Dual communication in a social network: Contributing and dedicating attention

Communication between individuals often involves two types of dual activities. On social media such as Facebook, for example, users produce content (posts) and pay attention to their friends' posts. These activities are dual as a user is more inclined to produce posts the more friends react to them and is more inclined to dedicate attention to a friend's posts the more numerous these posts are. This paper builds and analyzes a simple game with dual activities and dedicated attention when agents communicate through a follower-influencer network (say, X-Twitter). Equilibria can be multiple, each characterized by its attention network, which describes who pays attention to whom, resulting in a partition of cohesive subgroups who pay and receive attention from each other and do not communicate with agents in other subgroups. The stars-equilibria, where attention in each subgroup is focused on a single influencer, stand apart: activities and payoffs are high on average but unequal. Furthermore, they are the only equilibria stable to perturbations or to self-enforcing deviations from coalitions (coalition-proofness).