Dynamic pricing schemes are increasingly employed across industries to maintain a self-organized balance of demand and supply. However, throughout complex dynamical systems, unintended collective states exist that may compromise their function. Here we reveal how dynamic pricing may induce demand-supply imbalances instead of preventing them. Combining game theory and time series analysis of dynamic pricing data from on-demand ride-hailing services, we explain this apparent contradiction. We derive a phase diagram demonstrating how and under which conditions dynamic pricing incentivizes collective action of ride-hailing drivers to induce anomalous supply shortages. We identify characteristic patterns in the price dynamics reflecting these supply anomalies by disentangling different timescales in price time series of ride-hailing services at 137 locations across the globe. Our results provide systemic insights for the regulation of dynamic pricing, in particular in publicly accessible mobility systems, by unraveling under which conditions dynamic pricing schemes promote anomalous supply shortages.
Complex engineered systems are known to exhibit unintended states in their collective dynamics that often disrupt their function. In complex mobility systems, examples include the emergence of congestion, anomalous random walks in human travel patterns8, and cascading failures of mobility networks. As urban mobility becomes more and more self-organized and digitized, mobility services increasingly employ dynamic pricing, in general serving two main purposes. First, dynamic pricing adjusts the price of a product or service to compensate for changes in its intrinsic base cost. Second, it creates incentives for all market participants to equilibrate demand–supply imbalances by increasing the price if demand exceeds supply and vice versa. A higher price both imposes higher costs to customers incentivizing them to decrease their demand and, at the same time, offers higher profit for identical service to suppliers, in turn motivating them to increase their supply. However, recent reports on on-demand ride-hailing indicate that dynamic pricing may have the opposite effect and instead cause demand–supply imbalances. https://rdcu.be/b7ILj