Customer and retailer rebates under risk aversion

In a supply chain setting, we analyze a manufacturers customer and retailer rebates, which are sales incentives offered to the end buyers and retailers, respectively. The performance of both rebates is influenced by the retailers objective and response to the promotion due to his intermediary position in the channel. Earlier studies investigating rebates in distribution channels have traditionally assumed that the retailer is risk neutral with the objective of maximizing expected profits. In our paper, we consider a risk-averse retailer. We formally model risk aversion by adopting the Conditional-Value-at-Risk (CVaR) decision criterion. Using a stochastic and (effective) price dependent demand, we analyze the manufacturers rebate amount decisions and the retailers joint inventory and pricing decisions in a game theoretical framework. We provide several structural properties of the objective functions and show monotonicity of the retailers decisions in the degree of risk aversion. For the case of retailer rebates, we characterize the unique equilibrium, and for the case of customer rebates, we prove the existence of an equilibrium. Using numerical examples, we provide further insights on the impact of risk aversion. For example, given an exogenous wholesale price, we observe a threshold value on the retailers risk-aversion parameter below (above) which the manufacturer is better off with retailer rebates (customer rebates); implying that the manufacturers preferred rebate type can be different depending on whether the retailer is risk neutral or sufficiently risk averse.