Product Pricing when Demand Follows a Rule of Thumb

We analyze the strategic behavior of firms when demand is determined by a rule of thumb behavior of consumers. We assume consumer dynamics where individual consumers follow simple behavioral decision rules governed by imitation and habit as suggested in consumer research. On this basis, we investigate monopoly and competition between firms, described via an open-loop differential game which in this setting is equivalent to but analytically more convenient than a closed-loop system. We derive a Nash equilibrium and examine the influence of advertising. We show for the monopoly case that a reduction of the space of all price paths in time to the space of time-constant prices is sensible since the latter in general contains Nash equilibria. We prove that the equilibrium price of the weakest active firm tends to marginal cost as the number of (non-identical) firms grows. Our model is consistent with observed market behavior such as product life cycles.