Mary can choose to open her restaurant in Darlinghurst (D) or Newtown (N). Mary’s choice is observed by Jim, who can then choose to set up his establishment in either D or N. If Mary chooses D and then Jim D, the payoffs are (80, 40) to Mary and Jim, respectively. If the actions are (D, N), the payoffs are (40, 50). If the actions taken by the two restauranteurs are N followed by D, the payoffs are (30, 40). Finally, if the actions are (N, N) the payoffs are (50, 80). In the credible (subgame perfect) equilibria, what actions do we see being played by Mary and Jim, respectively?Group of answer choicesN and ND and ND and DN and DNone of the other answers are correct
Question
Mary can choose to open her restaurant in Darlinghurst (D) or Newtown (N). Mary’s choice is observed by Jim, who can then choose to set up his establishment in either D or N. If Mary chooses D and then Jim D, the payoffs are (80, 40) to Mary and Jim, respectively. If the actions are (D, N), the payoffs are (40, 50). If the actions taken by the two restauranteurs are N followed by D, the payoffs are (30, 40). Finally, if the actions are (N, N) the payoffs are (50, 80). In the credible (subgame perfect) equilibria, what actions do we see being played by Mary and Jim, respectively?Group of answer choicesN and ND and ND and DN and DNone of the other answers are correct
Solution
This is a game theory problem. The subgame perfect equilibrium is found by backward induction, meaning we start from the end of the game and move backwards.
First, consider Mary's choice of location. If she chooses D, Jim can choose between D (earning him 40) and N (earning him 50). Jim would choose N because 50 > 40.
If Mary chooses N, Jim can choose between D (earning him 40) and N (earning him 80). Jim would choose N because 80 > 40.
Now, consider Mary's choice again knowing Jim's responses. If Mary chooses D, she earns 40 (because Jim would choose N). If Mary chooses N, she earns 50 (because Jim would choose N). Mary would choose N because 50 > 40.
So, in the subgame perfect equilibrium, Mary chooses N and Jim chooses N. Therefore, the correct answer is "N and N".
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