The problem of allocating courses to students is a famously hard problem of market design. The reasons include the fact that, in most applications, it isn't acceptable to sell the most desirable class places at higher prices to richer students. Also, students take multiple classes, and may have preferences for how their bundle is composed. So the problem is substantially more difficult than how to auction multiple goods, or how to allocate each student a single place, as comes up e.g. in assigning students to schools.
Eric Budish, who defended his Ph.D. dissertation at Harvard this week, has made a substantial, practical dent in the problem. His motivation comes from a detailed study, with Estelle Cantillon, of how classes are assigned to second year MBA students at the Harvard Business School, and how students approach this assignment problem strategically: Strategic Behavior in Multi-Unit Assignment Problems: Theory and Evidence from Course Allocations .
Largely motivated by what they learn about the good and not so good properties of the HBS mechanism, Eric then proposes a new mechanism: The Combinatorial Assignment Problem: Approximate Competitive Equilibrium from Equal Incomes. Eric's work, like market design in general, is eclectic. Among other things, he formulates new notions of what constitutes "fair" outcomes in cases hedged in by the impossibility results that abound when allocating indivisible goods.
Although allocating multiple indivisible items to each student makes the standard economic goals involving efficiency and incentives more difficult to achieve, it gives the designer somewhat more leeway to think about fairness, since although class places are indivisible, the package of classes that each student gets is not. And Eric’s investigations of existing course allocation institutions has convinced him that concerns about avoiding excessive ex-post unfairness are an important constraint on what kinds of mechanisms can be implemented in practice.
Eric's mechanism looks like it has legs, and may be ready for practical implementation in the not so distant future. Perhaps he'll get a chance to have more than the usual impact next year when he brings market design to U. Chicago's Booth School of Business (until recently Chicago GSB).
Welcome to the club, Eric.