Foraging motion of swarms with leaders as Nash equilibria

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Yıldız A., Ozguler A. B.

AUTOMATICA, vol.73, pp.163-168, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 73
  • Publication Date: 2016
  • Doi Number: 10.1016/j.automatica.2016.07.024
  • Journal Name: AUTOMATICA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.163-168
  • Keywords: Leader-follower, Rendezvous problem, Ordered graph, Directed star, Nash equilibrium, Swarm, Foraging, Multi-agent systems, Differential game theory, FORMATION FLIGHT, OPTIMIZATION, PARTICLE, SAVINGS
  • TED University Affiliated: No


The consequences of having a leader in a swarm are investigated using differential game theory. We model foraging swarms with leader and followers as a non-cooperative, multi-agent differential game. The agents in the game start from a set of initial positions and migrate towards a target. The agents are assumed to have no desire, partial desire or full desire to reach the target. We consider two types of leadership structures, namely hierarchical leadership and a single leader. In both games, the type of leadership is assumed to be passive. We identify the realistic assumptions under which a unique Nash equilibrium exists in each game and derive the properties of the Nash solutions in detail. It is shown that having a passive leader economizes in the total information exchange at the expense of aggregation stability in a swarm. It turns out that, the leader is able to organize the non-identical followers into harmony under missing information. (C) 2016 Elsevier Ltd. All rights reserved.