Economics question Image transcription text Exercise 8.]. John and Mary are discussing whether to go to the ballet, to the boxing match, or to stay

Economics question Image transcription text Exercise 8.]. John and Mary are discussing whether to go to the ballet,
to the boxing match, or to stay home tonight. They have a random-
number generator, and they can agree to let their decision depend on
its output in any way, so as to create a lottery with any probability
distribution over the three possible outcomes (go to the ballet, go to
boxing, or stay home). If they cannot agree, they will stay home. John
wants to go to the boxing match, and he is indifferent between going
to the ballet and staying home. For Mary, going to the ballet would be
best, staying home would be worst, and she would be indifferent be-
tween going to the boxing match or taking a lottery with probability V4 Exercises 413 of going to the ballet and probability 5% of staying home. They both
satisfy the axioms of von Neumann-Morgenstern utility theory. a. Describe this situation by a two-person bargaining problem (F ,v)
and compute its Nash bargaining solution. How should they implement
the Nash bargaining solution? b. The above description of this situation does not specify a specific
two-person bargaining problem, as defined in Section 8.2. Which axi-
omatic properties of the Nash bargaining solution permitted you to
answer part (a) anyway? c. Find natural utility scales for John and Mary in which the egali-
tarian and utilitarian solutions both coincide with the Nash bargaining
solution. d. If the television set were broken, the prospect of staying home
would become much worse for John. To be specific, John would be
indifferent between going to the ballet and a lottery with probability W3
of going to boxing and probability 1/3 of staying home with a broken
television set. A broken television set would not affect Mary’s prefer-
ences. If Mary breaks the television set, her brother (who is a television
repairman, and who is coming for breakfast tomorrow) will fix it for
free. How would breaking the television set change the probability of
going to the ballet in the Nash bargaining solution?

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