# Iterating influence between players in a social network

Working paper

Issue number:

2010.89

Publisher:

Centre d’Economie de la Sorbonne

Year:

2010

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.