Optimal Pricing for a Multinomial Logit Choice Model with Network Effects

37 Pages Posted: 9 Aug 2014

See all articles by Chenhao Du

Chenhao Du

University of Minnesota - Minneapolis

William Cooper

University of Minnesota - Twin Cities

Zizhuo Wang

The Chinese University of Hong Kong, Shenzhen

Date Written: July 25, 2014

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 (MNL) customer 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. These results can be compared to the optimal pricing policy for the classical MNL model (without network effects) in which it is optimal to set identical prices and obtain identical sales quantities for homogeneous products. We 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 of settings with heterogeneous products as well as to settings with inter-product network effects, and we describe efficient computational methods.

Keywords: multinomial logit model; network effects; revenue management

Suggested Citation

Du, Chenhao and Cooper, William and Wang, Zizhuo, Optimal Pricing for a Multinomial Logit Choice Model with Network Effects (July 25, 2014). Available at SSRN: https://ssrn.com/abstract=2477548 or http://dx.doi.org/10.2139/ssrn.2477548

Chenhao Du

University of Minnesota - Minneapolis ( email )

110 Wulling Hall, 86 Pleasant St, S.E.
308 Harvard Street SE
Minneapolis, MN 55455
United States

William Cooper

University of Minnesota - Twin Cities ( email )

420 Delaware St. SE
Minneapolis, MN 55455
United States

Zizhuo Wang (Contact Author)

The Chinese University of Hong Kong, Shenzhen ( email )

2001 Longxiang Road
Longgang District
Shenzhen, Guangdong 517182
China

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