Two students are sitting in a lecture and considering whether to ask a question from the professor (both of them are considering the same question).
If they both ask, the question cannot be answered properly (e.g., because they would both speak at the same time so the question would not be heard), and each student incurs a cost C for not learning the answer. Of course, if neither student asks, they will not learn the answer either, so they also incur the cost C.
If a student does not ask the question, he incurs a psychological cost of G for having to suppress the temptation to ask. Regardless of what happens, every student gets a utility B simply from sitting in the lecture.
(a) Write down the normal form of this game.
(b) Suppose B = 10, C = 5, and G = 4. Does this game have any Dominant Strategy
Equilibria? Does it have any Nash Equilibria? If so, find them.
(c) Suppose B = 10, C = 4, and G = 5. What about DSE and NE in this case?
(d) In case (c) above, the sum of players' payoffs could be higher if they acted differently. Can you suggest a mechanism the professor could use that would make the students pick better strategies?