Cooperative, non-cooperative and greedy pursuers strategies in multi-player pursuit-evasion games

In this paper we consider three different strategies for N pursuers and one evader in a multi-player Pursuit-Evasion game. Each pursuer's objective function reflects a desire to minimize the distance between itself and the evader while the evader's objective function reflects a need to escape by maximizing the distance between itself and a weighted measure of the distances between itself and the pursuers. The first strategy is characterized by pursuers who cooperate as a team in their effort to catch the evader. The resulting game is referred to as a Cooperating Pursuers Game. The second strategy is characterized by non-cooperating pursuers who act in a non-cooperative manner among themselves and the evader. The resulting game is referred to as a Non-Cooperating Pursuers Game. The third strategy is characterized by greedy pursuers who act independently and selfishly each on its own in an attempt to catch the evader. The resulting game is referred to as Greedy Pursuers Game. To treat these strategies under one common framework a general all-against-one linear quadratic dynamic game is considered and the corresponding closed-loop Nash solution is discussed. Using this framework, the three pursuers' strategies are then developed separately. Implementation of several scenarios of these games are also investigated where neither the pursuers nor the evader have knowledge of the objective functions of the other side and hence need to implement strategies that are secure against possible worst strategies by the other side. A Monte Carlo analysis over the parameters space of the objective functions is preformed to yield probabilities of capture of the evader under each of the studied scenarios. Results of the Monte Carlo simulation show that in general, pursuers do not always benefit from cooperating as a team and that acting as non-cooperating players may yield a higher probability of capturing the evader depending on what strategy the evader may use.