Abstract
This paper presents an analytic framework to study the dynamics of the opinion in multi-agent systems. In the proposed framework, each agent is associated with an attribute which represents its opinion, and the opinion of an agent changes because of interactions with other agents, without supervised coordination. Each interaction involves only two agents, and it corresponds to an exchange of messages. The framework assumes that time is modeled as a sequence of discrete steps, which do not necessarily have the same duration, and that at each step two random agents interact. Various sociological phenomena can be incorporated in the proposed framework, and the framework allows studying macroscopic properties of a system starting from microscopic models of such phenomena, obtaining analytic results. In detail, the proposed framework is inspired by the kinetic theory of gas mixtures, which relies on the use of balance equations that can be properly adopted to study opinion dynamics in a multi-agent system. After a short introduction on the kinetic theory of gas mixtures, this paper shows how the main ideas behind it can be generalized to study the dynamics of the opinion in multi-agent systems starting from a detailed description of microscopic interactions among agents.
The work presented in this paper is partially supported by Gruppo Nazionale per il Calcolo Scientifico (GNCS).
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References
1. D. Stauffer and T. J. P. Penna, “Crossover in the Cont-Bouchaud percolation model for market fluctuations,” Physica A: Statistical Mechanics and Its Applications, vol. 256, pp. 284–290, 1998.
2. F. Schweitzer and J. Holyst, “Modelling collective opinion formation by means of active brownian particles,” European Physical Journal B, pp. 723–732, 2000.
3. G. Toscani, “Kinetic models of opinion formation,” Communications in Mathematical Sciences, vol. 4, pp. 481–496, 2006.
4. W. Weidlich, Sociodynamics: A systematic approach to mathematical modelling in the social sciences. Amsterdam: Harwood Academic Publisher, 2000.
5. L. Pareschi and G. Toscani, Interacting Multiagent Systems: Kinetic Equations and Montecarlo Methods. Oxford: Oxford University Press, 2013.
6. S. Monica and F. Bergenti, “A study of consensus formation using kinetic theory,” in Proceedings of the 13th International Conference on Distributed Computing and Artificial Intelligence (DCAI 2016), Sevilla, Spain, June 2016, pp. 213–221.
7. F. Bergenti and S. Monica, “Analytic study of opinion dynamics in multi-agent systems with two classes of agents,” in Proceedings of 17th Workshop “Dagli Oggetti agli Agenti” (WOA 2016), Catania, Italy, July 2016.
8. S. Monica and F. Bergenti, “Opinion dynamics in multi-agent systems: Selected analytic models and verifying simulations,” Computational and Mathematical Organization Theory, accepted September 2016.
9. R. P. Abelson, Contributions to Mathematical Psycology. New York: Frederiksen N., Gulliksen H. eds., 1964.
10. E. Bonabeau, “Agent-based modeling: Methods and techniques for simulating human systems.” Proc. Natl. Acad. Sci, pp. 7280–7287, 2002.
11. A. Nowak, J. Szamrej, and B. Latan, “From private attitude to public opinion: A dynamic theory of social impact,” Psycol. Rev., vol. 97, pp. 362–376, 1990.
12. M. Mäs and A. Flache, “Differentiation without distancing. Explaining bipolarization of opinions without negative influence,” PLOS One, vol. 8, 2013.
13. S. Galam, Y. Gefen, and Y. Shapir, “Sociophysics: A new approach of sociological collective behavior,” Journal of Mathematical Sociology, 2009.
14. M. Mäs, A. Flache, and D. Helbing, “Individualisazion as driving force of clustering phenomena in humans,” PLOS One, vol. 6, no. 10, 2010.
15. E. Yildiz, A. Ozdaglar, D. Acemoglu, A. Saberi, and A. Scaglione, “Noisy continuous opinion dynamics,” Journal of Statistical Mechanics, vol. 9, pp. 1–13, 1982.
16. R. Hegselmann and U. Krause, “Opinion dynamics and bounded confidence models, analysis, and simulation,” Journal of Artificial Societies and Social Simulations, vol. 5, no. 3, 2002.
17. S. Monica and F. Bergenti, “Simulations of opinion formation in multi-agent systems using kinetic theory,” in Proceedings of 16 th Workshop “Dagli Oggetti agli Agenti” (WOA 2015), Napoli, Italy, June 2015.
18. S. Monica and F. Bergenti, “A kinetic study of opinion dynamics in multi-agent systems,” in Atti del Convegno AI*IA 2015, Ferrara, Italy, September 2015.
19. S. Monica and F. Bergenti, “Kinetic description of opinion evolution in multi-agent systems: Analytic model and simulations,” in Proceedings of the 18th International Conference on Principles and Practice of Multi-Agent Systems (PRIMA 2015), Bertinoro, Italy, October 2015, pp. 483–491.
20. S. Monica and F. Bergenti, “An analytic study of opinion dynamics in multi-agent systems with additive random noise,” in Atti del Convegno AI*IA 2016, Genova, Italy, December 2016.
21. S. Monica and F. Bergenti, “An analytic study of opinion dynamics in multi-agent systems,” Computer and Mathematics with Applications, accepted March 2017.
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Monica, S., Bergenti, F. (2018). Outline of a Generalization of Kinetic Theory to Study Opinion Dynamics. In: Omatu, S., Rodríguez, S., Villarrubia, G., Faria, P., Sitek, P., Prieto, J. (eds) Distributed Computing and Artificial Intelligence, 14th International Conference. DCAI 2017. Advances in Intelligent Systems and Computing, vol 620. Springer, Cham. https://doi.org/10.1007/978-3-319-62410-5_37
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