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 simultanerely whether to offer payment facilities or not to their customers. b) Characterize the type of the game and argue why the equilibrium in (a) is also equilibrium in strictly dominant strategies. ,

Answer 1

B)

Payoff matrix

Suzuki / Nissan	Offer	doesnt offer
Offer	(400*,400•)	(800*, 300)
Doesnt offer	(300,800•)	(600,600)

Both Firms have two actions

( Offer & doesnt offer) payment facilities

each has a Dominant strategy : offer payment facility

• bcoz each gets higher Payoff from option : offer facility,

for any choice of the other player

• if Nissan plays offer, then Suzuki gets higher π = 400, from offer

• similarly, if Nissan plays doesn't offer , then Suzuki gets higher π= 800, from offer

This both have Dominant strategy,

( It is strict, bcoz both gets strictly higher Payoff from offer , as compared to doesn't offer, for any choice of other player)

So game has strictly Dominant strategy NE : ( offer, offer)

.

since both players could have earn higher payoff of 600 , if both decide to Cooperate , & play : doesn't offer

So both will be strictly better off as compared to NE of game , if they cooperate

So the type of game : Non- Cooperative game ,

( Similar to Prisoners dilemma );