Optimal Pricing for a Multinomial Logit Choice Model with Network Effects

Abstract

We consider a seller’s problem of determining revenue-maximizing prices for an assortment of products that exhibit network effects. Customers make purchase decisions according to a multinomial logit choice model, modified—to incorporate network effects—so that the utility each individual customer gains from purchasing a particular product depends on the market’s total consumption of that product. In the setting of homogeneous products, we show that if the network effect is comparatively weak, then the optimal pricing decision of the seller is to set identical prices for all products. However, if the network effect is strong, then the optimal pricing decision is to set the price of one product low and to set the prices of all other products to a single high value. This boosts the sales of the single low-price product in comparison to the sales of all other products. We also obtain comparative statics results that describe how optimal prices and sales levels vary with a parameter that determines the strength of the network effects. We extend our analysis to settings with heterogeneous products and establish that optimal solutions have a structure similar to that found in the homogeneous case: either maintain a semblance of balance among all products or boost the sales of just one product. Based on this structure, we propose an effective computational algorithm for such general heterogeneous settings.