Trust Off the Equilibrium Path: Recall the trust game depicted in Figure. We argued that for δ ≥ 1/2 the following pair of strategies is a sub game perfect equilibrium.
For player 1: "In period 1 I will trust player 2, and as long as there were no deviations from the pair (T, C) in any period, then I will continue to trust him. Once such a deviation occurs then I will not trust him forever after."
For player 2: "In period 1 I will cooperate, and as long as there were no deviations from the pair (T, C) in any period, then I will continue to do so.
Once such a deviation occurs then I will deviate forever after." Show that if instead player 2 uses the strategy "as long as player 1 trusts me I will cooperate" then the path (T, C) played forever is a Nash equilibrium for δ ≥ 1/2 but is not a subgame-perfect equilibrium for any value of δ.
