A time and space routing game model applied to visibility competition on online social networks

Companies or users that want to do advertising on Online Social Networks, need to know in which News Feed it would be more efficient to post, at what time of day the posts would have more visibility and which topic of message they should choose to reach popularity. We propose to answer these questions with the help of the Routing Game Theory, which considers a finite number of players and splittable demands. First, we propose a visibility measure on a News Feed. Next, we present our game based on visibility measures, which is similar to the Weighted Allocation Game. Following this consideration, we provide the uniqueness of the Nash Equilibrium, a characterization via concave programming, and its closed form. Then, we propose a two time scale decentralized algorithm where each user estimates the total flow of messages in each News Feed and uses stochastic gradient algorithm to update their own flows. Finally, we use a real data set in order to estimate the parameters of our model. The goal of this model is to provide to the Online Social Network Authority a better knowledge of posting behavior of competitive users.