Multi-pursuer pursuit-evasion games under parameters uncertainty: A Monte Carlo approach

The traditional pursuit-evasion game considers a situation where one or more pursuers try to catch an evader, while the evader is trying to escape. Instead of moving entities, a more general scope of the pursuit-evasion game could also consider systems of systems. In a system consisting of many subsystems, when one subsystem decides to dissent and operate in a manner that is inconsistent with the others, a game situation similar to the pursuit-evasion game occurs. The dissenting subsystem can be viewed as an evader and the remaining conforming subsystems can be viewed as pursuers who oppose and try to prevent the dissention from succeeding. This is a more general system of systems, approach to the pursuit-evasion problem where the players are now subsystems of a system rather than moving entities. Clearly, any control strategy by any one of the subsystems to separate needs to be assessed against a variety of options that the remaining subsystems may use. In this paper, we consider a game where the pursuer subsystems consider three possible strategies: (1) act independently as Nash players, (2) act optimally as a team, and (3) act individually as greedy pursuers. The evader subsystem, on the other hand, will consider strategies against all possible strategies by the pursuer subsystems. We assume that no subsystem knows which strategies the other subsystems are implementing and none of the subsystems has information about any of the parameters in the objective functions of the other subsystems. We deal with these uncertainties by first developing the Nash strategies for each of the resulting games for all possible options available to both sides. Given the prevailing parameter uncertainty in developing the strategies, we perform a Monte Carlo analysis to determine probabilities of success (or failure) for each of the strategies considered by each side. We illustrate the results using two simulation scenarios of a pursuit-evasion example consisting of three pursuers moving on a plane and chasing one evader.