We investigate the minimal seed size required for successful innovation adoption in networks of growing size, such as scale-free networks, which are widely used to model real-world social networks. We use the bootstrap percolation dynamics model, where agents adopt the innovation if a certain fraction of their neighbors has already adopted it. Our main contribution is to provide an upper and lower bound 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. We demonstrate this result through simulations. Our study contributes to a better understanding of innovation diffusion in scale-free 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)

We study repeated games where players pay a certain cost each time they change their actions. In the zero-sum settings, we derive the properties of the value and the optimal strategies as a function of the ratio between the switching costs and the stage payoff.

In the non-zero-sum settings, we prove that the Folk Theorems still hold and characterize the shape of the feasible set for symmetric switching costs using the primitives of the game. In addition, we study the suboptimality in playing history-independent strategies, which are simpler and often used in these scenarios.

Three papers were published as part of this project:

1. The zero-sum paper (Mathematics of Operations Research, 2023)​

2. The non-zero-sum paper (Games and Economic Behavior, 2024)

3. The price of history-independent strategies (Dynamic Games and Applications, 2024)

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