Foraging Swarms as Nash Equilibria of Dynamic Games

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Ozguler A. B., Yıldız A.

IEEE TRANSACTIONS ON CYBERNETICS, vol.44, no.6, pp.979-987, 2014 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 6
  • Publication Date: 2014
  • Doi Number: 10.1109/tcyb.2013.2283102
  • Journal Name: IEEE TRANSACTIONS ON CYBERNETICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.979-987
  • Keywords: Artificial potentials, differential game, Hamilton-Jacobi, multiagent systems, Nash equilibrium, swarm, STABILITY ANALYSIS, ARTIFICIAL POTENTIALS, COOPERATIVE CONTROL
  • TED University Affiliated: No

Abstract

The question of whether foraging swarms can form as a result of a noncooperative game played by individuals is shown here to have an affirmative answer. A dynamic game played by N agents in 1-D motion is introduced and models, for instance, a foraging ant colony. Each agent controls its velocity to minimize its total work done in a finite time interval. The game is shown to have a unique Nash equilibrium under two different foraging location specifications, and both equilibria display many features of a foraging swarm behavior observed in biological swarms. Explicit expressions are derived for pairwise distances between individuals of the swarm, swarm size, and swarm center location during foraging.