  In the repeated Prisoner's Dilemma, when every player has a different
discount factor, the grim-trigger strategy is an equilibrium if and only if the
discount factor of each player is higher than some threshold. What happens if
the players have incomplete information regarding the discount factors? In this
work we look at repeated games in which each player has incomplete information
regarding the other player's discount factor, and ask when a pair of
grim-trigger strategies is an equilibrium. We provide necessary and sufficient
conditions for such strategies to be an equilibrium. We characterize the states
of the world in which the strategies are not triggered, i.e., the players
cooperate, in such equilibria (or $\epsilon$-equilibria), and ask whether these
"cooperation events" are close to those in the complete information case, when
the information is "almost" complete, in several senses.
