1 Introduction
One of the most celebrated articles in the consumer search literature is the article by Stahl (1989).
Stahl (1989) studies a search model with two types of consumers and where firms price strategically.
Fully informed consumers (referred to as shoppers in his article) have no opportunity cost of time
and search for all prices at no cost; non-shoppers search sequentially, i.e., they first observe one price
and then decide whether or not to observe a second price, and so on.1 Stahl (1989) assumes that
consumers observe the first price quotation for free, as many other papers in the search literature,2
which implies that every buyer makes at least one search. In this paper, we study the implications
of relaxing this assumption.
The optimal sequential search rule implies that a consumer continues searching if, and only if,
the observed prices are above a certain reservation price. Knowing this, no firm will wish to charge
prices above the reservation price. Therefore, under the assumption that obtaining the first price
observation is costless, buyers search exactly once in equilibrium and buy at the observed price. In
this note, we call this the full participation equilibrium. This equilibrium is one of the two possible
equilibrium configurations when the first price quotation is not for free. The new equilibrium that
arises is one of partial participation, where some consumers decide not to search at all as they
rationally expect prices to be so high that they are indifferent between searching and not searching.
The existence and characterization of this new equilibrium is one of the two main contributions of
this note.
The other main contribution is to provide a full comparative statics analysis of the effects of
all the possible changes in the exogenous parameters. The main comparative statics effects under
partial participation are as follows. A first result is that when search costs decrease, expected
price increases. This result is mainly due to the fact that an increase in search cost implies more
participation of non-shoppers who search only once. As firms have monopoly power over these
consumers, they raise their prices. A second result is that an increase in the number of shoppers
does not have an effect on expected price as their presence is exactly offset by an increase in the
participation of non-shoppers. A last important result is that, unlike in Stahl’s model, expected
price does not tend to the monopoly price when the number of shoppers converges to zero, nor
1The implications of sequential consumer search are also examined in, e.g., Anderson and Renault (1999), Rein-
ganum (1979), Rob (1985), Stahl (1996) and Stigtlitz (1987).
2An important example in the non-sequential search literature using this assumption is Burdett and Judd (1983).
Janssen and Moraga-Gonzalez (2004) is an exception. This paper studies the implications of entry in a model of
non-sequential search.