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.