Competitive Harvesting of a Renewable Common Resource : A Non-cooperative Stochastic Impulse Control Game

We examine a game of harvesting a renewable common resource and investigate the ramifications of competition. We formulate the problem as an impulse control game between two competing harvesters and devise a new formulation of closed-loop impulse control strategies. In the case of non-zero setup cost, we find a continuum of (s,S)-type non-subgame-perfect Nash equilibria with tit-for-tat strategies. Remarkably, in the case of zero setup cost, the model yields a continuum of (s,S)-type subgame perfect equilibria. The (s,S) characteristic is a novel feature in the absence of setup cost; in the single-player model, the model yields an optimal policy characterized by a single reflective threshold of harvesting. The result shows the possibility of an extreme tragedy of the commons: there exists a continuum of equilibria that completely deplete the common resource. On the other hand, there is also a Pareto-dominant equilibrium, which can serve as a focal point that prevents depletion