Dominance Relationship Among the Retailer’s Strategies Under the Semi-Stackelberg Newsvendor Situation with Quantity Discounts

Abstract

In this paper, we investigate the retailer’s behavior under the supplier-driven semi-Stackelberg newsvendor situation in which (i) the supplier plays as a semi-Stackelberg leader with or without his discounts schedule being offered to the retailer, (ii) the retailer plays as a Stackelberg follower with or without her discounts schedule being offered to the end customer, and (iii) neither party has perfect information on the endogenous price-dependent demand function or exogenous probability distribution of demand. In this situation, the retailer’s concern is identifying the dominant strategy by which she can safely implement her own scheme for customer discounts regardless of the order quantity rather than finding the best strategy yielding the optimal order quantity that maximizes her expected profit. We show that a consistent dominance relationship exists among the retailer’s strategies when the newsvendor chooses to offer progressive multiple discounts to customers regardless of the supplier’s strategy of offering the retailer either all-units discounts or no-discounts.