Nash Equilibrium in a Special Case of Symmetric Resource Extraction Games

The study complements available results on the existence of Nash equilibrium in resource extraction games with an arbitrary number of agents. It is assumed that the players have identical preferences in the proposed model, the utility function is a power function, and the sequence of states from the joint investments is determined via a geometric random walk. An iterative method is used for constructing a nonrandomized stationary Nash equilibrium in the infinite horizon game. It is shown that the equilibrium belongs to the set of Pareto inefficient strategies.