Q. You've been assigned a group paper with one other person. The paper costs c to produce and a good grade is worth v to each of you, and you both get assigned the same grade. Further assume that c > 0, v > 0, and c > v > c.

(a) Assume that this is a pass/fail assignment, where the passing grade is low enough that one person can produce a passing paper by him or herself by incurring the full cost c. Set up the pay matrix and the Nash equilibrium. What type of game is this?

(b) Assume that the paper has a continuous grade (e.g. 0% to 100%), and that it is impossible to produce a 100% paper without both of you working on the paper, but that you are collectively capable of producing a 100% paper with a total cost of c. Set up the pay matrix assuming that each of you can individually produce a paper worth v=2 with an individual cost of c.