Switching Costs in Frequently Repeated Games

We demonstrate the surprising effect of two simple variations on the usual finitely repeated game model. In particular, we add a small cost of changing actions and consider the effect of increasing the frequency of repetitions within a fixed period of time. We illustrate the wide range of commitments this can make credible and the effects these have. Not surprisingly, switching costs can make it credible to not change one’s action. However, this effect can occur even for very small switching costs, but only for certain actions. For example, because of this kind of commitment, we get a unique subgame perfect equilibrium in coordination games when the Pareto dominant and risk dominant outcomes coincide, but not otherwise. In other games, switching costs can make certain commitments less credible even as some are made more credible. For example, in the repeated Prisoners’ Dilemma, these costs reduce the incentive to deviate from mutual cooperation. However, they also reduce the incentive to switch from cooperation to punish a deviator. As a result, we show that switching costs might or might not enable cooperation in the finitely repeated Prisoners’ Dilemma depending on which of these effects dominates. More surprisingly, switching costs can make some very complex threats credible, leading to some unexpected possibilities. For example, we show that in some games, this commitment ability can enable a player to obtain a payoff strictly above his Stackelberg payoff. Also, we show that in some games, actions must be changed along the equilibrium path in the unique subgame perfect equilibrium.