We consider sales force compensation where the firm has ambiguity about the output distribution:the parameters of the output probability distribution are in an ellipsoidal uncertainty set.The firm evaluates every contract by its worst-case performance over all possible parameters in the uncertainty set.Similarly, the incentive compatibility condition for the sales agent must hold for all possible parameters in the uncertainty set.
The firm is financially risk neutral and the sales agents has limited liability. We find that when the sales agent is financially risk neutral the optimal robust contract is a linear contract---paying the sales agent a base payment and a fixed share of the output.Moreover, the linear contract is the only type of contracts that are robust to the parameter uncertainty.
We also find that when the sales agent is risk-averse, the piecewise linear is approximately optimal and robust to the parameter uncertainty.
We provide a new explanation for the popularity of linear contracts as well as piecewise linear contracts in practice.We also provide the analysis for the trade-off between robustness and worst-case performance.
Our results are robust to a variety of settings, such as cases with general output distribution, general Lp norm uncertainty sets, multiple effort levels and the risk-averse sales agent with a mean-variance utility. Our paper also introduces a flexible modeling approach for robust contract designs with model uncertainty.
Yimin Yu is an associate professor of Management Sciences at City University of Hong Kong. He received his PhD degree in Industrial Engineering from the University of Minnesota, Twin Cities in 2009. He conducts research in different areas of operations management, with an emphasis on inventory management, service operations, and the marketing-operations interface. His current research projects explore how incomplete information affects business strategies, and in general the robustness of microeconomic models, including contracting problems, mechanism designs and their applications, in the presence of model uncertainty. His papers have been published in journals such as Marketing Science, Product