A backwardly solvable search equilibrium model

So-called "search equilibrium models" typically have multiple equilibria. In almost all studies on these models, only steady states are considered mainly because it is difficult to find non-stationary equilibria. This difficulty does not disappear even if we consider finite-horizon versions of these models. In this note, we propose an approach that might be useful to study non-stationary equilibria in these models. In particular, we consider a discrete-time and finitehorizon version of Diamond's (1982. JPE) model and show how to solve it backwardly. As an illustration, we compute a non-stationary equilibrium of a specific example, which exhibits a three-period cycle.