CAJ | 학술논문

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。
기우배경약속、과기창신화요소집취삼유인소，연구다가동류산품제조기업재완전신식조건하진행적비합작박혁，통과설정상응적리윤함수화약속조건，건립차류박혁모형，분석매개기업여하제정합괄적산품생산량、배오권구매량、과연투입자화제고요소배치효솔비용，사저류박혁체도Nash균형상태。차조변분불등식적산법급출차류박혁적Nash균형점계산방법，병통과계산결과분석배경약속、과연투입자、제고요소배치효솔비용대기업리윤적종합영향。연구결과표명，당기업전략방안적가취범위시유계폐철집，동시매개기업적변제리윤수산품생산량、배오량、과연투입자금화제고요소배치효솔비용정부상관관계，저류박혁존재Nash균형상태。통과장저류박혁문제전화성변분불등식문제，이용변분불등식투영수축산법계산Nash균형점적수치。수치분석표명，재배경약속하，과연투입자금화제고요소배치효솔비용존재최우적투자조합，기업재Nash균형상태시채취적방안수연대박혁대수적방안주출료최우반응，단장박혁치우합작상태하능사정개행업획득경대리윤。
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.