Stability and chaos in demand-based pricing under social interactions

Abstract

Demand-based pricing is often used to moderate demand fluctuations so as to level resource utilization and increase profitability. However, such pricing policies may not be effective when customers’ purchase decisions are influenced by social interactions. This paper investigates the demand dynamics, under a demand-based pricing policy, of a frequently purchased service when social interactions are at work. Customers are heterogeneous and adaptively forward-looking. Existing customers’ re-purchase decisions are based on adaptively formed price expectations and reservation prices. Potential customers are attracted through social interactions with existing customers. The demand process is characterized by a two-dimensional dynamical system. It is shown that the equilibrium demand can be unstable. For a given reservation price distribution, we first analyze the stability of the equilibrium demand under various scenarios of social interactions and customers’ adaptively forward-looking behavior, and then characterize their dynamics using the bifurcation plots, Lyapunov exponents and return maps. The results indicate that the demand process can be stable, periodic or chaotic. The study shows that the intended effect of a demand-based pricing policy may be offset by customers’ adaptively forward-looking behavior under the influence of social interactions. In fact, the interplay of these factors may even lead to chaotic demand dynamics. The result highlights the complex dynamics produced by a simple demand-price mechanism under social interactions. For a demand-based pricing strategy to be effective, companies must take social interactions into account.