A game theoretical analysis of the quantity discount problem with perfect and incomplete information about the buyer's cost structure

Abstract

In this paper, we analyze the quantity discount problem by considering the competitive nature of the problem and the informational structure regarding the buyer's cost structure. We formulate the problem as two-person nonzero-sum game and analyze the seller's optimal quantity discount schedule and the buyer's optimal order quantity by using Stackelberg equilibrium. We show that it is always possible for the seller and the buyer to gain from quantity discount. However, a quantity discount schedule under which the buyer orders more than his EOQ at the discounted price is necessary for the seller and the buyer to gain. The optimal quantity discount schedule when the seller knows the buyer's cost parameters is given by a single break point. When the seller does not know the buyer's cost parameters, an optimal quantity discount schedule may not exist. Two approaches have been developed for the seller to offer quantity discount in this case. The application of our analysis is discussed. Our results can be especially useful when the seller has many buyers.