Uncertainty of consumer preferences and product differentiation in two three-stage Hotelling models

Two three-stage Hotelling models are established by introducing firms' uncertainty about consumer preferences. Through the two dynamic game models, location decisions and product differentiation problems are discussed. Under assumptions of quadratic transportation costs, consumer distributed uniformly and firms pricing (or locating) orderly, it is proved that each model has unique subgame perfect Nash equilibrium. The equilibrium results indicates that uncertainty can increase product differentiation and the firm who first prices (or locates) locates closer to market center, fixes higher equilibrium price and gains more equilibrium profit than the other one. At last, the socially optimal locations under uncertain consumer preferences are analyzed. The results show that the uncertainty also improves social product differentiation.