Optimal Price Reaction Strategies in the Presence of Active and Passive Competitors

Abstract

Sales applications are characterized by competitive settings and changing market environments. Hence, prices have to be adjusted frequently. We analyze stochastic dynamic pricing models under competition for the sale of durable goods. Given a competitor’s pricing strategy, we show how to derive optimal response strategies that take the anticipated competitors’ price adjustments into account. We study resulting price cycles and the associated expected long-term profits. We show that reaction frequencies have a major impact on a strategy’s performance. In order not to act predictable our model also allows to include randomized reaction times. Additionally, we study to which extent optimal response strategies of active competitors are affected by additional passive competitors that use constant prices. It turns out that optimized feedback strategies effectively avoid a decline in price. They help to gain profits, especially, when aggressive competitors are involved.