Recent empirical work highlights the heterogeneity of social competitions such as political campaigns: proponents of some ideologies seek debate and conversation, others create echo chambers. Symmetric and static network structure is typically used as a substrate to study such competitor dynamics. In a paper currently in revision, our group argues that network structure can instead be interpreted as a signature of the competitor strategies, yielding competition dynamics on adaptive directed networks. Using the directed stochastic block model to encode these strategies, we obtain general analytical solutions for the voter model dynamics and study specific cases with tradeoffs between aggressiveness and defensiveness (i.e., targeting adversaries vs. targeting like-minded individuals). We show that these tradeoffs yield interesting, and even paradoxical, behaviors such as long transient dynamics, sensitive dependence to initial conditions, and non-transitive dynamics.
We now wish to extend this work in multiple directions: to study the importance and impacts of adaptive (or time-dependent) strategies; to look into the role of opinion aggregation in competitions between large number of competing opinions; to investigate biological life cycles by dividing the system in sub-environments; and to relate our previous results to group cohesion in the study of collective animal behavior with heterogeneous signals.