A group of n firms uses a common resource (a river or a forest, for example) to produce output, as more of the resourc
A group of n firms 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 by xi the amount of the resource used by firm I (= 1,....n). Assume specifically that firm i's output is xi , [1-(x1 + x2 + ...... + x)] if x1 + x2 + .....+ xn â‰¤ 1, and zero otherwise.
Each firm i chooses xi to maximize output (its payoff is equal to its output).
(i) Formulate this situation as a game in strategic form.
(ii) Find the set of Nash equilibria in pure strategies of this game.
(iii) Find a strategy profile (x1.........xn) at which each firm's output is higher than it is at the Nash equilibria (proving that the Nash equilibria are inefficient).