Answer :
Final answer:
In equilibrium, the highest quality player that could be transferred has a quality of Q = 1, as this is when the current team's valuation matches the acquiring team's valuation.
Explanation:
The equilibrium in the game of a soccer team acquiring a player with a uniform distribution of quality Q ~ U[0,1] involves analyzing the valuations of both teams. The current team values a player of quality Q at 150000 + 800000Q while the acquiring team values them at 250000 + 1000000Q. In equilibrium, the player will be transferred when the acquiring team's valuation equals or exceeds the current team's valuation. At equilibrium, the value to the acquiring team must at least match the value to the current team.
To find the maximum quality Q of player that could be transferred, set the current team's valuation equal to the acquiring team's valuation and solve for Q:
- 150000 + 800000Q = 250000 + 1000000Q
- This simplifies to 200000 = 200000Q
- Divide both sides by 200000 to solve for Q, which gives Q = 1
Therefore, in equilibrium, the highest quality player that could be transferred has a quality of Q = 1. This means that in theory, any player of any quality could be transferred since the distribution is from 0 to 1, but practically the highest possible quality that can be observed and transferred is 1.
In the given scenario, the soccer team wants to acquire a player from another team. The quality of the player is given by a uniform distribution, Q ~ U[0,1]. The team that currently owns the player knows the quality of the player, but the acquiring team does not. Now, let us discuss the highest quality player that could be transferred.
In equilibrium of this game, the player that the team would be willing to sell to the other team would be the one that does not add to their utility. Firstly, we need to find the expected utility of the current team. Suppose the current team expects a utility of U(X).
If the team decides to sell a player with quality q, their expected utility would be:E[U(X−q)]where X represents the level of the overall team quality.The acquiring team does not know the quality of the player, so the expectation of the acquiring team is: E[maxQ] / 2 where maxQ is the highest quality player that could be transferred.
Now we need to find the quality of the player that maximizes the expected utility of the current team. Let us denote this by q∗.To find q∗, we differentiate the expected utility of the current team with respect to q and equate it to zero.d/dq E[U(X−q)] = 0
Solving the above equation, we get:q∗ = X/2Therefore, the highest quality player that could be transferred is X/2. Hence, we can conclude that the player that the team would be willing to sell to the other team would be the one that does not add to their utility.
To know more about expected utility here
https://brainly.com/question/31833525
#SPJ11
