管理科学
管理科學
관이과학
MANAGEMENT SCIENCES IN CHINA
2014年
4期
51-58
,共8页
环境约束%要素集聚%Nash均衡%变分不等式
環境約束%要素集聚%Nash均衡%變分不等式
배경약속%요소집취%Nash균형%변분불등식
environmental constraints%factor agglomeration%Nash equilibrium%variational inequality
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、科研投入资金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、科研投入资金、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。
基于環境約束、科技創新和要素集聚三維因素，研究多傢同類產品製造企業在完全信息條件下進行的非閤作博弈，通過設定相應的利潤函數和約束條件，建立此類博弈模型，分析每箇企業如何製定閤適的產品生產量、排汙權購買量、科研投入資金和提高要素配置效率費用，使這類博弈達到Nash均衡狀態。藉助變分不等式的算法給齣此類博弈的Nash均衡點計算方法，併通過計算結果分析環境約束、科研投入資金、提高要素配置效率費用對企業利潤的綜閤影響。研究結果錶明，噹企業戰略方案的可取範圍是有界閉凸集，同時每箇企業的邊際利潤隨產品生產量、排汙量、科研投入資金和提高要素配置效率費用呈負相關關繫，這類博弈存在Nash均衡狀態。通過將這類博弈問題轉化成變分不等式問題，利用變分不等式投影收縮算法計算Nash均衡點的數值。數值分析錶明，在環境約束下，科研投入資金和提高要素配置效率費用存在最優的投資組閤，企業在Nash均衡狀態時採取的方案雖然對博弈對手的方案做齣瞭最優反應，但將博弈置于閤作狀態下能使整箇行業穫得更大利潤。
기우배경약속、과기창신화요소집취삼유인소，연구다가동류산품제조기업재완전신식조건하진행적비합작박혁，통과설정상응적리윤함수화약속조건，건립차류박혁모형，분석매개기업여하제정합괄적산품생산량、배오권구매량、과연투입자금화제고요소배치효솔비용，사저류박혁체도Nash균형상태。차조변분불등식적산법급출차류박혁적Nash균형점계산방법，병통과계산결과분석배경약속、과연투입자금、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 which produce similar products , based on the environmental constraints , scientific research investment , and factor agglomeration .By establishing the game model by setting the profit function and corresponding constraints , the study investigates how each firm makes 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 equilibrium state.Based on the above research , we establish an algorithm to solve the Nash equilibrium point by using variational inequality method .We also investigate the comprehensive influence of environmental constraints , scientific research investment and the cost of improving the efficiency of production factor allocation on the firm profit by numerical analysis .It reveals that there is a Nash equilibrium 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 , the amount of pollutants discharged , the basic sci-entific research investment , and the cost of improving the efficiency of production factor allocation .With transferring the game problem to a variational inequalities problem , we then calculate the value of Nash equilibrium by a projection and contraction method.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 an optimal reaction according to the Nash equilibrium solution , the whole industry could obtain greater profits if the game is in a co-operative state .
