Probability, Risk, and Value of Information: Pro Sports Contracts

Suppose there are 10 identical athletes graduating college and entering the draft, where 10 pro sports teams must each choose one player to draft for a guaranteed payment of money. One of these ten athletes has an invisible career-ending injury and will actually be worth $0 after being drafted and paid. Each athlete only knows their own health status and the teams have zero information about this. There is an equal chance that each of the ten players has the injury. The teams cannot observe any difference between any of the players, but they can reveal whether or not a player is healthy or injured with 100% accuracy if a physical health exam is conducted.

a) Assume all pro players are immediately paid $2,000,000 by the team that drafts them. How much would a risk-neutral team with the first draft pick (this means the team is first in line to select a player) be willing to pay to conduct a physical exam on one of the ten players chosen at random?

b) Now assume that pro teams can pay any amount they want, but a healthy player is worth $2 mil and there is a large competitive market internationally which is open to the players in case they are not offered their fair value. How much would one of the 9 healthy players be willing to pay for a physical if the team is not allowed to request it and the player must purchase the exam to prove their health?

c) Assuming that physical exams only cost a few hundred dollars, how much would the injured player be willing to pay the league to make a rule preventing all players from receiving any exams or otherwise signaling or sharing their health information?

d) Explain one market intervention / policy / new rule that could help to mitigate the cost of asymmetric information in a way that benefits the teams.

e) Explain one market intervention / policy / new rule that could help to mitigate the cost of asymmetric information in a way that benefits the players.