Period adding bifurcations in dynamic pricing processes

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Conference Proceeding
IEEE Xplore, 2019
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Price information enables consumers to anticipate a price and to make purchasing decisions based on their price expectations, which are critical for agents with pricing decisions or price regulations. A company with pricing decisions can aim to optimise the short-term or the long-term revenue, each of which leads to different pricing strategies thereby different price expectations. The choices between the two optimisation objectives consider the maximal revenue and the robustness of a chosen pricing strategy against market volatility. However the robustness is rarely identified in a volatile market. Here, we investigate the robustness of optimal pricing strategies with the short-term or long-term optimisation objectives through the analysis of nonlinear dynamics of price expectations. Bifurcation diagrams and period diagrams are introduced to compare their change in dynamics. Our results highlight that period adding bifurcations occur during the dynamic pricing processes studied. These bifurcations would challenge the robustness of an optimal pricing strategy. The consideration of the long-term revenue allows a company to charge a higher price, which in turn increases the revenue. However, the consideration of the shortterm revenue can avoid period adding bifurcations, contributing to a robust pricing strategy. This allows a company to harvest a good revenue through a robust pricing strategy in a volatile market and to satisfy regulations of a control in price volatility.
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