Cooperation in a resource extraction game
An exhaustible stock of resources may be exploited by N players. An arbitrarily long duration of the game is only possible, if the utility function satisfies certain restrictions at small values R of extraction. We find that stability against unilateral defection occurs if the elasticity of the marginal utility turns out to be larger than (N - 1 )/N, however independent of the value of the discount factor. Hence we find that cooperation does not depend on the discount factor for a certain range of elasticities. Analogy to phase transitions in statistical physics is discussed.
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