Answer Happy

Agent A is going to their financial adviser to buy some life
insurance. The adviser can sell them insurance that does not cover
heart attacks but for which the adviser receives a huge sales
commission (bad insurance). Or the adviser can sell Agent A
comprehensive insurance for which their sales commission is lower
(good insurance).
The payoffs (x,y) for each decision are
indicated in the game tree below, with x being the
satisfaction of Agent A and y being the satisfaction of
the adviser. Please answer the questions below. You may find it
helpful to redraw the tree with different payoffs as the payoffs
change in the questions.
a) Let's assume the adviser only cares about the payoffs
indicated. What would the adviser do if Agent A chooses to
purchase? [1 mark]
b) What would Agent A do, anticipating the choice of the
adviser? [1 mark]
c) Suppose the adviser has social preferences, with a distaste
for inequality. If the payoffs x for Agent A and
y for the adviser are unequal, the adviser experiences a
dissatisfaction and their payoff becomes y - 3. What would
happen to the outcome in this case? [1 mark]
d) Alternatively, suppose now that Agent A can complain to the
regulator if they are sold bad insurance. If Agent A is successful,
they can cancel the insurance but would suffer a cost of -3 due to
the effort involved. If cancelled, the adviser would receive a
payoff as though there were no sale. Would this change the outcome
of the game? [1 mark]
e) Suppose Agent A has a reputation for seeking revenge and
would experience satisfaction of +4 from complaining to the
regulator (in addition to the effort cost of -3). How would this
change the outcome of the game? [1 mark]
Agent A No purchase Purchase Adviser (0,0) Good insurance Bad insurance (2,2) (-2,4)