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

In this paper, the authors analyze the quantity discount problem by considering the competitive nature of the problem and the informational structure regarding the buyer’s cost structure. They formulate the problem as a 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. The authors 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 then 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 the present analysis is discussed. The results can be especially useful when the seller has many buyers.