Consider the game theory model for a Drug Test. Player 1 is an athlete who chooses whether to use steroids or not. Player 2 is the official who decides whether to conduct a drug test on Player 1. Payoffs to players are presented below. Check Pass Dope -alpha, alpha 1, -1 Clean 0, -1 0, 0 Assume alpha > 1, which of the following statements is TRUE? If α increases, athletes will be more likely to dope and drug tests are less likely to be carried out If α decreases, athletes will be less likely to dope and drug tests are more likely to be carried out If α increases, athletes will be less likely to dope and drug tests are less likely to be carried out If α decreases, athletes will be less likely to dope and drug tests are less likely to be carried out
Question
Consider the game theory model for a Drug Test. Player 1 is an athlete who chooses whether to use steroids or not. Player 2 is the official who decides whether to conduct a drug test on Player 1. Payoffs to players are presented below.
Check Pass
Dope -alpha, alpha 1, -1 Clean 0, -1 0, 0
Assume alpha > 1, which of the following statements is TRUE?
If α increases, athletes will be more likely to dope and drug tests are less likely to be carried out
If α decreases, athletes will be less likely to dope and drug tests are more likely to be carried out
If α increases, athletes will be less likely to dope and drug tests are less likely to be carried out
If α decreases, athletes will be less likely to dope and drug tests are less likely to be carried out
Solution
The correct statement is: "If α increases, athletes will be less likely to dope and drug tests are less likely to be carried out."
Here's why:
In this game theory model, α represents the penalty for being caught doping. If α increases, the penalty for being caught doping becomes more severe. This makes doping a less attractive option for the athlete (Player 1), so they are less likely to dope.
On the other hand, if the athlete is less likely to dope, the official (Player 2) has less incentive to conduct a drug test. This is because the cost of conducting a drug test (-1) is higher than the payoff of catching a clean athlete (0). Therefore, if α increases, drug tests are less likely to be carried out.
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