Two drivers, player 1 and player 2, are simultaneously approaching an intersection from different directions. They may choose to stop (S) or continue (C) at the intersection. If they both stop they prevent a crash and each receives a payoff of 1. If they both continue they crash and each receives a payoff of 0. If only player 2 stops, then player 1 gets a payoff of 2 whereas player 2 gets a payoff of 1 c, where c reflects the dislike of the player being the only one to stop. Conversely, if only player 1 stops, then she gets 1 c and player 2 gets 2. Assume 0 < c < 1.

(a) Formulate this situation as a strategic form game.

(b) Find all the Nash equilibria (in pure and mixed strategies). Find the expected payoff of each player at the mixed strategy equilibrium