Some soccer players are high quality. The current club of a high quality player would need to be paid a transfer fee of $150m to give up the player, while the bidding club would be willing to pay a transfer fee of $200m to acquire the player. Other players are lower quality; for such a player, the current club would need to be paid a transfer fee of $60m to give them up, and the bidding club would be willing to pay a transfer fee of $80m to acquire them. Bidding clubs cannot tell the quality of a given player, while current clubs can. What happens if it is common knowledge that 50 percent of players are high quality and 50 percent are low?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 26EQ
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Some soccer players are high quality. The
current club of a high quality player would
need to be paid a transfer fee of $150m to
give up the player, while the bidding club
would be willing to pay a transfer fee of
$200m to acquire the player. Other players
are lower quality; for such a player, the
current club would need to be paid a transfer
fee of $60m to give them up, and the bidding
club would be willing to pay a transfer fee of
$80m to acquire them.
Bidding clubs cannot tell the quality of a given
player, while current clubs can. What happens
if it is common knowledge that 50 percent of
players are high quality and 50 percent are
low?
Transcribed Image Text:Some soccer players are high quality. The current club of a high quality player would need to be paid a transfer fee of $150m to give up the player, while the bidding club would be willing to pay a transfer fee of $200m to acquire the player. Other players are lower quality; for such a player, the current club would need to be paid a transfer fee of $60m to give them up, and the bidding club would be willing to pay a transfer fee of $80m to acquire them. Bidding clubs cannot tell the quality of a given player, while current clubs can. What happens if it is common knowledge that 50 percent of players are high quality and 50 percent are low?
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