Cooperation in a resource extraction game - Frank Stähler; Friedrich Wagner (Kiel Institute of World Economics (IfW); ZBW – Leibniz Information Centre for Economics, 1998)
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.
Keywords: C72; C73; Q30; 330