A group ofnfirms uses a common resource (a river or a forest, for example) to produce output. As more of the resource is used, any given firm can produce less output. Denote byxi, the amount of the resource used by firmi(i= 1, ..., n). Assume specifically that firmi's output isxi(1(x1+ +xn)) ifx1+x2+ +xn<1, and zero otherwise. Each firmichoosesxi, to maximize its output. Formulate this situation as a strategic game.

1. Find the Nash equilibrium of the game.
2. Find an action profile (x1,x2,...,xn) at which each firm's output is higher than it is at the Nash equilibrium.
3. Could the firms collude so that each obtains a higher payoff than the Nash equilibrium payoff?