A Kinetic Model of the Dynamics of Compromise in Large Multi-Agent System

Compromise is one of the primary phenomena that govern the dynamics of the opinion in multi-agent systems. In this paper, compromise is isolated from other phenomena, and it is studied using a statistical framework designed to investigate collective properties of large multi-agent systems. The proposed framework is completed with the details needed to model compromise, and differential problems which describe the dynamics of the opinion under suitable hypotheses are presented. Long-time asymptotic solutions of obtained differential problems are discussed to confirm that compromise makes multi-agent systems tend to reach consensus. It is proved that compromise makes all agents tend to share the same opinion, and that the value of the asymptotic opinion can be expressed in terms of the characteristics of the multi-agent system and of the initial distribution of the opinion. Obtained analytic results are confirmed by independent simulations in an illustrative case.

[1]  Federico Bergenti,et al.  An Analytic Study of Opinion Dynamics in Multi-agent Systems with Additive Random Noise , 2016, AI*IA.

[2]  Stefano Cagnoni,et al.  Evolving binary classifiers through parallel computation of multiple fitness cases , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[3]  Wolfgang Weidlich,et al.  Sociodynamics: a Systematic Approach to Mathematical Modelling in the Social Sciences , 2000 .

[4]  Gene H. Golub,et al.  Matrix computations , 1983 .

[5]  Dirk Helbing,et al.  Individualization as Driving Force of Clustering Phenomena in Humans , 2010, PLoS Comput. Biol..

[6]  Federico Bergenti,et al.  An Analytic Model of the Impact of Skeptical Agents on the Dynamics of Compromise , 2017, WOA.

[7]  Federico Bergenti,et al.  A Study of Consensus Formation using Kinetic Theory , 2016, DCAI.

[8]  Federico Bergenti,et al.  A Kinetic Study of Opinion Dynamics in Multi-agent Systems , 2015, AI*IA.

[9]  Federico Bergenti,et al.  Outline of a Generalization of Kinetic Theory to Study Opinion Dynamics , 2017, DCAI.

[10]  S. Smale,et al.  On the mathematics of emergence , 2007 .

[11]  Federico Bergenti,et al.  Opinion dynamics in multi-agent systems: selected analytic models and verifying simulations , 2017, Comput. Math. Organ. Theory.

[12]  B. Latané,et al.  From private attitude to public opinion: A dynamic theory of social impact. , 1990 .

[13]  A. Flache,et al.  Differentiation without Distancing. Explaining Bi-Polarization of Opinions without Negative Influence , 2013, PloS one.

[14]  Federico Bergenti,et al.  Two Analytic Models of Compromise in Multi-Agent Systems , 2017, MATES.

[15]  Federico Bergenti,et al.  A Stochastic Model of Self-Stabilizing Cellular Automata for Consensus Formation , 2014, WOA.

[16]  Johannes Gehrke,et al.  Gossip-based computation of aggregate information , 2003, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..

[17]  Federico Bergenti,et al.  A Stochastic Model of Diffusion in Opinion Dynamics , 2018, ICAART.

[18]  F. Schweitzer,et al.  Modelling collective opinion formation by means of active Brownian particles , 1999, adap-org/9911005.

[19]  Eric Bonabeau,et al.  Agent-based modeling: Methods and techniques for simulating human systems , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[20]  F. Slanina.  Inelastically scattering particles and wealth distribution in an open economy. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[22]  Federico Bergenti,et al.  An analytic study of opinion dynamics in multi-agent systems , 2017, Comput. Math. Appl..

[23]  Raul Toral,et al.  Noisy continuous-opinion dynamics , 2009, 0906.0441.

[24]  Federico Bergenti,et al.  Simulations of Opinion Formation in Multi-Agent Systems Using Kinetic Theory , 2015, WOA.

[25]  Federico Bergenti,et al.  Analytic Study of Opinion Dynamics in Multi-Agent Systems with Two Classes of Agents , 2016, WOA.

[26]  H. Fischer,et al.  Mathematical Modeling of Complex Biological Systems , 2008, Alcohol research & health : the journal of the National Institute on Alcohol Abuse and Alcoholism.

[27]  Federico Bergenti,et al.  Kinetic Description of Opinion Evolution in Multi-agent Systems: Analytic Model and Simulations , 2015, PRIMA.

[28]  Kate Larson,et al.  Opinion dynamics of skeptical agents , 2014, AAMAS.