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Network effects are commonly seen among people engaging in social interactions, and come about from the “payoff externality”, where someone’s payoff depends on both their own actions and the actions of others. For example, an individual is more likely to adopt a program or application if their friends and colleagues already use it.

Because network effects largely enhance a person’s willingness to pay via the cascade of externalities, industries such as telecommunication networks, operating systems, cloud services, and mobile apps, to name a few, are extremely profitable, raising competition and potential to new levels. This competition gives rise to various phenomena that are not observed in conventional industry structures. For instance, it is widely believed that network effects create the “winner-take-all” phenomenon, whereby a product may capture a dominant market share over seemingly identical alternatives.

Network structure is also related to market segmentation, and product adoption may vary greatly from segment to segment in a network; for example, WeChat in China, Facebook Messenger in North America, and WhatsApp elsewhere around the world. Such market dominance and segmentation does not come about if the market is monopolised by a single firm.

A recent study by Ningyuan Chen and Ying-Ju Chen set out to get a better understanding of firms’ competitive strategies when customers’ purchasing decisions are influenced by network effects, with a primary focus being the emergence of market dominance and segmentation in the form of asymmetric equilibria. To do so, the authors considered two firms selling substitutable products to a market of network-connected customers, in which customers choose between two products or leave without making a purchase, and where decisions are based on price, quality, and the anticipated network effect; i.e., customers are influenced by the choices of others in the network. A multinomial logit model was chosen as it has been extremely successful in prior studies in capturing discreet choices due to its interpretability and analytical tractability.

However, despite the simplicity of the model, the authors found the equilibrium analysis to be very difficult indeed. As they explain, this was because of the network interactions, the nonconcave payoff function arising from the multinomial logit model, and the asymmetric equilibria. To get around the issue and find the pure-strategy Nash equilibria of the duopoly competition, the authors adopted an innovative approach that focused on the inverses of the best-response functions.

Ningyuan Chen and Ying-Ju Chen show that, depending on the products’ qualities and the strength of the network effects, the Nash equilibria exhibit highly distinct features. Specifically, they find that when the products are symmetric and customers are homogenous, a single Nash equilibrium arises if the network effects are weak, where the two firms evenly split the market. When the network effects are strong, three Nash equilibria exist: two stable asymmetric Nash equilibria, where one firm captures nearly all of the market, and one unstable symmetric Nash equilibrium. The authors point out that “When the product quality is low and the network effects are neither too weak nor too strong, the resulting market equilibrium is never symmetric, although the firms are ex ante symmetric”.

The study went on to consider products with heterogeneous qualities, finding that when the network effects were strong enough, two Nash equilibria existed that corresponded to the respective market-dominance positions of the firms, regardless of any difference in quality. This implies that, even though one product is inferior, it can still maintain market dominance due to the strong network effects.

When the network effects were heterogeneous among customers, the authors discovered that customers with higher social influence and larger price sensitivity were more likely to purchase either product in the symmetric equilibrium. They also studied networks consisting of two communities and found that market segmentation could arise under the network effects; i.e., one product dominates in one community, while the second product dominates in the other. Lastly, in order to explain first-mover advantage (i.e., a firm’s ability to be in a better position than its competitors by being the first to introduce a new product to the market), Ningyuan Chen and Ying-Ju Chen extended their research to a dynamic setting where customers are unable to coordinate perfectly and the network effects build up over time, revealing the existence of a pure-strategy, open-loop Nash equilibrium.

Overall, the authors are confident that the results of their study can be used to predict the competitive outcome under various market conditions, as well as consistently explain real-world market phenomena. They go on to express hope that their study opens up new research avenues related to firms’ competitive strategies when faced with network-connected customers.