Abstract: Tâtonnement processes in matching markets without transfers
I study two-sided many-to-one matching markets in which students are to be matched to schools and monetary transfers are not allowed. For each school, each student has an exogenously given score. I focus on tˆatonnement processes that can be interpreted as a simple model of dynamic matching markets in stationary environments. In these processes, (1) schools post minimal score requirements, or cuto↵s, (2) each student applies to her most preferred “a↵ordable” school, and (3) schools then react to demand-supply imbalances by adjusting their cuto↵s. An adjustment procedure describes how schools react to demand-supply imbalances. My main interest is to link the propensity to reach a market clearing cuto↵ vector to properties of adjustment procedures. The main condition is a regularity condition that requires cuto↵ adjustments to be bounded by the magnitude of demand-supply imbalances, that is, no over-demanded/under-demanded school should ever increase/decrease its cuto↵ by more than its excess demand/supply. It is shown that starting from any initial situation, a regular adjustment procedure always brings the market weakly closer to clearing. For the case where schools can at least temporarily maintain cuto↵s despite demand-supply imbalances, I introduce two simple adjustment procedures which always converge to market clearing. In case an instantaneous reaction to excess demand or excess supply is necessary, convergence to market-clearing can not be guaranteed if the market has more than one stable matching. However, all regular adjustment procedures are shown to eventually reach a point after which the cuto↵ of each school is always between the lowest and the highest level that is compatible with market clearing. In particular, regularity is enough to guarantee convergence when the market has a unique stable matching. I also relate my findings to the well known Boston mechanism.
|Event Information||Location Information|
|Oct 11, 2012 from 03:30 PM to 05:00 PM|
Tepper/GSIA Faculty Conference Center 322