Boltzmann Games in Heterogeneous Consensus Dynamics

Giacomo Albi, Lorenzo Pareschi, Mattia Zanella

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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.

Original languageEnglish
Pages (from-to)97-125
Number of pages29
JournalJournal of Statistical Physics
Issue number1
StatePublished - 15 Apr 2019
Externally publishedYes


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


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