Question

Two students sign up to prepare an honors thesis with a professor. Each can invest time in his own project: either no time, one week, or two weeks (these are the only three options). The cost of time is 0 for no time, and each week costs 1 unit of payoff. The more time a student puts in the better his work will be. A student will receive an A for a paper with two weeks of work, a B for one week of work, and a C for no time invested at all. But if both students put in the same amount of time, the professor will see that their thesis projects have the same quality and due to lack of excitement will give both papers a C.

The payoffs for getting an A = 4, B = 2, C = 0.

a) Write down this game in a matrix form.

b) Find all pure-strategy Nash equilibria.

c) Find the unique mixed-strategy Nash equilibrium. (Hint: A pure strategy that is never a best response in the pure-strategy NE will never be played in the mixed-strategy NE too.

Answer 1