Kellogg is raising money for a new building. The Dean and the Great and the Good and doing fundraising. Various committees are in charge of deciding how people should be allocated to offices. Given by lack of political acumen and seniority, I know I will be next to the men’s restroom in the basement. The absence of amy ambiguity about the outcome means I am spending no time agonizing about my decision. But I imagine many of my colleagues are looking at proposed plans and wondering if they can get the corner office. Or will they prefer to be close to friends and co-authors at the cost of giving up a great view of the lake and fit young undergrads playing soccer on the lakeside fields?
Last week’s economic theory seminar speaker, Mariagiovanna Baccara, has a paper with several co-authors that offers an answer. The paper documents the experience of the faculty at an unnamed (but easily guessable) professional school which moved into a new building. The school decided to use a random serial dictatorship mechanism: the professors were split into four equivalence classes by rank (full professors, assistant etc.). Within each class, the order in which each player could choose an office was determined randomly. If there are no externalities, this mechanism achieves an efficient allocation. The first player to move gets the penthouse suite, the second player, the next best corner office etc. But if players care about which players they end up next to, the procedure is not efficient. Each player will not fully internalize the effects of his choice on others.
Before the move, the professors sat within departments and small clusters of like-minded fellow researchers. If the value of this and other networks is small, we would expect players to choose the “room with a view” strategy, picking the best physical location from the remaining offices. The authors compare the allocation that would have resulted if faculty chose offices based on physical characteristics alone with the allocation that actually arose. They find, for example, that co-authors are 36% more likely to be together in the actual allocation that the simulated allocations.
It is possible to estimate network effects a bit better. Aware of the possible inefficiencies of their mechanism, the designers relied on the Coase Theorem to help them out: The mechanism allowed faculty to exchange offices in exchange for cash from their research accounts. If arbitrary exchanges are implemented say between 10 faculty, then ex post exchange will achieve the surplus maximizing allocation. The initial allocation determined via the dictatorship will simply determine the status quo from which bargaining begins but not the final allocation: the famous idea of property right neutrality. But large scale exchanges involve transactions costs and there were few exchanges observed and the ones observed involved two professors. So the authors look at pairwise stable allocations. Combined with various separability assumptions on preferences, this equilibrium notion allows them to estimate network effects. They find co-authorship is more important than department affiliation and friendship. Once these effects are estimated and utilities identified, we can ask the value left on the table by pairwise stable allocations. The authors find an allocation that gives a 183% increases in utility compared to the implemented allocation.
As other schools move buildings, they will use other mechanisms. It will be interesting to study their experience.