Question

5. Consider the dynamic game represented by the game tree below. In this game, a buyer decides wether a relationship-specific investment with a supplier. If the buyer chooses to contract with the supplier, the supplier can attempt to raise the price agreed upon price of the input. If the supplier raises the price, the buyer is then forced to choose whether to keep the supplier at the new raised price or find a new supplier Find all the Nash equilibria. a. b. Find all the pure strategy subgame perfect equilibria. Buyer Don't Invest Invest Supplier (0,0) Raise Price Keep Price <Buyer (1000, 0) Change Supplier Keep Supplier (500,-1000) (250, 750)

Answer 1

Ans 1)      

  

		Seller
		RP	KP
	DI,CS	0;0	0;0
Buyer	DI,KS	0;0	0;0
	I,CS	(-500;-1000)	1000;0
	I,KS	250;750	1000;0

Bold payoffs are Pure strategy Nash equilibria

DI=Dont Invest

I=Invest

CS=Change Supplier

KS=Keep Supplier

We have 2 Pure strategy Nash Equilibria in this game and they are (I,KS ; RP) and (I,CS ; KP)

Ans 2)

We have 2 sub-games in this game that one starts in the initial node and other starts when supplier acts for Invest from Buyer

At terminal node Buyer will always choose to prefer Keep supplier over Change Supplier
hence payoff from Raise Price is (250,750) Now Supplier will always choose Raise Price over Keep Price therefor payoff from Invest is (250,750)

Hence At the first node Buyer will choose to invest over Dont Invest therefore Nash Equilibrium of whole game that is (I,KS ; RP) is Pure strategy Sub-game perfect equilibrium.

Where else ((I,CS ; KP) is not the Sub-game perfect Nash equilibrium

Only sub-game perfect Nash equilibrium is (I,KS ; RP)