可再生资源的一个寡头博弈模型及其均衡分析

Equilibrium of An Oligopoly Game Played in Renewable Resource Market

本文就具有固定自然增长率的资源市场,在需求函数与单位生产成本函数都为线性的条件下建立可再生资源的多寡头博弈模型,讨论对应的市场均衡策略的均衡方程,研究资源市场均衡路径上资源总储量与资源总供给的长期定性增长行为。数理分析结果表明,尽管资源是可再生的,但是不注重长期经济利益的资源开发策略必将使资源最终耗尽;而注重长期经济利益的策略选择会使得资源获得一定的持续增长从而可持续发展。

In this paper,we construct an oligopoly game of renewable resource extraction in which the growth rate is fixed at a constant and the unit production cost function takes the linear form. We study the equilibrium equation satisfied by the equilibrium strategy of the players,and discuss the long-run properties of the total resource reserve level and the total extraction rate on the equilibrium path of the game. The mathematical analysis shows that the extraction strategy which neglects the long-run profits will exhaust the resource at all in the long time and the one which emphasizes the long-run profits will make the resource grow hence get its sustainable development in the long run.