Question

2. In the class ic film, Mary Poppins, the Banks children are players in a strategic game with a number of different nannies. In their view of the world nannies are inherently harsh, and playing tricks on nannies is great fun. That is, they view themselves as playing a game in which the nanny moves first, showing herself to be either Harsh or Nice, and the chil dren move second, choosing to be either Good or Mischievous. The nanny prefers to have Good children to take care of but is also inherently harsh, and so she gets her highest payoff of 4 from (Harsh, Good) and her lowest payoff of 1 from (Nice, Mischievous ), with (Nice, Good) yielding 3 and (Harsh, Mischievous) yielding 2. The children similarly most prefer to have a Nice nanny and then to be Mischievous; they get their highest two payoffs when the nanny is Nice (4 if Mischievous; 3 if Good) and their lowes t two payoffs when the nanny is Harsh (2 if Mischievous, 1 if Good).

a. Draw the game tree for this game and find the subgame - perfect equilibrium in the absence of any strategic moves.

b. In the f il m, before the arrival of Mary Poppins, the children write their own ad for a new nanny in which they state: “If you won’t scold and dominate us, we will never give you cause to hate us; we won’t hide your spectacles so you can’t see, put toads in your bed, or pepper in your tea.” Use the tree from part (a) to arg ue that this statement constitutes a promise. What would the outcome of the game be if the children keep their promise?

c. What is the implied threat that goes with the promise in part (b)? Is that implied threat automatically credible? Explain.

d. How cou ld the children make the promise in part (b) credible ?

e. Is the promise in part (b) a compellent or deterrent? Explai n your answer by referring to the status quo in the game – namely, what would happen in the abs ence of the strategic move .   

Answer 1

a)

For subgame perfect equilibrium we see the payoff in each subgame.

when the nanny is nice so the best payoff for children is to be mischevious since 4>3 and hence the payoff for nice is (1,4)

now when the nanny is harsh , the best action for children is to be mischevious and which leaves the harsh with (2,2) .

so from (1,4) and (2,2) nanny gets higher payoff in (2,2) ie is being harsh .

the subgame equilibrium is to be ( harsh , mischievious ) ie (2,2) because no matter what the nanny chooses the children choose to be mischievous so nanny gets better off at being harsh.

b) if children keep their promise and be good given that the nanny is nice we arrive at (3,3)

c)the implied threat is that if the nanny is harsh , the children would be mischievious. tha implied threat is not credible because even when the nanny is nice , they prefer to be mischievious, so threat is of no use since they would be mischievious anyway.

d) children can make promise credible by being good to nanny if the nanny is nice. this way it would be credible on children's part for they would do what they had promised.