The policy game is a non-cooperative game, where the government decides the rate of inflation, whereas the private sector expects it. In the policy game, the sum of the payoffs is maximized when the government chooses an efficient action and the private sector responds to it appropriately. However, the policy game has only one inefficient Nash equilibrium because the government always takes the myopic action regardless of the private sector's expectation. In this paper, we analyze a specific model of the policy game with finite alternating repetitions. By applying backward induction, it is proved that only the efficient actions are chosen in subgame perfect equilibria.
