This thesis considers mean field games in a continuous time competitive Markov decision process framework. Each player's state has pure jumps modeled by a self-weighted compound Poisson process subject to impulse control. We focus on analyzing the steady-state (or stationary) equation system of the mean field game. The best response is determined as a threshold policy and the stationary distribution of the state is derived in terms of the threshold value. The numerical solution of the equation system is developed. We further generalize the model to an unbounded state space.