中文摘要：

基于环境约束、科技创新和要素集聚三维因素，研究多家同类产品制造企业在完全信息条件下进行的非合作博弈，通过设定相应的利润函数和约束条件，建立此类博弈模型，分析每个企业如何制定合适的产品生产量、排污权购买量、科研投入资和提高要素配置效率费用，使这类博弈达到Nash均衡状态。借助变分不等式的算法给出此类博弈的Nash均衡点计算方法，并通过计算结果分析环境约束、科研投入资、提高要素配置效率费用对企业利润的综合影响。研究结果表明，当企业战略方案的可取范围是有界闭凸集，同时每个企业的边际利润随产品生产量、排污量、科研投入资金和提高要素配置效率费用呈负相关关系，这类博弈存在Nash均衡状态。通过将这类博弈问题转化成变分不等式问题，利用变分不等式投影收缩算法计算Nash均衡点的数值。数值分析表明，在环境约束下，科研投入资金和提高要素配置效率费用存在最优的投资组合，企业在Nash均衡状态时采取的方案虽然对博弈对手的方案做出了最优反应，但将博弈置于合作状态下能使整个行业获得更大利润。

英文摘要：

The research study a non-cooperative game with perfect information for a finite number of manufacturing firms whichproduce similar products, based on the environmental constraints, scientific research investment, and factor agglomeration. Byestablishing the game model by setting the profit function and corresponding constraints, the study investigates how each firmmakes a rational decision on the quantity of expected production, the amount of pollutants discharged, the basic scientific re-search investment, and the cost of improving the efficiency of production factor allocation for firms to reach a Nash equilibriumstate. Based on the above research, we establish an algorithm to solve the Nash equilibrium point by using variational inequalitymethod. We also investigate the comprehensive influence of environmental constraints, scientific research investment and the costof improving the efficiency of production factor allocation on the firm profit by numerical analysis. It reveals that there is a Nashequilibrium state when the value of the strategy of each firm is included in bounded closed convex sets, with existing negative cor-relations between the marginal profit and the quantity of expected production, file amount of pollutants discharged, the basic sci-entific research investment, and the cost of improving the efficiency of production factor allocation. With transferring the gameproblem to a variational inequalities problem, we then calculate the value of Nash equilibrium by a projection and contractionmethod. Numerical analysis reveals that there is an optimal portfolio on the scientific research investment and the cost of impro-ving the efficiency of production factor allocation under the environmental constraints. Besides, although a firm could make anoptimal reaction according to the Nash equilibrium solution, the whole industry could obtain greater profits if the game is in a co-operative state.