Dynamic pricing with stochastic reference effects based on a finite memory window

Abstract

Inspired by the latest empirical studies, we propose a new updating model for reference prices by assuming that consumers’ memories are limited and their recall of previous prices obeys a first-order Markov stochastic process. We investigate a dynamic pricing model with stochastic reference effects and finite memory. Consistent with the exponential smoothing model, we indicate that reference effects lead to monotonic convergence of the optimal price path to an expected steady-state price. The steady-state range tends to widen as consumers become loss-averse. The results of our numerical experiments differ from findings of certain models under the assumption of stochastic recall memory of consumers. The optimal price path fluctuates consistently around the steady state instead of remaining constant. The effect of the first price on the memory window and long-term profits decreases as the length of memory window increases.