Stochastic Dynamic Product Search

Abstract

Before making purchase decisions, consumers often search for information on product attributes. In this paper, we incorporate a key feature of consumer search behavior---namely, search intensity---into a stochastic dynamic model. Specifically, motivated by industry evidence, we model search intensity as a mean-reverting square root process which is fed back to consumers' valuation. Due to this stochastic dynamic search intensity, the consumers' decision-making subjects to a two-dimensional (consumers' product valuation and search intensity) optimal stopping problem. We develop an asymptotic expansion technique to facilitate the solution procedure. We also prove that the value of consumers continuing a search is smaller, as (i) the search intensity becomes smaller, (ii) the search intensity decreases faster, (iii) the mean-reverting value of the search intensity becomes smaller, and (iv) the market is more volatile. Given this, we also evaluate the firm's pricing strategy of the product.