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 can illegally pay top players to enroll and thus
increase the winning percentage of the team, or each program 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 receive from 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?