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Time Consistency in Alternating-Move Policy Games

We examine alternating-move policy games where the government and the private sector alternate their moves. In contrast with the standard policy game, the set of equilibrium payoffs of the present model is bounded away from the payoff under the one-shot Nash equilibrium, called the Kydland-Prescott outcome, and the upper bound is close to the payoff under the optimal policy (called the Ramsey policy) if the government is sufficiently patient. In other words, the Kydland-Prescott outcome is not time consistent, while the Ramsey outcome could be approximated by a time-consistent policy of the same game.