Technical note-dynamic pricing with gain-seeking reference price effects

We study a dynamic pricing problem of a firm facing reference price effects at an aggregate demand level, where demand is more sensitive to gains than losses. We find that even the myopic pricing strategy belongs to one type of discontinuous maps, which can exhibit complex dynamics over time. Our numerical examples show that, in general, the optimal pricing strategies may not admit any simple characterizations and the resulting reference price/price dynamics can be very complicated. We then show for a special case that a cyclic skimming pricing strategy is optimal, and we provide conditions to guarantee the optimality of high-low pricing strategies.