Persuasion in Networks: Public Signals and k-Cores

We consider a setting where agents in a social network take binary actions, which exhibit local strategic complementarities. In particular, the payoff of each agent depends on the number of her neighbors who take action 1, as well as an underlying state of the world. The agents are a priori uninformed about the state, which belongs to an interval of the real line. An information designer (sender) can commit to a public signaling mechanism, which once the state is realized reveals a public signal to all the agents. Agents update their posterior about the state using the realization of the public signal, and possibly change their actions. The objective of the information designer is to maximize the expected activity level, i.e., the expected total number of agents who take action 1. How should the information information designer choose her public signaling mechanism to achieve this objective? This is the first paper to study the design of public signaling mechanisms in social networks, and its main contribution is to provide an answer this question.