Referral, Learning and Inventory Decisions in Social Networks

With the proliferation of digital social networks and social media like Facebook, Twitter, and Instagram, businesses increasingly used referral programs to increase market exposure and sales. We study the interactions between social learning and referral programs and examine their impact on demand uncertainty and firms' inventory decisions. We characterize customers' purchasing strategies based on their knowledge of their own preference types and their observation of others' purchasing decisions and then derive the demand distributions when customers are involved in social learning in a referral program. While customers who lack knowledge of their own preferences introduce bias to the demand expectation, social learning reduces the bias at the expense of increasing demand variance. We examine two effects of stock-outs: (i) the \emph{market exposure effect} is the negative effect of stock-out of one product on the sales of another product due to the structure of referral program, and (ii) the \emph{demand substitution effect} on customer's choices when one product goes out of stock. We characterize the optimal inventory levels for a different number of referrals. We find that the optimal inventory levels are governed by different combinations of the two effects under different ranges of the number of referrals. For a low number of referrals, the market exposure effect is dominant because the stock-out of one product can end the referral chains while for a high number of referrals the substitution effect is dominant because the referral chains do not end until either both products are out of stock or all customers are reached through referral chains. In the middle range of values for the number of referrals, both effects become important because the stock-out of the more popular product can lead to the end of referral chains while the stock-out of the less popular product may not end referral chains and cause substitution by customers. These effects are not observed in traditional inventory problems and are present due to the rich interaction between social learning and referral program structure.