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

Diamond result in the limit since at some point the economy turns to a partial participation
equilibrium. Figure 5 below illustrates the comparative statics results discussed above.

(a) c = 0.5 and μ = 0.8

(b) c = 0.05 and μ = 0. 1

Figure 5: The impact of N on expected price

5 Conclusion

In this note, we have taken the seminal model of Stahl (1989) on sequential consumer search and
oligopolistic pricing and studied the implications of relaxing the assumption that consumers obtain
the first price quotation for free. When also the first price quotation is obtained at a positive
search cost, a new type of equilibrium arises where consumers randomize between not searching
and searching for one price, i.e., where there is less than full consumer participation. The partial
participation equilibrium exists when search costs are above a certain threshold (depending on the
other parameter values). This threshold can be made arbitrarily low provided that the number of
firms is large enough and/or the number of shoppers is sufficiently small. Therefore, especially in
markets with many firms and/or with few shoppers, this partial participation equilibrium should
be seriously considered. This new equilibrium exhibits interesting comparative statics properties.
In particular, the expected price increases as search cost decreases, and is constant in the number
of shoppers and in the number of firms. Finally, the paper shows that, starting from an equilibrium
with full participation, a Diamond result never obtains when the number of shoppers goes to zero
and/or the number of firms goes to infinity because with truly costly search the economy eventually
moves to an equilibrium with partial consumer participation.

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