Foraging Swarms as Nash Equilibria of Dynamic Games
IEEE TRANSACTIONS ON CYBERNETICS, vol.44, no.6, pp.979-987, 2014 (SCI-Expanded, Scopus)
- 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
- Open Archive Collection: AVESIS Open Access Collection
- 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.