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Problem: Consider the rivalry between Toyota, Honda and Nissan to develop a new fuel efficient eco-car. Suppose Toyota is ahead in the development process and Honda and then Nissan are considering whether to enter the eco-car competition. If Honda and Nissan stays out, they earn a zero profit, whereas Toyota enjoys a monopoly and earns $100 billion. If Honda and Nissan decide to enter and develop the eco-car, then Toyota has to decide whether to accommodate Honda and Nissan peaceably or to wage a price war. In the event of peaceful competition between the three, each will make a profit of £30 billion, and if there is a price war between the three, each firm will lose $5 billion. If only one enters, then the payoff for peaceful competition will be $40 billion for each, a loss of $7 billion in a price war and zero profit for the firm that stays out.
a) Draw the three diagram for this game with related payoffs.
b) List down each firms complete pure strategies.
c) Find the Nash equilibrium and describe each firms' optimal strategies.
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