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We discuss a class of explicitly solvable mean field type controlproblems/mean field games with a clear economic interpretation. More precisely,we consider long term average impulse control problems with underlying generalone-dimensional diffusion processes motivated by optimal harvesting problems innatural resource management. We extend the classical stochastic Faustmannmodels by allowing the prices to depend on the state of the market using a meanfield structure. In a competitive market model, we prove that, under naturalconditions, there exists an equilibrium strategy of threshold-type andfurthermore characterize the threshold explicitly. If the agents cooperate witheach other, we are faced with the mean field type control problem. Using aLagrange-type argument, we prove that the optimizer of this non-standardimpulse control problem is of threshold-type as well and characterize theoptimal threshold. Furthermore, we compare the solutions and illustrate thefindings in an example.

Competition versus Cooperation: A class of solvable mean field impulse control problems