Six students are working to complete their video for the First Year Challenge Project.

Label as the amount of effort provided by student (where = 1, ... ,6), and denote by the vector of efforts of all six students (i.e. = (, ... , )). The maximum level of effort that a student can dedicate to the work is = 8.

The payoff of student has the following form () = 1.5. That is, every unit of effort has a benefit of 1 for every person of the group but there is a cost of effort of 1.5 for every unit of effort that a student puts in.

(a) Each student chooses her level of effort independently, simultaneously and without communicating with others (imagine that every student contributes a specific element to the joint FYC project).

Does this game have a strictly dominated strategy (or strategies)? Describe what it is (they are).

Does the game have a Nash equilibrium (or equilibria)? Prove what it is (they are) and how you found it (them).

If there is a Nash equilibrium, is the outcome of the equilibrium Pareto efficient? Explain your answer.