Managing Consumer Retention via Pricing and Switching Cost Under Discrete Mixed Multinomial Logit Demand

This paper studies dynamic pricing and switching cost game under discrete mixed multinomial logit (MMNL) demand. Competing firms can dynamically change prices and redesign their products to in- crease or decrease switching costs in each period to influence the repeat consumers’ purchase behavior. Consumers are divided into segments according to their purchase history and incur a one-time switching cost when they switch to the other firm. We characterize the conditions for the existence of equilibrium in single- and multi-period games and identify a key driver for firm’s pricing and switching cost strategies: the ”demand-SC relationship.” Our theoretical results formally document three effects of switching costs: the anti-monopoly effect of small switching costs that boosts price competition, the monopoly effect of large switching costs, and the investment effect for forward-looking firms under any switching costs. For the joint effect of the pricing and switching cost strategies, a case study from the smartphone market shows that investing in switching cost can significantly increase firms’ profit in a market with relatively small switching costs. However, under relatively large switching costs, switching cost competition may turn into a ”Prisoner’s Dilemma” game. Our results show that switching costs could be, ironically, beneficial to consumers and detrimental to firms. The analysis explains why and how proactively controlling consumer switching costs profoundly boosts firms’ profitability. Our tractable framework can be used by firms operating in dynamic environments to devise their competitive pricing and switching cost strategies