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

Now consider the case where the game is repeated indefinitely. For what discount factors is it a Nash equilibrium for the outcome to be that the acquiring team offers a high price, and the trading team always offers a high quality player?

Answer 1

	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 )

The strategy ; acquiring team offers a high price, and the trading team always offers a high quality player , is a strategy of cooperation

If the two teams cooperate with each other, then series of payoff:

Vc = 200,000 + 200,000^2 + ..........

Vc = 200,000 / (1 - )

where is the discount factor

If one of the team player deviates, then the gets "450,000" and afterward play "Trade Low Quality Player, Offer Low Price"

Series of payoff in deviation case:

Vd = 450,000 + 50,000 + 50,000^2 + ..........

= 450,000 + 50,000 / 1 -

Both the teams will cooperate if,

Vc    Vd

200,000 / (1 - ) 450,000 + 50,000 / 1 -

200,000   450,000 - 450,000 + 50,000

400000 250000

0.625

So, discount factor has to greater or equal to 0.625 for achieving a given nash equilibrium