Eric Budish and Estelle Cantillon study this issue in a recent paper.  Suppose any mechanism that allocates students to slots in courses must be ex post efficient – i.e. there should be no room for making trades that make all students better off ex post – and that it is must be a dominant strategy for students to report their preferences truthfully (strategyproofness). It is well-known that the only mechanism that satisfies these two properties is random serial dictatorship (RSD): students are randomly assigned in order and each student gets to pick his entire course schedule in order.

In practice, at HBS, students choose one course at a time.  This cannot satisfy ex post efficiency and strategy-proofness and students must lie in equilibrium.  How do they lie and what welfare implications does it have relative to RSD?  Budish and Cantillon are able to answer this question because they have two sets of data: (1) they have data on how students actually played the mechanism and (2) they have data on the students’ true preferences from a survey.  The second set of data is rarely available.

First, by comparing actual play with reported preference they can see how students game the system.  Second, by using the reported preferences in the survey they can simulate what would have happened in the RSD. They can then compare the RSD outcome with the outcome in the mechanism used and make judgements about welfare.

Their results: Students gamed the system to take slots in popular courses.  For example, even if a popular course ranked low in a student’s ranking, he signed up for the course at the earliest opportunity fearing it would be gone if he waited.  This causes congestion and popular courses fill up quickly and people who value the course highly may not get in. Moreover, by the time the student bids on less popular courses, that course may be full even though it is high in his own ranking. So, there are two inefficiencies.  But still the HBS mechanism can dominate the RSD in terms of ex ante welfare. If a student is picked late and really values some course highly it may already be gone by the time they get to pick.  At least the HBS mechanism gives them some change to get some of their picks in early.  Despite the gaming, this can increase welfare ex ante.

This is a cool paper.  Some predictions of theory are borne out which is always nice.  More importantly, the welfare comparisons using real data make the paper quite original. Perhaps there is some room to tinker with the HBS mechanism and tis might lead to other insights.

As someone who knows more about Bayesian mechanism design than the strategyproofness literature, I am still trying to grope my way towards some unification of these approaches. It seems one should start off with some welfare criterion and some solution concept and maximize welfare subject to incentive constraints which depend on the solution concept.  If the solution concept is dominant strategy equilibrium, then this leads to dominant strategy incentive constraints.  This may not lead to ex post efficient allocations (see Jeff’s timely post about Myerson-Satterthwaite!) but it can improve ex ante welfare.  There is a large literature on Bayesian mechanism design; there is large literature on revenue equivalence.  But even in the latter case, the mechanism designer has a belief.  I guess this implies there is some room for dominant strategy mechanism design without a prior which I suppose is robust mechanism design.  Has this been approach been applied to market design?  My impression is that it has not…..

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