为保障天然气开采及出口供应稳定, 一些出口国正大力投资天然气开采技术. 基于天然气市场的不确定性, 文章构建了两出口国关于开采技术投资的非合作与合 作的博弈模型, 运用微分对策与随机控制理论, 求得双方对开采技术投入等策略的最优路径及效用期望. 结果表明, 最优路径主要与双方初始开采技术存量大小以及它们的平 均值有关; 市场波动率越大, 使得双方最优策略的稳态值以及合作时的效用期望 越低, 而非合作时的效用期望与波动率之间却呈倒``U''型关系; 如果市场波动率较大或对方初 始开采技术存量较高, 那么自身在非合作情形的效用期望可能会更高; 此外, 在不确定的开采技术投资环境下, 与合作情形相比, 双方在非合作情形的联合效用期望可能反而 更高.

In order to improve natural gas exploitation technology and ensure export supply security, some exporting countries are investing heavily in these areas. To analyze the potential impact of investment uncertainty, we develop a noncooperative and cooperative dynamic game model for two exporting countries that are investing in natural gas exploitation technologies. The theory of stochastic control and differential game is used to study its optimal solutions, including optimal investment paths and maximal expected utilities. Results show that, optimal paths are particularly affected by initial technology stocks and their average level. The higher the market volatility is, the lower the steady-state values of the optimal strategies and the expected utilities are in the cooperative case, but the expected utilities are of an inverted-U shape in the noncooperative case. If one player's volatility is large enough or the rival's initial technology stock is sufficiently high, its expected utility may achieve a higher level in the noncooperative game. In contrast to the common conclusion for a deterministic game that the total benefit of cooperation is usually no less than that of noncooperation, the total expected utility may become even higher in the noncooperative game than in the cooperative game under our stochastic environment.