Two stars-the 100-meter gold medalist and the 200-meter gold medalist-from the p

Question

Two stars-the 100-meter gold medalist and the 200-meter gold medalist-from the past Olympic Games have agreed to a 150-meter duel. Before the race, each athlete decides whether to improve his performance by taking anabolic steroids. Each athlete's payoff is 60 from winning the race, 30 from tying, and 0 from losing. Furthermore, each athlete's utility from taking steroids is 18. Model this scenario as a game in which the players simultaneously decide whether to take steriods Athlete 1 Steroids No Steroids What is the Nash equilibrium? 12 Steroids ( A. The Nash equilibrium is for both athletes to use steroids O B. The Nash equilibria are for both athletes to use steroids and for both 12 athletes to not use steroids Athlete 2 ° C. The Nash equilibrium is for Athlete 1 to not use steroids and Athlete 2 42 30 to use steroids No Steroids D. The Nash equilibrium is for Athlete 1 to use steroids and Athlete 2 to not use steriods 30 E. The Nash equilibrium is for neither athlete to use steroids Is the game a prisoners' dilemma? Explain This game ( A. is a prisoners' dilemma because joint utility is maximized when neither O B. is not a prisoners' dilemma because joint utility when both athletes use ° C. is not a prisoners' dilemma because joint utility is maximized when both Athlete 1 athlete uses steroids Steroids No Steroids steroids is equal to joint utility when both athletes do not use steroids 12 athletes use steroids Steroids D. is not a prisoners' dilemma because joint utility is maximized when both 0 E. is a prisoners' dilemma because joint utility is maximized when one Suppose that one athlete's (Athlete 2's) utility of taking steroids is 36 What is the Nash equilibrium? athletes do not use steroids 24 Athlete 2 athlete uses steroids and the other athlete does not. 42 30 No Steroids 30 Click to select your answer

Explanation / Answer

In the first question the Nash equilibrium is when both the players use steroids. This is because steroids is a dominant strategy for both the players. This indicates that the correct option in option A

The game resembles prisoner's dilemma because when they use steroids as a chosen strategy their joint utility is less. They could have achieve the higher utility by choosing for no steroid. In this case also option A is correct.

In the third figure player 1 has dominant strategy of using steroids while player 2 has a dominant strategy of not using steroids. Thus, the Nash equilibrium is option C.

This is again prisoner's dilemma game because the joint utility is maximized when both choose no steroids. Option E is correct

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