A Demand System for a Dynamic Auction Market with Directed Search

We develop a demand system for a dynamic auction market with directed search. In each period, heterogeneous goods are exogenously supplied and sold by second price auction, and incumbent bidders choose which good to bid on and how much to bid. Bidder valuations are multidimensional, private and perfectly persistent, and the population of bidders evolves according to an exogenous entry and endogenous exit process. We prove that the state of the market | which includes active bidders' types and information sets | evolves as a geometrically ergodic Markov process. We characterize best responses as solutions to a partially observed Markov decision problem and provide conditions under which the econometrician can identify equilibrium strategies from time series data. We provide additional conditions under which this allows nonparametric identi cation of preferences. When the market is large so that each bidder's actions are informationally small, we show bidderwise identi cation: the valuations of bidders whose individual time series includes a bid on every product are identifi ed. Two-stage nonparametric and semiparametric estimation procedures are proposed, and shown to work well in Monte Carlo and counterfactual simulations