The NCAA prohibits schools that are caught paying athletes from participating in
ID: 1207090 • Letter: T
Question
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?
Explanation / Answer
a.
b. In a one shot version of the game, since there is no punishment in the second round, both the schools would like to maximize there profits and thus would like not to pay to the athlete and earns a profit of $7.
Hence, in one shot version of the game, both school would like to play "Don't Pay" stategy of the game
However, if the game is repeated for 5000 times then both the schools have an advantage to maximize there profits by paying there athlete. Following there competitors, other shool will also like to maximize its profit by paying its athlete and thus in a repeated game, the outcome would be (Pay, Pay) i.e. both the schools are earning (1,1)
c. With indefinitly repeated games, both the schools will collude and would not pay there athletes and earns an aggregate payoffs of $14 ($7 each). But due to grim trigger strategy, if any one school cheats and try to earn higher profit by paying its athlete then his competitor will follow the same strategy to pay its athlete and both ends up having a profit of $1 each
d. In order to have cooperation, the actual interest rate has to be lower than every firm's maximum, in order to guarantee that no firm has incentive to cheat.
In this case, monopoly profit is $14 which is divided equally between the two firms thus In order for a firm not to cheat, it must be:
7 + 7/(1+r) > 14 + 0/(1+r)
which reduces to r < 0. For the interest rate to be less than 0, it means that firms have to value the future more than they value the present. Or, you have to invest more than one dollar this year to have one dollar next year.
School B's Profit Pay Don’t Pay School A's Profit Pay (1,1) (15,-15) Don’t Pay (-15,15) (7,7)Related Questions
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