Answered: Common pool resource game) Consider a…

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.5P

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Common pool resource game) Consider a common pool resource game with two appropriators. (If you don’t know what is a common pool resource, read the Wikipedia article about the ”Tragedy of the Commons”.) Each appropriator has an endowment e > 0 that can be invested in an outside activity with marginal payoff c > 0 or into the common pool resource. Let x ∈ X ⊆ [0, e] denote the player’s investment into the common pool resource (likewise, y denotes the opponent’s investment). The return from investment into the common pool resource is x x+y · ((x + y) − (x + y) 2 ). So the symmetric payoff function is given by π(x, y) = c · (e − x) + x x+y · ((x + y) − (x + y) 2 ) if x > 0 and c · e otherwise. Assume 1 − e < c < 1. Find Nash equilibrium of the game. Proceed by deriving the best response correspondences first. How does Nash equilibrium depend on parameters c and e (varying one at a time and keeping the others fixed)?

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