Dynamic sustainability games for renewable resources - A computational approach

We consider a dynamic Nash game among firms harvesting a renewable resource (e.g., in a fishery) and propose a differential variational inequality (DVI) framework for modeling and solving such a game. We suppose the firms compete over demand as well as over regulated harvest effort that we interpret as a sustainability constraint on the fleet's aggregate harvest effort. We suppose each firm is based in a home market that is not protected by trade barriers implying that each firm can sell its catch in any of the markets. Within this setting, we consider how harvest effort, catch, and sustainability of the resource are affected by the length of the planning horizon of the firms. We show results that contrast myopic planning versus long-term perspectives. To derive solutions for this game, we propose a DVI framework that is converted to a fixed-point problem. This allows us to employ a computationally efficient algorithm for the solution of the game.