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The NCAA prohibits schools that are caught paying athletes from participating in bowl games, and sometimes the punishment is more severe. To understand why schools don't break away from the NCAA and form a league in which athletes can legitimately be paid, let's analyze the following normal-form game: Assume there are only two schools (A and B). If both schools pay athletes, then athletes extract virtually all of the profits, and each school is left with only $1 million in profits. If both schools don't pay athletes, each school earns $7 millions in profits, since less money goes to the athletes. If one school pays athletes and the other school does not, the school that pays athletes earns profits of $15 million and the school that does not pay athletes loses $15 million.
a. Write the normal form representation of this game
b. Find the Nash equilibrium for a one-shot version of this game. Find the Nash equilibrium if this game is repeated 5000 times.
c. Now suppose the game is infinitely repeated. Describe the Grim trigger strategies that the schools can use to sustain the outcome with the highest aggregate payoff (the collusive outcome).
d. For what values of the interest rate can collusion be sustained?
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