The optimal strategies in a two-echelon supply chain with risk-aversion and customers rebates

Consider a supply chain consisting of one risk-averse retailer and one risk-neutral manufacturer with endogenous manufacturer rebates (rebate to consumers), and the demand faced by the retailer is stochastic, price-dependent. We adopt Conditional Value-at-Risk (CVaR) as the retailer´s decision criterion. The demand uncertainty is assumed to be multiplicative, and the expected demand depends on the effective price of the product. We characterize the manufacturer and retailer´s optimal strategies simultaneously. We show the existence of Nash equilibrium between the manufacturer and the risk-averse retailer.