Sam and dean take their cars to opposite ends of main street in the middle of nowhere, USA, at midnight and start to drive toward each other. The one who swerves to prevent a collision is a "chicken" and the one who keeps driving straight is the "winner". If both players maintain a straight course, there is a collision in which both cars are damaged and both players are injured. This scenario cost each $2000. The earnings for the "winner" are $1000, which are paid by the "chicken". There are no consequences if both swerve to safety.
A. Draw the payoff matrix. Make sure to include the players, actions and payoffs and determine the Nash Equilibrium or equilibria for this game. Explain the intuition behind your result.
B. What is the mixed strategy Nash Equilibrium? Explain the intuition behind your result. Clearly state the probabilities each should choose for each action.
C. Assume now that Dean's car is more expensive than Sam's so that repairs cost him $4000 instead of $2000 (Sam's car value remains the same as in a and b). What is the new mixed strategy equilibrium? Explain the intuition behind your result. Clearly state the probabilities each should choose for each action.