A study of the dynamic of influence through differential equations

The paper concerns a model of influence in which agents make their decisions on a certain issue. It is assumed that each agent is inclined to make a particular decision, but due to a possible influence of the others, his final decision may be different from his initial inclination. Since in reality the influence does not necessarily stop after one step, but may iterate, we present a model which allows us to study the dynamic of influence. The use of continuous variable permits the application of differential equations systems to the analysis of the convergence of agents' decisions in long-time. In particular, by applying the approach based on differential equations of the influence model, we recover the results of the discrete model on classical influence functions and the results on the boss and approval sets for the command games equivalent to some influence functions.

[1]  U. Krause.  A DISCRETE NONLINEAR AND NON–AUTONOMOUS MODEL OF CONSENSUS FORMATION , 2007 .

[2]  Jan Lorenz,et al.  A stabilization theorem for dynamics of continuous opinions , 2005, 0708.2981.

[3]  R. Berger.  A Necessary and Sufficient Condition for Reaching a Consensus Using DeGroot's Method , 1981 .

[4]  Michel Grabisch,et al.  A model of influence with an ordered set of possible actions , 2010 .

[5]  Michel Grabisch,et al.  Different approaches to influence based on social networks and simple games , 2010 .

[6]  M. Degroot.  Reaching a Consensus , 1974 .

[7]  Michel Grabisch,et al.  A model of influence in a social network , 2010 .

[8]  C. Hoede,et al.  A theory of decisional power , 1982 .

[9]  Lloyd S. Shapley,et al.  On authority distributions in organizations: equilibrium , 2003, Games Econ. Behav..

[10]  Michel Grabisch,et al.  Measuring influence in command games , 2008, Soc. Choice Welf..

[11]  Sandip Roy,et al.  The influence model , 2001 .

[12]  Michel Grabisch,et al.  Iterating influence between players in a social network , 2010 .

[13]  Michel Grabisch,et al.  A Model of Influence with a Continuum of Actions , 2010 .

[14]  Matthew O. Jackson,et al.  Naïve Learning in Social Networks and the Wisdom of Crowds , 2010 .

[15]  Noah E. Friedkin,et al.  Social positions in influence networks , 1997 .

[16]  Michel Grabisch,et al.  Influence functions, followers and command games , 2011, Games Econ. Behav..

[17]  Lloyd S. Shapley,et al.  On authority distributions in organizations: controls , 2003, Games Econ. Behav..

[18]  Michel Grabisch,et al.  A model of influence based on aggregation functions , 2013, Math. Soc. Sci..

[19]  P. DeMarzo,et al.  Persuasion Bias, Social Influence, and Uni-Dimensional Opinions , 2001 .

[20]  Noah E. Friedkin,et al.  Social influence and opinions , 1990 .