How to set price and quality in a supply chain of virtual products under bi-criteria and risk consideration

Virtual products are characterized by ample production capacity, zero lead time, and no holding costs. We consider a two-echelon supply chain of a virtual product, consisting of a single manufacturer and a single retailer who face random demand. Demand depends on both price and quality of the product, and its stochastic nature exposes the supply-chain members to financial risk. Each party adopts profit criteria that reflect his or her attitude toward this risk, including the use of bi-criteria. By formulating a model that follows a Stackelberg game and using the stochastic dominance property, we show that one can analytically obtain equilibrium by assuming certain common structures of the demand function and of the risk attitudes. The contribution of this study is fourfold: (i) analyzing multiplicative and additive demand forms and comparing the properties of the decisions under the two forms; (ii) showing that under the multiplicative demand form, the pricing strategies are not affected by the parties' attitudes toward risk, whereas the manufacturer's decision on quality-investment is affected by his risk attitude; (iii) showing that under the additive demand form, the manufacturer's utility function and the demand uncertainty affect pricing and investment strategies; and (iv) suggesting a method to construct the efficient set of decisions and the non-dominated set of profit criterion values.