Question

There are two competing companies in the car sector, say Suzuki and Nissan, that have chosen to offer a new car model. Each should decide whether to offer payment facilities to its customers, an action that will increase its market share, but at the same time will generate a cost for the company. Both companies prefer not to offer such payment facilities, but each company fears that if its rival offers them, then it will lose many customers. In particular, each of these two companies’ profits will be 400 if both offer payment facilities and 600 if none offers them. If a company does not offer payment facilities and its rival offers them, then it will obtain a profit of 300, while its rival will obtain a profit of 800. Suzuki and Nissan decide simultaneously whether to offer payment facilities or not to their customers.

a) Represent this game in matrix form and find its Nash equilibrium.
b) Characterize the type of the game and argue why the equilibrium in (a) is also equilibrium in strictly dominant strategies.
c) Now Suzuki decides first whether to offer payment facilities or not and then Nissan takes its decision. Represent the game in extensive form and find its subgame perfect Nash equilibrium. d) If the game in which Suzuki and Nissan decide simultaneously whether to offer payment facilities or not is repeated two times, do you think that these companies will obtain higher profits per period? Argue why or why not.
e) If the game in (d) is repeated instead for an infinite number of times and both companies have a discount factor ?=0.8, will your answer in (d) be the same? Explain in detail.

I NEED ONLY QUESTION e, thank you

Answer 1

Payoff matrix

Suzuki/ Nissan	Offer	don't offer
Offer	(400*,400•)	(800*,300)
Don't offer	(300,800•)	(600,600)

D) in simultaneous Game

NE: both firms offer payment facilities

E) infinitely repeated game ;

using Grim Trigger strategy

if both Firms Cooperate & decide dont offer payments, then both could earn higher payoff, as compared to NE

so if both Cooperate, the present discount value of payoffs

Vc = 600 + 600d + 600d² + 600d³ + ...

( Let d is discount factor )

Vc = 600/(1-d)

= 600/.2

Vc = 3000

if any one deviates , while other is Cooperating, then it gets 800,

Next punishment starts from next period onwards, where both will play only NE of stage game, next period onwards

So present discount value of cheating payoff

Vd = 800 + 400d + 400d² + 400d³ +....

= 800 + 400d/(1-d)

= 800 + 400*.8/.2

= 800 + 1600

= 2400

Now as Vc > Vd

so Cooperation is possible,

a new eqm , where both ;dont offer payment , could be sustained as SPNE of infinitely repeated game