We analyze Bayesian persuasion in networks where a sender communicates with multiple receivers, who also observe their neighbors' messages. This complicates the sender's problem of finding the optimal communication protocol and hinders her ability to reach a desired quota of persuaded individuals.

We demonstrate that the sender can strategically disregard specific agents, effectively partitioning the network into non-communicating groups and simplifying the problem to one of weighted voter persuasion. This approach renders some of the network connections irrelevant, as no information spills over between some of the neighboring agents.

In addition, we characterize optimal communication protocols for various sender utility functions and study how strategic receivers can protect themselves from being misinformed by the sender.

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We investigate the minimal seed size required for successful innovation adoption in networks of growing size, such as attachment networks. We use the bootstrap percolation dynamics, where agents adopt the innovation if a certain fraction of their neighbors have already adopted it. Our main contribution is to provide upper and lower bounds on the size of the seed set and to prove that in growing networks, the minimal seed required to reach the entire network cannot be sub-linear in the network size. 

Our study contributes to a better understanding of innovation diffusion in networks and offers potential applications in marketing, public health, and social policy. Our results provide a theoretical foundation for future research to investigate optimal seeding strategies in more complex network structures and dynamics.

We develop a formal framework to measure the centrality of individuals in opinion dynamics on a network, that takes into account both their position in the network and the way opinions propagate in it.​ Our methodology is based on an axiomatic approach in the tradition of coalitional game theory. We show that the unique solution concept satisfying our axioms is a generalization of the "authority distribution" notion of Hu and Shapley (2003).

We extend our basic model to smooth dynamics (where the opinion set is continuous) and study the solution concepts arising from other sets of axioms.

Previous, as well as new network centrality measures are obtained in this way.

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Link to the paper (SSRN)

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