6 point) You are a user on an online Q&A platform like Quora, where users can
post questions and receive answers from others.
• Being a nice person, you enjoy seeing a question being answered, whether by
yourself or another user besides the poster (the user who posted the question).
When this occurs, you enjoy satisfaction equivalent to earning a payoff of 100.
• On the other hand, writing up an answer to a question incurs an effort cost
of 50.
For simplicity, we don’t differentiate between scenarios where a question receives
a high-quality answer and is resolved and those where it receives a low-quality
answer and remains unresolved. Any answer is considered sufficient to resolve the
question. Therefore, just one answer is needed for resolution and for you to enjoy
satisfaction.
Now suppose that someone posted a question and 3 fellow users (besides the
poster) see the post, including you. Each fellow user then decides whether to
answer the question or to skip it. At a symmetric Nash equilibrium, everyone
answers the question with a probability p.
(a) (1 point) What is the probability that a fellow user will skip the question (as
a function of p)?
(b) (1 point) If you skip the question, what is the probability that no one else
answers it (as a function of p)?
(c) (1 point) If you skip the question, what is the probability that you will enjoy
seeing it being answered (as a function of p)?
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(d) (1 point) If you skip the question, what is your payoff (as a function of p)?
(e) (1 point) If you answer the question, what is your payoff?
(f) (1 point) What is the equilibrium strategy of each fellow user?