Bifurcation analysis of dynamic pricing processes with nonlinear external reference effects

Publication Type:
Journal Article
Communications in Nonlinear Science and Numerical Simulation, 2019, 79
Issue Date:
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© 2019 Elsevier B.V. Dynamic pricing has been widely implemented to hedge against volatile demand. One challenging problem is the study of optimal price choices under the influence of this volatility. Stochastic demand is a prevalent assumption when it comes to model the volatility on pricing decisions. However, the demand volatility might also be produced by deterministic chaos, which has rarely been studied in this field of research to-date. We propose deterministic dynamic pricing processes that aim to maximise the revenue and to mimic a real pricing decision. Our model includes nonlinear consumer expectations that explain the effects of external information on consumers and discrete optimisations due to a non-smooth demand function that considers asymmetries in the perceptions of gains or losses of consumers and finite price choices of companies. Volatile markets can show up because of non-periodic consumer expectations, period adding bifurcations, codimension-2 points and coexisting solutions. Results highlight that optimal pricing strategies should agree with the dynamics of consumer expectations. Disregarding deterministic dynamics may not only cause revenue losses in practice but might also mislead regulators about the underlying mechanisms that consumers and companies respond to. We introduce for the first time an irregular pricing strategy: a company can make the first return iteration of each sales price non-periodic to follow non-periodic consumer expectations when having finite price choices. These results may justify implementing irregular pricing strategies in the case of practical pricing decisions. Here, the existence of coexisting solutions can assist to identify potential market manipulations within a monopoly market. This not only contributes to a fresh look on volatile markets but also emphasises the importance of initial conditions to pricing decisions and price regulations.
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