Free shipping and purchasing decisions in B2B transactions: A game-theoretic analysis

Free shipping offers by eBusiness companies have become an effective means of attracting and keeping customers. Many business-to-consumer and business-to-business (B2B) companies now offer free shipping to buyers who spend more than a specific amount. In this paper we consider a B2B environment and assume that the buyer may be enticed to increase her purchase amount in order to qualify for free shipping. The seller's and the buyer's decisions (i.e., free shipping cutoff level and purchase amounts, respectively) affect each other's objective functions. Thus, we model the problem as a leader-follower game under complete information where the leader is the seller and the follower is the buyer. We assume that if the cutoff level announced by the seller is lower than the buyer's purchase amount, the seller absorbs the shipping cost. Otherwise, the buyer compares the values of two functions to determine whether she should increase her purchase amount to qualify for free shipping. We first determine the best response function for the buyer for any given value of the seller's cutoff level and present some structural results related to the response function. We then compute the Stackelberg solution for the leader-follower game and discuss the managerial implications of our findings. The results obtained are demonstrated with the help of two examples. We also present a complete sensitivity analysis for the Stackelberg solution and the objective function values for variations in the unit shipping cost.