Strategic disclosure of opinions on a social network

We study the strategic aspects of social influence in a society of agents linked by a trust network, introducing a new class of games called games of influence. A game of influence is an infinite repeated game with incomplete information in which, at each stage of interaction, an agent can make her opinions visible (public) or invisible (private) in order to influence other agents' opinions. The influence process is mediated by a trust network, as we assume that the opinion of a given agent is only affected by the opinions of those agents that she considers trustworthy (i.e., the agents in the trust network that are directly linked to her). Each agent is endowed with a goal, expressed in a suitable temporal language inspired from linear temporal logic (LTL). We show that games of influence provide a simple abstraction to explore the effects of the trust network structure on the agents' behaviour, by considering solution concepts from game-theory such as Nash equilibrium, weak dominance and winning strategies.