Positioning–pricing problem of heterogeneous duopoly with uncertain consumer preferences

Small- and medium-sized firms in China have competed passively with advantaged enterprises since 2000, and the prosperity indexes have always been in the recession. This paper aims to find the optimal positioning–pricing strategies for disadvantaged small- and medium-sized firms and explore the complex influence of consumer preference uncertainty in the optimal strategies in duopoly market. In order to do so, the classic Hotelling model is modified to be a heterogeneous duopoly game model under consumer preference uncertainty. By using the backward recurrence algorithm, we first get the optimal equilibrium and then figure out the expected equilibrium solution through mathematical expectation method. The computational results show that disadvantaged enterprises could survive themselves in fierce competition as long as they choose appropriate strategies. In addition, consumer preference uncertainty plays a significant role in affecting the optimal strategy decisions of positioning and pricing in duopoly since producers can hardly obtain complete and perfect information about the market. Specifically, the increased uncertainty of consumer preference generally raises the expected equilibrium price and profit of duopoly enterprises. However, the expected equilibrium profit of the advantaged enterprise in a duopoly decreases with consumer preference uncertainty increasing under certain conditions.