A Note on Costly Sequential Search and Oligopoly Pricing (new title: Truly Costly Sequential Search and Oligopolistic Pricing,)

Figure 1: Equilibrium conditions sequential search (N = 2)

When there are many shoppers (Figure 1(a)), for large search cost parameters, say c1, non-
shoppers participate in the market only with probability less than one. This probability is given by
the point at which Φ(∙) and c 1 /v, intersect. It can be seen that as search cost falls relative to the
value of the purchase, these consumers find it beneficial to search more intensively. When search
cost is low enough, e.g. c2 , non-shoppers search for one price with probability one.

The region of parameters for which an equilibrium with partial consumer participation exists is
sensitive to the parameters μ and N. As mentioned above the function Φ(∙) falls as μ decreases or N
increases (see equation (14)). Moreover, when μ approaches 0 or N becomes very large, Φ(θ 1; μ, N)
approaches 0 for all values of θ 1. Figure 1(b) illustrates a market where μ = 0. 1. The figure reveals
that the existence region of a partial participation equilibrium covers almost the entire parameter
space. The same happens when the number of firms grows large. This indicates that the partial
participation equilibrium is relevant when the number of firms in the market is large and there are
few shoppers.

4 Comparative Statics

In this section we study the influence of changes in the parameters of the model on the average price
charged in the market. The results are summarized in Table 1. The results for the Stahl (1989)
case are known; the others are new. An upwards (downwards) arrow means that the variable under
consideration increases (falls); the symbol ‘-’ means that the variable remains constant. In what
follows, our discussion shall concentrate on the most striking and interesting observations of the

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