Satisficing Search and Price Competition

The rising prevalence of algorithmic pricing in industry calls for a closer study of market outcomes that arise when these algorithms interact in a competitive environment. In this paper, we study the impact of boundedly rational customer choice on the landscape of joint demand curves in competition, and its consequences on the properties of competing pricing algorithms derived from the online convex optimization framework. In particular, we study price competition in a duopoly under a new customer behavior model motivated by online platforms offering perfectly substitutable services, e.g., ride-hailing. In this model, a customer samples the firms in an idiosyncratically preferred order until she finds one priced below her willingness-to-pay. We exhaustively characterize the equilibrium profile of the resulting pricing game when customers' willingness-to-pay distribution has a monotone hazard rate. We show that these games are plagued by a particular strictly-local Nash equilibrium, in which the price of the firm with a smaller market share is only a local best-response to the competitor's price, when a globally optimal response with a potentially unboundedly higher payoff is available. Through numerical experiments, we show that price dynamics resulting from distributed online gradient descent may often converge to this undesirable outcome, causing the smaller firm to incur linear regret relative to its best-response price. Our results thus suggest that algorithms that adaptively rely on local information for pricing, despite faring well in monopolistic settings, may suffer from serious drawbacks in competitive environments. We finally propose and test a practical resolution of this concern in the context of our model.