This paper presents decentralized solutions for pursuit-evasion problems involving high-order integrators with intracoalition cooperation and intercoalition confrontation. Distinct error variables and hyper-variables are introduced to ensure the control strategies to be independent of the relative velocities, accelerations and higher order information of neighbors. Consequently, our approach only requires agents to exchange position information or to measure the relative positions of the neighbors. The distributed strategies take into consideration the goals of intracoalition cooperation or intercoalition confrontation of the players. Furthermore, after establishing a sufficient and necessary condition for a class of high-order integrators, we present conditions for capture and formation control with exponential convergence for three scenarios: one-pursuer-one-evader, multiple-pursuer-one-evader, and multiple-pursuer-multiple-evader. It is shown that the conditions depend on the structure of the communication graph, the weights in the control law, and the expected formation configuration. Finally, the effectiveness of the proposed algorithm is demonstrated through simulation results.