles constitute a subset of the Nash equilibria of the stage game. JEL codes C72, D41.