Pricing Decisions in the Presence of Interacting and Strategic Buyers Purchasing Multiple Units

We study the pricing problem of a seller offering a single item to buyers purchasing multiple units in two periods. Each buyer aims to maximize her total utility over two periods, and is strategic in two dimensions: she may delay the purchase in anticipation of a price discount (at the expense of a reduced utility), and takes other buyers into account when determining her purchase quantity. The seller sequentially sets the price in each period to maximize his profit. We show the existence and uniqueness of the Nash equilibrium of the game between the buyers and derive the equilibrium of the two-stage sequential game between the seller and the buyers. Analysis reveals that strategic buyer interaction shifts the purchases to the later period, which in turn leads the seller to lower the price. Thus, buyer interaction decreases the seller’s profit while almost always benefiting the buyers. The seller’s profit decreases further if he ignores the buyer interaction. Through numerical analysis, we quantify the loss to the seller due to buyer interaction and due to ignoring the interaction. As a remedial policy to deter strategic buyer behavior, we study commitment pricing where the retailer announces a price path at the beginning of the selling horizon. The seller prefers commitment pricing over sequential pricing when the buyers are impatient or when the cost of the item in the earlier period is relatively low since the seller can induce early purchases in such cases