演化博弈论文学习分享

　　惩罚机制下的演化分析
　　前面的论文中提到，在没有惩罚机制的模型里，供应商和制造商在碳减排投入上存在搭便车的行为。为了使双方都主动进行碳排放投入，在这部分，引入了惩罚机制，即双方签订碳减排契约，如果在实际生产运营活动中，其中一方进行碳减排投入，而另一方未进行碳减排投入，则未进行碳减排投入的一方将受到惩罚，且罚金交给进行碳减排投入的一方; 若双方均未进行碳减排投入， 则都不受到惩罚。在该碳减排契约的调节下， 供应商和制造商的碳减排博弈的支付矩阵将发生变化。假设该罚金为K( K ＞0) ， 此时供应链的支付矩阵如表 2 所示。
　　As mentioned in the previous paper, in a model without a penalty mechanism, suppliers and manufacturers have free-rider in their carbon emissions reduction investment. In order to make both parties take the initiative to invest in carbon emissions, a penalty mechanism is introduced in this part, that is, the two parties sign a carbon emission reduction contract. If both parties do not invest in carbon emission reduction, the party who does not invest in carbon emission reduction will be punished, and the fine will be given to the party who invests in carbon emission reduction; if both parties do not invest in carbon emission reduction, they will not be punished. Under the regulation of this carbon emission reduction contract, the payment matrix of the carbon emission reduction game between suppliers and manufacturers will change. Assuming that the penalty is K (K> 0), the payment matrix of the supply chain is shown in Table 2.
　　根据支付矩阵，计算得到供应商、制造商的复制动态方程以及该系统的平衡点。并对系统的平衡点进行分析。
　　According to the payment matrix, the replication dynamic equations of suppliers and manufacturers and the balance point of the system are calculated. And analyze the balance point of the system.
　　已知平衡点的迹的值＜0，且平衡点的行列式的值＞0时，该平衡点为系统的演化稳定点，因为我们需要通过该契约使得制造商和供应商都倾向于选择进行碳排放投入，我们下面我们将分析（1，1）为ESS点时，需要满足的条件。
　　When the value of the trace of the known equilibrium point is less than 0, and the value of the determinant of the equilibrium point is greater than 0, the equilibrium point is the evolutionary stable point of the system, because we need to use the contract to make manufacturers and suppliers both inclined to choose carbon For emission input, we will analyze the conditions that need to be met when (1, 1) is the ESS point.
　　此时，系统演化的相位图如下图所示。
　　由此可知，供应商和制造商都会趋向于进行碳减排投入。因此，供应商和制造商通过建立供应链契约与惩罚机制，可以调整供应链各方的收益矩阵，使＂搭便车＂行为无利可图，减少＂搭便车＂的概率，从而提高供应链各节点企业进行碳减排投入的概率。
　　It can be seen that both suppliers and manufacturers tend to invest in carbon reduction. Therefore, by establishing supply chain contracts and punishment mechanisms, suppliers and manufacturers can adjust the profit matrix of all parties in the supply chain, make free-riding behavior unprofitable, reduce the probability of free-riding, and improve the supply chain. Probability of node companies investing in carbon emission reduction.
　　数值模拟
　　基于对以牛仔服饰企业的调查，获得以下信息：
　　供应商和制造商存在＂搭便车＂动机的数值仿真：
　　由图 2 可知，S2随着供应商单独减排时的碳减排投入收益比 α0的减小而增大; 当 α0 一定时， α1 越小， S2越大。这表明，S2随着双方都减排时，供应商碳减排投入收益比 α1 的减小而增大。由图 3 可知，S2随着F公司单独减排时的碳减排收益投入比 β0 的增大而增大; 当 β0 一定时，β1 越大，S2 越大; 这表明S2随着双方都减排时，F 公司碳减排投入收益比β1 的增大而增大。由图 2 和图 3 可知: F公司的供应商进行碳减排投入的收益比越小，供应商进行碳减排投入的动机越小，F公司进行碳减排投入的收益比越大， 其进行碳减排投入的动机越大， 博弈的均衡状态为( N， D) 的概率越大。反之，博弈的均衡状态为( N， D) 的概率越小。
　　It can be seen from Figure 2 that S2 increases as the carbon emission reduction input income ratio α0 decreases when the supplier reduces emissions alone; when α0 is constant, the smaller α1 is, the larger S2 is. This shows that S2 increases as the ratio α1 decreases when both parties reduce emissions. From Figure 3, it can be seen that S2 increases with the increase of the carbon emission reduction income input ratio β0 when the company F reduces emissions alone; when β0 is constant, the larger β1, the larger S2; this indicates that S2 decreases with both parties. At the time of emission reduction, the investment income of company F＂s carbon emission reduction will increase with the increase of β1. It can be seen from Figures 2 and 3 that the smaller the revenue ratio of the F company’s suppliers for carbon emission reduction investment, the smaller the supplier’s motivation to invest in carbon emission reduction, and the greater the revenue ratio of company F’s carbon emission reduction investment. The greater the motivation to invest in carbon emission reduction, the greater the probability that the equilibrium state of the game is (N, D). Conversely, the probability that the equilibrium state of the game is (N, D) is smaller.
　　由图 4 和图 5 可知: 供应商碳减排投入成本越大，其进行碳减排投入的动机越小，F公司碳减排投入成本越小，其进行碳减排投入的动机越大，博弈的均衡状态为( N， D) 的概率越大。反之，博弈的均衡状态为( N， D) 的概率越小。与命题 4的结论一致。
　　It can be seen from Figures 4 and 5 that the greater the cost of a supplier’s carbon emission reduction input, the smaller its motivation to invest in carbon emission reduction. The smaller the input cost of company F’s carbon emission reduction, the greater its incentive to invest in carbon emission reduction. The greater the probability that the equilibrium state of the game is (N, D). Conversely, the probability that the equilibrium state of the game is (N, D) is smaller. It is consistent with the conclusion of Proposition 4.
