234. Essay: Dell and Gateway are close competitor…
Question Dell and Gateway are close competitors in the personal computer market.
Suppose that each year Dell and Gateway have to decide whether to spend money
on costly research and development (R&D). If both spend money on R&D, each
firm will earn $30 million. If neither spends money on R&D, each firm will earn $40
million. If one firm spends money on R&D and the other does not, the firm that
engaged in R&D would earn $45 million and the firm that did not would earn $25
million.
a) Use a payoff matrix to depict this problem.
b) What is the noncooperative solution to this game?
235. Essay: Two large universities, Humongous Sta...
Question 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 pro basketball. Each school could choose to illegally pay top
players to attend their schools and thus increase the winning percentage of the
team, or each program can follow the rules and not pay top athletes to play college
basketball, thus losing them to the pro ranks. The table shows the payoff matrix of
winning percentages that each school would receive from their recruiting decision,
given the recruiting decision of their rival. Winning percentages in each cell of the
payoff matrix are given as (HSU, BSU).
a) What is the noncooperative Nash equilibrium?
b) Suppose that 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 the
same. If one school breaks the agreement and pays players, the other school will
do the same and continue to do so 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?
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