By Gabriele Camera and Jaehong Kim
The directed search model (Peters, 1984) is static; its dynamic extensions typically restrict strategies, often assuming price or match commitments. We lift such restrictions to study equilibrium when search can be directed over time, without constraints and at no cost. In equilibrium trade frictions arise endogenously, and price commitments, if they do exist, are self-enforcing. In contrast to the typical model, there exists a continuum of equilibria that exhibit trade frictions. These equilibria support any price above the static price, including monopoly pricing in arbitrarily large markets. Dispersion in posted prices can naturally arise as temporary or permanent phenomenon despite the absence of pre-existing heterogeneity.
I think directed search holds much promise, foremost because we all search with some direction, not randomly. This paper also shows that directed search can get to many of the stylized facts that hard (but not impossible) to achieve with random search models, such as price dispersion, multiple equilibria, and endogenous frictions. I most intrigued by self-enforcing price commitments: This is like reputation, and to get that endogenously is not obvious.