Research on dynamics in a resource extraction game with bounded rationality

Based on bounded rationality, a linear dynamic system is proposed in this work for the duopoly game of renewable resource extraction. This dynamics reflects the decision-makers' dynamical output strategy consisting of all the Nash equilibriums in every two adjacent periods. The resource growth rate, the discount rate and the expected extraction rate are the major parameters in this system. The system stability and the equilibrium characteristics of the stable state are analyzed. Numerical simulations are made to show the influence of all the parameters on the speed for the system to approaches its stable equilibrium. By the mathematical analysis we find that, if the discount is smaller or the expected extraction rate is larger, the system will converge in shorter time and approach a stable state with lager resource reserve and with larger resource output. So we draw the conclusion that decision-makers' focusing on the long-term profits is helpful to sustainable development on natural resource market in the long run.