PRICING STRATEGIES IN A DYNAMIC DUOPOLY - A DIFFERENTIAL GAME MODEL

We formulate a differential game model for dynamic pricing in a duopol istic market. Firms' demand functions are derived from utility maximiz ing behavior of consumers with the demand for a brand given by the leg it model. Preferences for brands are assumed to evolve over time in th e market in a manner akin to learning models postulated in the marketi ng literature. We derive the differential equations governing the equi librium open-loop price paths over time and show that in steady state, the brand with the higher preference level charges the higher price. The formulation is extended to include the effects of consumer heterog eneity, and equilibrium steady-state prices are compared with those ob tained when heterogeneity is ignored. A comparison of steady-state dyn amic prices with myopic prices is provided. An empirical example is di scussed to show how steady-state model predictions may be obtained fro m actual longitudinal purchase data.