Synergistic Development Model of China Railway Express Under Government Reward-Penalty Mechanism
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摘要:
为减少中欧班列运营商竞相低价揽货、抢夺货源现象的发生，基于地方政府对中欧班列运营商和中欧班列供货商的补贴，并结合中欧班列运营过程中实际情况，构建政府奖惩机制下的“政府-运营商-供货商”非对称性三方演化博弈模型；在此基础上，通过数值仿真分析政府补贴、惩罚等主要因素对系统演化稳定策略的影响，并据此为中欧班列协同发展提供理论参考. 研究结果表明：政府增大惩罚力度将有效推动运营商和供货商的协同发展；根据运营商和供货商的不同策略实行差额补贴，不同补贴力度之间的差值越大越有益于协同；合理设置政府提供给运营商的单位集装箱最大补贴额，并视情况逐渐减小额度直至补贴完全退出，是促进协同的有效途径；政府的额外社会效益是决定政府策略选择的正向影响因素.
Abstract:To reduce the phenomenon in which China-Europe Railway Express operators compete for cargo sources by offering excessively low prices, an asymmetric tripartite evolutionary game model of “government-operator-supplier” was constructed under the reward-and-punishment mechanism of the government. The model was based on local government subsidies to China Railway Express operators and suppliers and took into account the actual conditions in the operation process of China Railway Express. Through numerical simulation, the influence of the main factors, including the reward and punishment of the government, on the evolutionary stability strategy of the system was analyzed, providing theoretical references for the coordinated development of the China Railway Express accordingly. The results have shown that the increased government punishment will effectively promote synergistic development between operators and suppliers. Differential subsidies are given according to the different strategies of operators and suppliers. As the difference between different subsidy levels becomes larger, it is more beneficial for synergistic development. Reasonable setting of the maximum subsidy per unit of container provided by the government to operators, and gradually reducing the amount until the subsidy is completely withdrawn, is an effective way to promote synergistic development. The additional social benefits of the government are a positive influence in determining the choice of government strategies.
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图 5 初始数值下系统的演化博弈仿真
Figure 5. Evolutionary game simulation of systems with initial values
图 8 $ \alpha 、\beta 、\gamma $的差值变化对系统演化结果的影响
Figure 8. Effect of $ \alpha ,\beta ,\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{a}\mathrm{n}\mathrm{d}\;\gamma $ changes on evolutionary results of system
表 1 模型符号及其含义
Table 1. Model symbols and their meanings