　　由图 6 和图 7 可知: 双方均不进行碳减排投入时， 供应商的收益越小，其进行碳减排投入的动机越小，F公司的收益越大，其进行碳减排投入的动机越大，博弈的均衡状态为( N， D) 的概率越大。反之，博弈的均衡状态为 ( N， D) 的概率越小。与命题 5 的结论一致。
　　It can be seen from Figure 6 and Figure 7 that when both parties do not invest in carbon emission reduction, the smaller the supplier’s revenue, the less motivated it is to invest in carbon emission reduction, the greater the revenue of Company F, and the greater its contribution to carbon emission reduction. The greater the motivation, the greater the probability that the equilibrium state of the game is (N, D). Conversely, the probability that the equilibrium state of the game is (N, D) is smaller. It is consistent with the conclusion of Proposition 5.
　　由图 8 和图 9 可知: 当供应商＂搭便车＂减排收益越大， 则其进行碳减排投入的动机越小; 当 F公司＂搭便车＂碳减排收益越小，其进行碳减排投入的动机越大，博弈的均衡状态为( N， D) 的概率越大。反之，博弈的均衡状态为( N， D) 的概率越小。与命题 6 的结论一致。
　　It can be seen from Figure 8 and Figure 9 that when a supplier’s ＂free-riding＂ emission reduction revenue is greater, its motivation to invest in carbon emission reduction is less; when F company’s ＂free-riding＂ carbon emission reduction revenue is smaller, The greater the motivation for reducing emissions, the greater the probability that the equilibrium state of the game will be (N, D). Conversely, the probability that the equilibrium state of the game is (N, D) is smaller. It is consistent with the conclusion of Proposition 6.
　　结论
　　结论的写作不能简单重复研究结果，需要对研究结果有进一步的认识， 结论应该反映研究结果的理论价值和实际意义 。结合该文章的结论部分，研究结论包括了：
　　The writing of the conclusion should not simply repeat the research results. It requires a further understanding of the research results. The conclusions should reflect the theoretical value and practical significance of the research results. Combined with the conclusion part of the article, the research conclusions include: 说明了什么问题，得到其理论价值（与前文研究紧密结合，要与引言相呼应，这一点是必不可少的） 本文结论部分：本文通过演化博弈论研究了作为供应链低碳管理主体的供应商和制造商的碳排放投入行为策略， 研究结果表明: 供应商与制造商的策略选择与其碳减排投入收益比密切相关， 与其＂搭便车＂行为所获得的收益大小亦相关． 当双方碳单独进行碳减排投入和共同进行碳减排投入的收益比不断从小向大变化时， 会依次出现( 不进行碳减排投入， 不进行碳减排投入) 、( 进行碳减排投入， 不进行碳减排投入) 、( 不进行碳减排投入， 进行碳减排投入) 和( 进行碳减排投入， 进行碳减排投入) ．同时， 如果＂搭便车＂行为从对方碳减排投入中获得的收益很大， 会降低供应链节点企业进行碳减排投入的概率。Conclusion of this paper: This paper uses evolutionary game theory to study the carbon emission input behavioral strategies of suppliers and manufacturers as the main body of supply chain low-carbon management. The research results show that the strategic choice of suppliers and manufacturers and their carbon emission reduction input income ratio It is closely related, and also related to the size of the profit gained from its ＂free-riding＂ behavior. When the revenue ratio of both parties’ carbon emissions reduction investment alone and the joint carbon emissions reduction investment continues to change from small to large, there will be (no carbon emissions reduction investment, no carbon emissions reduction investment), (carbon emissions reduction investment) Investment, no carbon emission reduction investment), (no carbon emission reduction investment, carbon emission reduction investment) and (carbon emission reduction investment, carbon emission reduction investment). At the same time, if the ＂free rider＂ behavior gains a lot of benefits from the counterparty＂s carbon emission reduction investment, it will reduce the probability of the supply chain node enterprises making carbon emission reduction investment.有待进一步解决的问题以及展望（指出本文还没有考虑的潜在影响因素） 本文结论部分：但是， 本文仅考虑了消费者对低碳产品的偏好会导致低碳产品价格高于普通产品， 未考虑消费者低碳产品需求量的改变对演化博弈均衡的影响． 而随着消费者的低碳环保意识的增强， 其不仅愿意支付的产品价格更高， 对低碳产品的需求往往也会增加． 因此， 在后续研究中，将尝试同时考虑这两个因素对供应链碳减排投入决策的影响．The conclusion of this article: However, this article only considers that consumers＂ preference for low-carbon products will cause low-carbon products to be more expensive than ordinary products, and does not consider the impact of changes in consumer demand for low-carbon products on the evolutionary game equilibrium. As consumers＂ awareness of low-carbon environmental protection increases, not only are they willing to pay higher prices for products, but their demand for low-carbon products tends to increase. Therefore, in the follow-up research, we will try to consider the influence of these two factors on the supply chain carbon emission reduction investment decision at the same time.
　　英语翻译：谷歌翻译
　　参考文献：
　　[1]付秋芳,忻莉燕,马士华.惩罚机制下供应链企业碳减排投入的演化博弈[J].管理科学学报,2016,19(04):56-70.
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