Two people are engaged in a joint project. If each person i puts in the effort 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. Formulate this situation as a strategic game. Find the Nash equilibria of the game when (a) f(x1,x2)= 3x1x2 and c(xi) = xi^2 for i = 1, 2, and (b) f(x1, x2) = 4x1x2 and c(x) = xi for i = 1, 2. In each case, is there a pair of effort levels that yields both players higher payoffs than the Nash equilibrium effort levels?

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