We construct a model of the housing market in which agents differ in their flow values while searching. Agents enter the market relaxed (with high flow values) but move to a desperate state (low flow values) at a Poisson rate if they have not already transacted. We characterize the equilibrium steady‐state matching pattern and the joint distribution of price and time to sale (for sellers). The expected price conditional on time to sale falls with time spent on the market, whereas the conditional variance of price first rises and then falls with time on the market.

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This paper introduces a general model of matching that includes evolving public Bayesian reputations and stochastic production. Despite productive complementarity, assortative matching robustly fails for high discount factors, unlike in (Becker 1973). This failure holds around the highest (lowest) reputation agents for 'high skill' ('low skill') technologies.We find that matches of likes eventually dissolve. In another life-cycle finding, young workers are paid less than their marginal product, and old workers more. Also, wages rise with tenure but need not reflect marginal products: Information rents produce non-monotone and discontinuous wage profiles.

We consider a differential game in which the joint choices of the two players influence the variance, but not the mean, of the one-dimensional state variable. We show that a pure strategy perfect equilibrium in stationary Markov strategies (ME) exists and has the property that patient players choose to play it safe when sufficiently ahead and to take risks when sufficiently behind. We also provide a simple condition that implies both players choose risky strategies when neither one is too far ahead, a situation that ensures a dominant player emerges "quickly."