Stackelberg Mean-Field-Type Games with Polynomial Cost

Zahrate El Oula Frihi, Julian Barreiro-Gomez, Salah Eddine Choutri, Boualem Djehiche, Hamidou Tembine

Research output: Contribution to journalConference articlepeer-review


This article presents a class of Stackelberg mean-field-type games with multiple leaders and multiple followers. The decision-makers act in sequential order with informational differences. The state dynamics is driven by jump-diffusion processes and the cost function is non-quadratic and has a polynomial structure. The structures of Stackelberg strategies and costs of the leaders and followers are given in a semi-explicit way in state-and- mean-field-type feedback form. A sufficiency condition is provided using an infinite dimensional partial integro-differential system. The methodology is extended to multi-level hierarchical systems. It is shown that not only the set of decision-makers per level matters but also the number of hierarchical levels plays a key role in the global performance of the system. We also identify specific range of parameters for which the Nash equilibrium coincides with the hierarchical solution independently of the number of layers and the order of play.

Original languageEnglish (US)
Pages (from-to)16920-16925
Number of pages6
Issue number2
StatePublished - 2020
Event21st IFAC World Congress 2020 - Berlin, Germany
Duration: Jul 12 2020Jul 17 2020


  • Mean-field-type games
  • Stackelberg solutions
  • hierarchical game design
  • semi-explicit solutions

ASJC Scopus subject areas

  • Control and Systems Engineering


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