Scaling limits for continuous opinion dynamics systems

Annals of Applied Probability

Volumn 21, Issue 4, 2011, Pages 1537-1567

  Como, Giacomo ^a   Fagnani, Fabio ^b  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b POLITECNICO DI TORINO   (Italy)

Author keywords

Bounded confidence; Multi agent systems; Opinion dynamics; Probability measure valued Odes; Scaling limits; Social networks

Indexed keywords

EID: 80051604036     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/10-AAP739     Document Type: Article

References (32)

1. ACEMOGLU, D., COMO, G., FAGNANI, F. and OZDAGLAR, A. (2010). Opinion fluctuations and disagreement in social networks. Unpublished manuscript. Available at http://arxiv. org/abs/1009.2653.
2. ALON, N. and SPENCER, J. H. (2008). The Probabilistic Method, 3rd ed.Wiley, Hoboken, NJ. MR2437651
3. AMBROSIO, L., GIGLI, N. and SAVARé, G. (2005). Gradient Flows in Metric Spaces and in the Space of Probability Measures. Birkhäuser, Basel. MR2129498
4. AXELROD, R. (1997). The dissemination of culture. J. of Conflict Resolution 42 203-226.
5. BEN-NAIM, E., KRAPIVSKY, P. L. and REDNER, S. (2003). Bifurcation and patterns in compromise processes. Phys. D 183 190-204. MR2006633
6. BLONDEL, V. D., HENDRICKX, J. M. and TSITSIKLIS, J. N. (2009). Continuous-time average-preserving opinion dynamics with opinion-dependent communications. Unpublished manuscript.
7. BLONDEL, V. D., HENDRICKX, J. M. and TSITSIKLIS, J. N. (2009). On Krause's multiagent consensus model with state-dependent connectivity. IEEE Trans. Automat. Control 54 2586-2597. MR2571922
8. BORKAR, V. S. (1995). Probability Theory: An Advanced Course. Springer, New York. MR1367959
9. BOYD, S., GHOSH, A., PRABHAKAR, B. and SHAH, D. (2006). Randomized gossip algorithms. IEEE Trans. Inform. Theory 52 2508-2530. MR2238556 (Pubitemid 43898906)
10. CANUTO, C., FAGNANI, F. and TILLI, P. (2008). A Eulerian approach to the analysis of rendez-vous algorithms. In Proc. of 2008 IFAC Conf., Seoul, Korea, July 6-11 9039-9044. Available at http://calvino.polito.it/~fagnani/ coordincontrol/IFAC08CFT.pdf.
11. CASTELLANO, C., FORTUNATO, S. and LORETO, V. (2009). Statistical physics of social dynamics. Rev. Mod. Phys. 81 591-646.
12. CUCKER, F. and SMALE, S. (2007). Emergent behavior in flocks. IEEE Trans. Automat. Control 52 852-862. MR2324245 (Pubitemid 46796070)
13. CUCKER, F. and SMALE, S. (2007). On the mathematics of emergence. Jpn. J. Math. 2 197-227. MR2295620
14. DEFFUANT, G., NEAU, D., AMBLARD, F. andWEISBUCH, G. (2000). Mixing beliefs among interacting agents. Adv. Complex Syst. 3 87-98.
15. DEFFUANT, G., NEAU, D., AMBLARD, F. andWEISBUCH, G. (2004). Modelling group opinion shift to extreme: The smooth bounded confidence model. In Proc. Europ. Social Simulation Assoc. Conf. Valladolid, Spain.
16. EDELSTEIN-KESHET, L. and ERMENTROUT, G. B. (1990). Models for contact-mediated pattern formation: Cells that form parallel arrays. J. Math. Biol. 29 33-58. MR1083664
17. FAGNANI, F. and ZAMPIERI, S. (2008). Asymmetric randomized gossip algorithms for consensus. In Proc. of 2008 IFAC Conf., Seoul, Korea, July 6-11 9052-9056. Available at http://www.ifac-papersonline.net/World-Congress/ Proceedings-of-the-17th-IFAC-World-Congress-2008/index.html.
18. FAGNANI, F. and ZAMPIERI, S. (2008). Randomized consensus algorithms over large scale networks. IEEE J. Select. Aereas Commun. 26 634-649. (Pubitemid 351658779)
19. FORTUNATO, S. (2005). On the consensus threshold for the opinion dynamics of Krause- Hegselmann. Int. J. Mod. Phys. 16 259-270. (Pubitemid 40900715)
20. FOURNIER, N. and MéLéARD, S. (2004). A microscopic probabilistic description of a locally regulated population and macroscopic approximations. Ann. Appl. Probab. 14 1880-1919. MR2099656 (Pubitemid 41449199)
21. HA, S.-Y. and LIU, J.-G. (2009). A simple proof of the Cucker-Smale flocking dynamics and mean-field limit. Commun. Math. Sci. 7 297-325. MR2536440
22. KRAUSE, U. (2000). A discrete nonlinear and non-autonomous model of consensus formation. In Communications in Difference Equations (Poznan, 1998) (S. Elaydi, G. Ladas, J. Popenda and J. Rakowski, eds.) 227-236. Gordon and Breach, Amsterdam. MR1792007
23. LORENZ, J. (2005). A stabilization theorem for dynamics of continuous opinions. Phys. A 355 217-223. MR2143285 (Pubitemid 40915182)
24. LORENZ, J. (2007). Continuous opinion dynamics under bounded confidence: A survey. Internat. J. Modern Phys. C 18 1819-1838.
25. LORENZ, J. (2007). Repeated averaging and bounded confidence? Modeling analysis and simulation of continuous opinion dynamics. Ph.D. thesis, Univ. Bremen. Available at http://elib.suub.uni-bremen.de/diss/docs/00010668.pdf.
26. LORENZ, J. (2010). Heterogeneous bounds of confidence: Meet, discuss and find consensus! Complexity 15 43-52. MR2643262
27. REMENIK, D. (2009). Limit theorems for individual-based models in economics and finance. Stochastic Process. Appl. 119 2401-2435. MR2532206
28. SHAH, D. (2008). Gossip algorithms. Foundations and Trends in Networking 3 1-125.
29. SHWARTZ, A. and WEISS, A. (1995). Large Deviations for Performance Analysis: Queues, Communications, and Computing. Chapman & Hall, London. MR1335456
30. VILLANI, C. (2009). Optimal Transport: Old and New. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 338. Springer, Berlin. MR2459454
31. WEISBUCH, G., DEFFUANT, G., AMBLARD, F. and NADAL, J. P. (2002). Meet, discuss, and segregate! Complexity 7 55-63. (Pubitemid 34687746)
32. WORMALD, N. C. (1995). Differential equations for random processes and random graphs. Ann. Appl. Probab. 5 1217-1235. MR1384372 (Pubitemid 126089079)