Satisficing Search and Price Competition

We consider price competition under a new customer behavior model in which a customer sequentially considers firms in the order of an idiosyncratic ranking until she finds one that is priced below her willingness-to-pay. The central tension here is between firms' desire to act as monopolists over their own pools of loyal customers, ie, who rank them the highest, and as competitors over the entire market. We show that for duopolies, while a price equilibrium may not exist in general, it always exists when the willingness-to-pay distribution has a monotone hazard rate (MHR). Moreover, in this case it has a surprisingly simple and interpretable structure: the firm with the larger loyalty share sets the monopolistic optimal price ignoring the competition, and the other firm undercuts with the best response price. In particular, we intricately leverage certain key properties of MHR distributions to show that this undercutting response does not trigger a race to the bottom or a price cycle. We discuss robustness of this finding to extended settings: when firms have finite capacities, when there is a fraction of utility maximizing customers, and when there are more than 2 firms.