Question

Let α1, α2 ∈ R. Consider the following version of prisoners’ dilemma (C
means “Confess” and N means “Do not confess”):
2
C N
1
C 0, 0 α1, −2
N −2, α2 5, 5
Suppose that the two players play the above stage game infinitely many times. Departing
from our in-class discussion, however, we assume that for each i ∈ {1, 2}, player i discounts
future payoffs at rate δi ∈ (0, 1), allowing δ1 and δ2 to differ.
(a) (10 points) The stage game above would be a proper prisoners’ dilemma only if
C is a strictly dominant strategy for each player. Find the conditions on α1 and α2 under
which this is true.
(b) (30 points) Assume, from now on, that the conditions identified in part (a) are
satisfied. Using grim trigger strategies, show that under appropriate assumptions on δ1
and δ2, it is possible to obtain a repeated play of (N, N) as the outcome of a subgame
perfect equilibrium

Answer 1