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(Game Theory)
Consider the following game:
Two brothers, Aidan and Asher, boast that they are the most brave. To prove this to each other they decide to play a game of chicken. Each of them tosses $100 on the table to back up their boast and all their friends come to watch them. They each get into their go-karts and shout defiance at the other as they begin to race towards the other person on a collision course. As they get close - they have to simultaneously make a decision: do they swerve or drive straight? If they both swerve - they each receive a payoff of 0. If one of the brothers swerves while the other one drives straight then the one that drove straight receives a payoff of 500 (the money plus the fame of being the bravest) while the other receives a payoff of -300 (the loss of money and reputation). If both brothers drive straight - they crash into each other and both suffer a payoff of -800 (the cost of repairs to their go-kart).
a. If Aidan believes that Asher is going to drive straight - what should Aidan do to maximize his payoff?
b. If Aidan believes that Asher is going to swerve - what should Aidan do to maximize his payoff?
c. If after they started to race towards each other - Asher was to throw his steering wheel out the side of the go-kart, which means that he could no longer steer to swerve his go-kart. What would be the only rational response from Aidan after seeing this?
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