Question

Elina has to choose between two projects, P1 and P2. If Elina chooses P1 the game is over and the payoffs are 4 to Elina and 13 to Bonnie. If Elina choose P2, Bonnie observes Elina's choice and then gets to choose between projects P3 and P4. If Elina chooses P2 and Bonnie chooses P3 the payoffs are 2 to Elina and 8 to Bonnie. If Elina chooses P2 and Bonnie chooses P4 the payoffs are 5 and 10 to Elina and Bonnie respectively.

Answer 1

20) The subgame here is the choice that Bonnie has between choosing P3 and P4. Bonnie would also like to maximise his profits. So if Bonnie chooses P3 , his payoff will be 8. If Bonnie chooses P4, his payoff will be 10. So Bonnie would choose project P4 over project P3. And this choice goves Elina a payoff of 5 which is higher than the payoff of 4, that Elina gets by choosing project P1. So the subgame perfect equilibria is (P2, P4). So option d is the correct answer.

21) In this game, Elina will not be paying anything to Bonnie to choose project P1, because Elina has a lower profit and Bonnie has a higher profit by doing so. So instead, Bonnie will be paying Elina for choosing project P1 as he will be earning very high profits if this happens. Now, as Elina has all the bargaining powers, she would choose to receive higher amount for choosing P1. Bonnie would pay a maximum of 3 to Elina for choosing P1. This is because the difference between the payoffs for Bonnie if Elina chooses P1 and the perfect subgame equilibrium. So we can conclude that Elina gets paid $3 by Bonnie and commits to choose P1.