Working Paper

Ex-ante Heterogeneity in Directed Search Games

Directed search models usually assume that workers' skills are drawn from the same distribution. I study a game in which finitely many workers, each knowing his own skill, apply to one of two firms, and each firm hires its most skilled applicant. The standard symmetric equilibrium turns out to be fragile: it is very sensitive to small differences in workers' skill distributions. I characterize an equilibrium that survives such differences, show that it always exists, and show that it is in a sense the only equilibrium robust to all small asymmetries. The robust equilibrium can be constructed by a recursive algorithm, and I relate it to the symmetric equilibrium used in the literature. 

Selling Mechanisms Under Misspecified Learning (Job Market Paper)

Buyers in a repeated selling mechanism do not observe its allocation rule. Each holds a possibly misspecified parametric model of his win probability, bids optimally under his current belief about the model’s parameter, and learns by Bayesian updating under that model from allocation outcomes alone. The mechanism generates those outcomes, so it shapes what buyers come to believe. For a given model and belief, we ask when there exists a mechanism that sustains that belief while buyers keep learning, and how such a mechanism does it. Such a mechanism exists when the win probability predicted by the model responds strongly enough to a change in belief, relative to how bidding behaviour responds. We give sufficient conditions of this kind for convergence from every initial belief with a single buyer, and for convergence from nearby beliefs with two buyers, where feasibility ties the win probability each faces to the other’s bids. To extend the basin of attraction beyond nearby beliefs, we work with discrete valuations and give a computational criterion in the form of a linear program, whose strictly feasible solutions yield mechanisms that sustain the belief from every more optimistic belief.