Competition for content spread over multiple social networks

We consider the competition between two competing content creators who can reach out to their potential consumers via two different online social networks. The efficiency of a network for information spread is characterized by two simple properties: the level of activity within the network and the popularity of the network among the population of consumers. We assume that the contents under our consideration are exclusive in nature, i.e., each consumer is interested in receiving only one of the competing contents. Each content creator optimizes the total budget spent across the two social networks. We study the non-cooperative game and characterize the best response functions for the content creators. From the best response functions we observe that there exists a hysteresis-like behavior when it comes to resource allocation across multiple networks, i.e., as a player responds to increasing budget of the competitor, there is an interval of the opponent´s budget between when the player saturates the resources in the better network and when he begins to invest in the worse network. A similar behavior is also observed when the player begins reducing resources, responding to a much higher budget of the competitor. We also observe that the larger the difference between the networks´ efficiency levels, the larger the interval. We then numerically evaluate the Nash equilibria from the best response functions and conclude with discussions on possible future scope of this work.