Grab the Dollar: Each of two players has two possible actions: grab the dollar or don't grab the dollar. Player i's payoff is 1 if he is the only one to grab the dollar, and his payoff is 0 if he does not. Each player's payoff is -1 if both players grab the dollar.

a. Find the Nash equilibria of this game of complete information.

b. Consider the following perturbation of the game. The payoff structure is the same, with the following addition: When player i is the only one to grab the dollar his payoff is 1+ θi, where θi is player i's type and it is uniformly distributed over [-ε, ε] with ε

c. Show that when ε converges to 0, the pure-strategy Bayesian Nash equilibrium converges to the mixed-strategy Nash equilibrium of the game with complete information.