(Interaction among resource-users) A group of n firms uses a common resource (a river or a… 1 answer below »

(Interaction among resource-users) 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 + ··· + xn)) if x1 + ··· + xn ≤ 1, and zero otherwise. Each firm i chooses xi to maximize its output. Formulate this situation as a strategic game. Find values of α and c such that the game is the same as the one studied in Exercise 59.1, and hence find its Nash equilibria. Find an action profile (x1,…, xn) at which each firm’s output is higher than it is at the Nash equilibrium.

 

 

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