Conformity Bias

Imagine two players playing the following variant of the one-shot prisoners' dilemma: C D C b - ctaxc -c+ axc D bta(1-xc) 0+a(1-x0) where b > c > 0, a > 0, and xc E [0, 1] is a constant that is intended to represent the proportion of people in players' reference group who are playing C (when ac = 0 no one is cooperating, and when xc = 1, everyone is cooperating). We say these payoffs exhibit 'conformity bias' because players' payoffs are increasing in the proportion of others who play the same strategy, and that a is the strength of this bias. (15 points) What are conditions on a, if any, such that all players playing D is a pure Nash equilibrium of the game? What are conditions on a, if any, such that all players playing C is a pure Nash equilibrium of the game? Interpret these results, comparing them to the case where a = 0