James and Dean are playing the Chicken game. They have noticed that their payout for being perceived as "tough" depends on the size of the crowd. The larger the crowd, the "cooler" they are when they drive straight and the other driver swerves. A smaller the crowd, of course, has the opposite exact. Let k > 0 represent the payoff to appearing "tough." The game is represented as follows:
Dean
D V
James D -10,-10 k,-1
V -1,k 0,0
(a) Expressed in terms of k, what is the probability p_ that each driver plays D in the mixed strategy? Nash Equilibrium of this game?
(b) Do James and Dean play D more often as k increases? Explain briefly.
(c) In terms of k what is the expected payout each player from the mixed strategy Nash Equilibrium?