Reserve Price in Search Models

Search models are used in a variety of fields. One of those is
consumer search and in it the Stahl model is one of the most
popular search models. The literature in search models concentrates
mainly on equilibria with a consumer reserve price. This is a
simplifying condition, which narrows down severely the freedom of
the consumer. For example, once the model has a finite number of
sellers who select different strategies a situation may arise where
reserve price may not exist. This paper addresses the possibility
of equilibria without reserve price, when sellers can use
asymmetric strategies. Here a condition is given which ensures
existence of reserve price in all equilibria. The condition
involves prices where sellers set mass points, and undercutting
those prices. The condition states that if a searcher is satisfied
with such price, she should be satisfied also when a small discount
is offered to that price. Assuming this, it is possible to
concentrate only on equilibria with reserve price, and investigate
also situations where the sellers are heterogeneous, or equilibria
are not symmetric.