Models and metrics of geometric cooperation

A basic way that entities can cooperate with one another is by sharing of tasks through synchronized movement to balance their geometric load. For example, players of a team defending a goal may be assigned equal-spaced zones to defend or units in a military force may be assigned equal-spaced sectors to control. As the dynamics of the situation unfold and as entities move, withdraw, or enter the space; the other entities cooperate by adjusting their positions to retain load balance. Various ways that this geometric cooperation can be accomplished, both from the perspectives of central and local control, are developed, analyzed, and simulated. This problem is related to other geometric cooperation problems such as movements in multi-player pursuit-evasion games and balancing loads for other generally non-geometric algorithms. The authors use the metrics to establish a framework for a theory of geometric cooperation. Simulations, metrics, and results of the algorithms' performance in various scenarios are presented.