Iterating influence between players in a social network

We generalize a yes-no model of influence in a social network with a single step of mutual influence to a framework with iterated influence. Each agent makes an acceptance-rejection decision and has an inclination to say either ‘yes’ or ‘no’. Due to influence by others, an agent’s decision may be different from his original inclination. Such a transformation from the inclinations to the decisions is represented by an influence function. We analyze the decision process in which the mutual influence does not stop after one step but iterates. Any classical influence function can be coded by a stochastic matrix, and a generalization leads to stochastic influence functions. We apply Markov chains theory to the analysis of stochastic binary influence functions. We deliver a general analysis of the convergence of an influence function and then study the convergence of particular influence functions. This model is compared with the Asavathiratham model of influence. We also investigate models based on aggregation functions. In this context, we give a complete description of terminal classes, and show that the only terminal states are the consensus states if all players are weakly essential.