A group of n firms uses a common resource (a river or a forest, for example) to produce output, as..

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 ≤ 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).

 

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