just see the questions on file, and I will upload the questions later.
Here’s an example:
A young man, Charles, and a young lady, Jane, admire each other, but neither is certain of
the other’s feelings. Jane has the choice to reveal her affection to Charles or not; while Charles, after
observing Jane’s choice, has the option of proposing to her or not. If Charles proposes, then Jane must
choose to accept the proposal or reject it. If Jane reveals her affection, then Charles thinks she will
accept his proposal for sure. Otherwise, Charles thinks his proposal has a 50% chance of being accepted.
If Jane does not reveal her feelings and Charles does not propose, each will have utility 0. If Jane reveals
her feelings, Charles proposes, and Jane accepts the proposal, they will make a lovely couple and each
will have utility 100. If Charles chooses to propose but Jane turns down his proposal, then Jane will
have utility 0 and Charles -100. If Jane reveals her feelings, but Charles chooses to not propose, then
Jane will have utility -100 and Charles 0.
(a) (15 points) Use the information above, write out the extensive form game between Charles and
Jane where Jane is the first mover. Remember to include their payoffs. Is there a Subgame Perfect
Nash Equilibrium in this game? If yes, find it; if not, explain why.
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