Swarming Behavior as Nash Equilibrium

The question of whether swarms can form as a result of a non-cooperative game played by individuals is shown here to have an affirmative answer. A dynamic game played by N agents in one-dimensional 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 Nash equilibrium that has all the features of a swarm behavior.