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(x_{i}), the outcome of the project is worth f(x_{1}; x_{2}). 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(x_{1}; x_{2}) = 3x_{1}x_{2,} c(x_{i}) = x^{2}_{i} , for i = 1; 2.
ii. f(x_{1}; x_{2}) = 4x_{1}x_{2}, c(x_{i}) = x_{i}, 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?