Question

Consider the scenario where two teams are looking to trade. The acquiring team can offer a high price or a low price. The trading team can offer a high quality player or a low quality player - the acquiring team can't differentiate between these player types before the trade is completed, though they can figure it out later.

The table reflects the payoffs to each strategy for each team.

	Offer High Price	Offer Low Price
Trade High Quality Player	200,000 ; 200,000	-200,000 ; 600,000
Trade Low Quality Player	450,000 ; -350,000	50,000 ; 50,000

a) If the two teams only trade once, what is the Nash equilibrium of this game? Explain.

Answer 1

Let us find the nash equilibrium using the best response function

The best response of trading team to the acquiring team offering a high price is to offer a low-quality player (450000>200000)

The best response of trading team to the acquiring team offering a low price is to offer a low-quality player (50000>-200000)

Thus, offering a low quality player is the dominant strategy for the trading team

The best response of acquiring team to the trading team offering a high quality player is to offer a low price (600000>200000)

The best response of acquiring team to the trading team offering a low quality player is to offer a low price (50000>-350000)

Thus, offering a low price is the dominant strategy for the acquiring team

Thus, there is a unique nash equilibrium, where, the trading team offers a low quality player and the acquring team offers a low price