Games With Possibly Naive Hyperbolic Discounters

We propose a solution concept for games that are played among hyperbolic discounters that are possibly naive about their own, or about their opponent's future time inconsistency. Our perception-perfect equilibrium essentially requires each player to take an action consistent with the subgame perfect equilibrium, given her perceptions concerning future types, and under the assumption that other present and future players have the same perceptions. Applications include a common pool problem and Rubinstein bargaining. When players are naive about their own time consistency and sophisticated about their opponent's, the common pool problem is exacerbated, and Rubinstein bargaining breaks down completely.