Learning Through Search

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  • Learning Through Search
  • Abstract:
    We consider a search and matching model, in which the two parties in the market are uncertain about their own quality. The uncertainty is in general persistent, but agents learn about their quality over time as they interact with the agents from the other side. For the match only the quality of the partner matters for an agent’s payoff. In the asymmetric version of our model firms arrive at random times, observe a worker’s type and either make a proposal or not. When a worker receives a proposal, he observes the firm’s type and decides whether or not to accept the proposal. Once a match is formed, both agents leave the market. We first consider a model where firms know their type and follow an exogenous decision rule: high types propose to high types only, low types to both types. We show that workers optimally use a cutoff rule. This rule, however, is non-monotone in the fraction of firms with high quality. We derive the steady state distribution for workers in a large market, assuming that exiting agents are replaced, and demonstrate that the workers’ average quality is smaller than the prior of the workers who enter the market. We then relax the assumption that firms know their type but keep the assumption that only firms can make proposals to form a match. We show that the learning dynamics of the workers change significantly, workers’ beliefs jump. We analyse the set of equilibria. Once we allow for proposals from both workers and firms a new phenomenon arises, which is akin to a bid-ask spread: The belief at which a proposal is made to a low type differs from the belief at which a proposal from a low type is accepted.