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Boltzmann Games in Heterogeneous Consensus Dynamics

  • Giacomo AlbiEmail author
  • Lorenzo Pareschi
  • Mattia Zanella
Article
  • 15 Downloads

Abstract

We consider a constrained hierarchical opinion dynamics in the case of leaders’ competition and with complete information among leaders. Each leaders’ group tries to drive the followers’ opinion towards a desired state accordingly to a specific strategy. By using the Boltzmann-type control approach we analyze the best-reply strategy for each leaders’ population. Derivation of the corresponding Fokker–Planck model permits to investigate the asymptotic behaviour of the solution. Heterogeneous followers populations are then considered where the effect of knowledge impacts the leaders’ credibility and modifies the outcome of the leaders’ competition.

Keywords

Multi-agent systems Differential games Boltzmann equation Opinion leaders Consensus dynamics Knowledge 

Mathematics Subject Classification

35Q20 35Q91 49N70 

Notes

Funding

MZ was supported by the “Compagnia di San Paolo” (Torino, Italy). GA, LP, and MZ thank the “INDAM-GNCS 2018” (CBGNCSALBI2018) contribution.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Computer SciencesUniversity of VeronaVeronaItaly
  2. 2.Department of Mathematics and Computer ScienceUniversity of FerraraFerraraItaly
  3. 3.Department of Mathematical SciencesPolitecnico di TorinoTorinoItaly

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