Two people are engaged in a joint project. If each person i puts in the e ort xi, a nonnegative number equal to at most 1, which costs her c(xi), the outcome of the project is worth f(x1; x2). The worth of the project is split equally between the two people, regardless of their effort levels.
(a) Formulate this situation as a strategic game.
(b) Find its Nash equilibria when i. f(x1; x2) = 3x1x2, c(xi) = x2i , for i = 1; 2.
ii. f(x1; x2) = 4x1x2, c(xi) = xi, for i = 1; 2.
(c) In each case, is there a pair of e ort levels that yields both players higher payoffs than the Nash equilibrium e ort levels?