Complexity of Ordering Dynamics under Pure Revenue-Sharing Contracts

This paper examines the ordering dynamics in a supply chain coordinated by pure revenue-sharing contracts by relaxing the complete rationality assumption in the literature. Analytical results demonstrate that the retailer´s ordering dynamics exhibits chaos with a positive (Lebesgue) measure in the long term no matter what percentage is adopted in a pure revenue-sharing contract as long as certain conditions are met. This unpredictability of ordering dynamics serves as a warning signal to a contract designer that s/he should pay attention to the profiles of external market and internal behavioral parameters that may lead to chaotic ordering dynamics, and then certain incentive terms may be installed in the contract to motivate the retailer to choose appropriate adjustment speed parameter values such that chaos is likely to be avoided and the supply chain can be coordinated.