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.