Two large universities, Humongous State (HSU) and Behemoth State (BSU), dominate
college basketball. Each basketball program aggressively recruits the best athletes to
attend the university, but the best athletes can skip college and jump immediately to
professional basketball. Each school has two options: they can either illegally pay top
players to enroll and thus increase the winning percentage of the team, or they can
follow the rules and lose the top players to the professional ranks. The table shows the
payoff matrix of winning percentages that each school would achieve based on its
recruiting decision, given the recruiting decision of its rival. Winning percentages in
each cell of the payoff matrix are given as (HSU, BSU).
A) What is the noncooperative Nash equilibrium?
B) Suppose each school considers the future and devises a tit-for-tat strategy. Neither
school will pay players to play basketball so long as the other does not. If one school
breaks the agreement and pays players, the other school will do the same until the first
school stops paying players. If both schools adopt the tit-for-tat strategy, what are the
winning percentages every year? Will this be effective at eliminating the illegal practice
of paying college athletes to play basketball?
(Scenario: Payoff Matrix for Two Firms) Use Scenario: Payoff Matrix for Two Firms.
Firm B has:
Scenario: Payoff Matrix for Two Firms
The following table provides the payoff matrix for two firms, firm A and firm B. They
are the only two firms in the industry and can either compete or cooperate with each
other, with the following profit results reflecting their actions.