A Renewable Resource Extraction Game with Uncertain Future Payoff Structures

An essential characteristic of time -- and hence decision making over time -- is that, though the individual may, through the expenditure of resources, gather past and present information, the future is inherently unknown and therefore (in the mathematical sense) uncertain. In renewable resouce extraction, often the horizon approaches infinity and future payoffs are uncertain. In this paper, we develop a resouce extraction game model in which the future payoffs are not known with certainty and the evolution of the resource stock dynamics is stochastic. In particular, stochasticity in future payoff structures is modeled as a steady braching process. The introduction of this additional stochastic element offers a fruitful alternative to modeling infinite-horizon game situations under uncertainty. A (feedback) Nash equilibrium is solved for the game.