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(a) Honda and Toyota are two car companies that are contemplating whether to invest in a big sum of money to enter the driverless cars market. If Honda enters the market but Toyota does not, then Honda earns $20 million profits and Toyota earns $0. Similarly, if Toyota enters the market but Honda does not, then Toyota earns $20 million profits and Honda earns $0. If both enter the market, then each suffers $10 million losses. If neither enters, each earns $0. (i) Construct the pay-off matrix for Honda and Toyota indicating the strategies they may choose. Solve for the Nash equilibrium for this game and explain whether this game is a prisoner’s dilemma game. (6 marks) (ii) How would your answer to (i) change if the game become a sequential game where Honda gets to move first. Explain with a tree diagram.
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