A coalition game-theoretic power allocation algorithm is put forward for the low probability of intercept (LPI) problem in a distributed radar network when tracking multiple targets. Firstly, guided by LPI, a utility function that integrates the multi-target tracking capability, the coalition structure and the power management of the radars is designed. Then, the power allocation optimization model is established to maximize the game utility function with the constraint of the predefined threshold of multi-target tracking performance and certain system transmit power resources. Subsequently, the existence of the equilibrium solution for the game is proven mathematically. To address the optimization model, a game iterative algorithm is proposed based on the sequential quadratic programming (SQP) algorithm. Simulation results indicate that this algorithm obtains the lowest total transmit power consumption compared with other general schemes while meeting the requirement on the target tracking capability, which reduces the probability of the radars being detected.