A Linear-Quadratic Common Resource Extraction Game with Many Players and Binding Constraints

We analyse a linear quadratic multistage game of extraction of a common renewable resource by many players with state dependent constraints for exploitation and infinite time horizon. We analyse social optimum and Nash equilibrium for feedback information structure and compare the results obtained in both. For Nash equilibria, we obtain a value function that is contrary to intuitions from standard linear quadratic games. We also study introduction of a tax in order to enforce socially optimal behaviour of the players. Besides, this game constitutes a counterexample to two techniques regarded as standard  in computation of Nash equilibrium and/or optimal control.