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Consider a game played between an athlete (player 1) and a drug testing officer (player 2). The athlete has two strategies: not use illegal drugs (N) or use illegal drugs (U). The drug testing officer also has two strategies: not test (N) or test (T).
If the athlete chooses not to use illegal drugs, his payoff is always 0. On the other hand, he gains g > 0 from using illegal drugs if he is not tested. He receives l < 0 from using illegal drugs if he is tested.
If the drug testing officer choose not to test, her payoff is always 0. On the other hand, if she chooses to test, she incurs a cost of c and she will get a benefit from reputation of catching cheaters b > 0 if she catches the athlete using illegal drugs.
The game is given as follows:
N
T
0,0
0,-C
U
g,0
-l,b-c
(Left is Player 1, Top is player2)
Provide the detailed analysis for finding all Nash equilibria in the cases of b < c, b = c and b > c.
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