Mean-field game for collective decision-making in honeybees via switched systems

L. Stella, D. Bauso, P. Colaneri

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Abstract

In this paper, we study the optimal control problem arising from the mean-field game formulation of the collective decision-making in honeybee swarms. A population of homogeneous players (the honeybees) has to reach consensus on one of two options. We consider three states: the first two represent the available options (or strategies), and the third one represents the uncommitted state. We formulate the continuous-time discrete-state mean-field game model. The contributions of this paper are the following: i) we propose an optimal control model where players have to control their transition rates to minimize a running cost and a terminal cost, in the presence of an adversarial disturbance; ii) we develop a formulation of the micro-macro model in the form of an initial-terminal value problem (ITVP) with switched dynamics; iii) we study the existence of stationary solutions and the mean-field Nash equilibrium for the resulting switched system; iv) we show that under certain assumptions on the parameters, the game may admit periodic solutions; and v) we analyze the resulting microscopic dynamics in a structured environment where a finite number of players interact through
Original languageEnglish
JournalIEEE Transactions on Automatic Control
Early online date3 Sep 2021
DOIs
Publication statusE-pub ahead of print - 3 Sep 2021

Keywords

  • Mean-Field Game Theory
  • Social Networks
  • Multi-Agent Systems
  • Switched Systems

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