Diffusion, Influence and Best-Response Dynamics in Networks : An Action Model Approach

Threshold models and their dynamics may be used to model the spread of ‘behaviors’ in social networks. Regarding such from a modal logical perspective, it is shown how standard update mechanisms may be emulated using action models – graphs encoding agents’ decision rules. A small class of action models capturing the possible sets of decision rules suitable for threshold models is identified, and shown to include models characterizing best-response dynamics of both coordination and anti-coordination games played on graphs. We conclude with further aspects of the action model approach to threshold dynamics, including broader applicability and logical aspects. Hereby, new links between social network theory, game theory and dynamic ‘epistemic’ logic are drawn.