Efficient Estimation of Network Games of Incomplete Information: Application to Large Online Social Networks

This paper presents a structural discrete choice model with social influence for large-scale social networks. The model is based on an incomplete information game and permits individual-specific parameters of consumers. It is challenging to apply this type of models to real-life scenarios for two reasons: (1) The computation of the Bayesian–Nash equilibrium is highly demanding; and (2) the identification of social influence requires the use of excluded variables that are oftentimes unavailable. To address these challenges, we derive the unique equilibrium conditions of the game, which allow us to employ a stochastic Bayesian estimation procedure that is scalable to large social networks. To facilitate the identification, we utilize community-detection algorithms to divide the network into different groups that, in turn, can be used to construct excluded variables. We validate the proposed structural model with the login decisions of more than 25,000 users of an online social game. Importantly, this data set also contains promotions that were exogenously determined and targeted to only a subgroup of consumers. This information allows us to perform exogeneity tests to validate our identification strategy using community-detection algorithms. Finally, we demonstrate the managerial usefulness of the proposed methodology for improving the strategies of targeting influential consumers in large social networks.