One of the major results announced in the static literature on the coordination of pricing decisions in bilateral monopolies states that vertical integration performs better than decentralization. The impact of uncoordinated pricing strategies from a dynamic perspective is a topic that has been neglected in channel literature despite its importance in a context where price changes have many consequences on consumers' behavior. Indeed, price fluctuations affect not only consumers' stockpiling behavior but also their perceptions of products' value, since this information allows them to build a reference price, a benchmark to which they compare the retail price levels observed in the marketplace before making their purchase decisions.

In this study, we examine whether the results obtained in a static setting still hold if the carry-over effects of pricing decisions are considered. To answer this question, we consider a differential game that takes place in a bilateral monopoly where the manufacturer and the retailer control their transfer and retail prices, respectively. The latter contributes to the building of a reference price, considered as the state variable in our model. We compute then compare the strategies, total channel profits and consumer surplus under two scenarios: vertical integration and decentralization.

One of our main findings states that for some values of the initial reference price, there is a time interval where the results obtained with static models do not hold when the carry-over effects of prices are considered. Indeed, this result is the first to prove that, with the introduction of the dynamic features in the pricing model, one can find situations where double-marginalization does not lead to higher prices and could even improve channel efficiency for some time periods during the planning horizon.