Problem 2: Game Theory. A team is choosing whether to Cheat (C) or Not Cheat (N) in the final tournament, and a league is deciding whether to be Strict (S) or Lenient (L) in monitoring the cheating.

If the team cheats and gets away with it, they get $40,000 payoff. If the team cheats and gets caught, they must pay $20,000 and hence get a -$20,000 payoff. If the team does not cheat, they get a payoff of $0.

If the league is strict and the team cheats, the team gets caught with probability pS = 3 . If

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When the league is Strict, their expected payoff is $0. When the league is Lenient, their expected payoff is $10,000.

a) What is the expected payoff of the team if they cheat when the league is strict? b) What is the expected payoff of the team if they cheat when the league is lenient?

c) Draw the normal form game. Add the (expected) payoffs to the matrix. d) Find all four best responses.

e) What is the Nash equilibrium?