Spring 2021
- What is the difference between “imperfect” and “incomplete” information?
Imperfect information: we don’t know what actions others take, but we know their intentions/preferences payoffs.
Incomplete information: don’t know other people’s types (we dont know their intentions/preferences payoffs)
- Give an example of a game of incomplete information not found in the lecture slides.
- Suppose on the dating market there are two types of people, Interested and Not Interested (in you). Use this to explain the difference between a “pooling” equilibrium and a “separating” equilibrium.
- In games of incomplete information, what is a “signal”, who sends signals, and why do signals make these games complicated? (Hint: consider the person who receives the signal). To fix thoughts, consider two actions on the dating market: Laugh (at your joke) and Not Laugh (at your joke).
- You are on a first date. Consider the statement “the probability this person is Interested given they Laugh.” Express this statement using probability notation.
- Is the probability in the question above a “posterior” or a “prior” probability? Explain the difference between the two.
- Suppose the probability that people Laugh given they are Interested is roughly 0.75. Does that mean there is a 75% chance this person likes you if they laugh at your joke? Why or why not?
- What information (hint: what other probabilities) would you need to calculate an estimate of “the probability this person is Interested given they Laugh.”
- This is your second date in your new town (you moved here for a new job), and you don’t yet know a lot of people. What is a reasonable estimate for the prior probability in this dating problem?
- Continue to assume the probability that people Laugh given they are Interested is roughly 0.75. This is your second date in your new town (you moved her for work); the first one didn’t go well, so you take your prior probability to be about 20%. But this date is going well: the person laughed at your first joke. Calculate the posterior probability that they are interested in you. Recall this version of the formula for Bayes’ Rule given events
and
:
- Incredibly, they laughed at your second joke. Calculate your new, updated posterior. Based on the math, do you have a chance at a second date with this person? Should you try based on this information alone? (Hint: think about laughs as signals.)