Countries A and B are engaged in a high stakes game of chicken. Both have two pure strategies: act tough or back down. They will make their decisions simultaneously. The payoffs are
B
Back Down Act Tough
A Back Down 0,0 -1, k
Act Tough k, -1 -10, -10
where k > 0 is the payoff from acting tough when your opponent backs down.
(a) Show that this game has two pure strategy Nash equilibria.
(b) The game also has a mixed strategy Nash equilibrium. Find the equilibrium probability that each country will act tough as a function of k.
(c) Does the equilibrium probability that a country will act tough rise, fall, or remain constant as k rises?