A note on costly sequential search and oligopoly pricing

We modify the paper of Stahl (1989) on sequential consumer search in an oligopoly context by relaxing the assumption that consumers obtain the first price quotation for free. When all price quotations are costly to obtain, a new equilibrium arises where consumers randomize between not searching at all and searching for one price. The region of parameters for which this equilibrium exists becomes larger as the number of shoppers decreases and/or the number of firms increases. The comparative statics properties of this new equilibrium are interesting. In particular, the expected price increases as search cost decreases, and is constant in the number of shoppers and in the number of firms. We show that the Diamond result never obtains with truly costly search.