符号 定义 符号 定义 $ {{R}}_{{1}} $ 政府积极监管带来的社会效益 $ {\alpha } $ 政府积极监管下，对积极协同运营商的补贴力度，$ {\alpha } $∈[0,1] $ {{R}}_{{2}} $ 政府消极监管带来的社会效益 $ {\beta } $ 政府消极监管下，对运营商的补贴力度，$ {\beta } $∈[0,1] $ {C} $ 政府积极监管机构监管的成本 $ {\gamma } $ 政府积极监管下，对消极协同运营商的补贴力度，$ {\gamma } $∈[0,1] $ {U} $ 政府积极监管下运营商和供货商协同发展为政府带来的额外社会效益 $ {{c}}_{{1}} $ 单位集装箱操作成本，包括集装箱装卸、搬运等成本 $ {{P}}_{{1}} $ 中铁集团向班列运营商提供的单位运力价格 $ {{c}}_{{2}} $ 单位集装箱货物价值 $ {{P}}_{{2}} $ 政府积极监管下，运营商积极协同时向供货商提供的单位集装箱运价 $ {{c}}_{{3}} $ 供货商的其他成本 $ {{P}}_{{3}} $ 政府积极监管下，运营商消极协同时向供货商提供的单位集装箱运价 $ {{Q}}_{{1}} $ 积极协同总集装箱数量 $ {{P}}_{{4}} $ 政府消极监管下，运营商积极协同时向供货商提供的单位集装箱运价 $ {{Q}}_{{2}} $ 消极协同总集装箱数量 $ {{P}}_{{5}} $ 政府消极监管下，运营商消极协同时向供货商提供的单位集装箱运价 $ {{r}}_{{1}} $ 政府积极监管运营商积极协同带来风险的风险水平系数 $ {{P}}_{{6}} $ 单位集装箱货物销售价格 $ {{r}}_{{2}} $ 政府消极监管运营商积极协同带来风险的风险水平系数 $ {{C}}_{{{\mathrm{P1}}}} $ 政府积极监管运营商选择积极协同需要付出的集货运费成本 $ {I} $ 协同收益 $ {{C}}_{{{\mathrm{P2}}}} $ 政府消极监管运营商选择积极协同需要付出的集货运费成本 $ {\sigma } $ 运营商和供货商对协同收益的分配比例，$ {\sigma } $∈ [0,1] $ {{C}}_{{{\mathrm{t1}}}} $ 政府积极监管供货商选择与积极协同运营商合作需要付出的集货时间成本 $ {{F}}_{{1}} $ 政府监管下，对消极协同运营商的罚金 $ {{C}}_{{{\mathrm{t2}}}} $ 政府消极监管供货商选择与积极协同运营商合作需要付出的集货时间成本 $ {{F}}_{{2}} $ 政府监管下，对与消极协同运营商合作的供货商、不与积极协同运营商合作的供货商的罚金 $ {M} $ 政府提供给运营商的单位集装箱最大补贴额 
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表 2 收益矩阵
Table 2. Revenue matrix
策略 收益对象 运营商积极协同 y 运营商消极协同 1−y 供货商合作 z 供货商不合作 1−z 供货商合作 z 供货商不合作 1−z 政府积极监管 x 政府
运营商
供货商$\begin{gathered} {\varPi _{{\rm{G1}}} } - \alpha M{Q_1} + U \\ {\varPi _{{\rm{O1}}} } + \alpha M{Q_1} + \sigma I \\ {\varPi _{{\rm{S1}}} } + (1 - \sigma )I \\ \end{gathered}$ $\begin{gathered} {\varPi _{{\rm{G1}}} } \\ {\varPi _{{\rm{O2}}} } + {F_2} \\ - {F_2} \\ \end{gathered}$ $\begin{gathered} {\varPi _{{\rm{G1}}} } - \gamma M{Q_2} + {F_1} + {F_2} \\ {\varPi _{{\rm{O3}}} } + \gamma M{Q_2} - {F_1} \\ {\varPi _{{\rm{S2}}} } - {F_2} \\ \end{gathered}$ $\begin{gathered} {\varPi _{{\rm{G1}}} } \\ - {F_1} \\ {F_1} \\ \end{gathered}$ 政府消极监管 1−x 政府
运营商
供货商$\begin{gathered} {\varPi _{{\rm{G2}}} } - \beta M{Q_1} \\ {\varPi _{{\rm{O4}}} } + \beta M{Q_1} + \sigma I \\ {\varPi _{{\rm{S3}}} } + (1 - \sigma )I \\ \end{gathered}$ $\begin{gathered} {\varPi _{{\rm{G2}}} } \\ {\varPi _{{\rm{O5}}} } \\ 0 \\ \end{gathered}$ $\begin{gathered} {\varPi _{{\rm{G2}}} } - \beta M{Q_2} \\ {\varPi _{{\rm{O6}}} } + \beta M{Q_2} \\ {\varPi _{{\rm{S4}}} } \\ \end{gathered}$ $\begin{gathered} {\varPi _{{\rm{G2}}} } \\ 0 \\ 0 \\ \end{gathered}$
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表 3 均衡点特征值
Table 3. Equilibrium point eigenvalues
均衡点 特征值 $ {\lambda }_{1} $ 特征值 $ {\lambda }_{2} $ 特征值 $ {\lambda }_{3} $ $ {E}_{1}\left(\mathrm{0,0},0\right) $ ${\varPi _{{\rm{G1}}} } - {\varPi _{{\rm{G2}}} }$ ${\varPi _{{\rm{O5}}} } < 0$ ${\varPi _{{\rm{S4}}} } > 0$ $ {E}_{2}\left(\mathrm{1,0},0\right) $ $- ({\varPi _{{\rm{G1}}} } - {\varPi _{{\rm{G2}}} })$ ${\varPi _{{\rm{O2}}} } + {F_1} + {F_2}$ ${\varPi _{{\rm{S2}}} } - {F_1} - {F_2}$ $ {E}_{3}\left(\mathrm{0,1},0\right) $ ${\varPi _{{\rm{G1}}} } - {\varPi _{{\rm{G2}}} }$ $- {\varPi _{{\rm{O5}}} } > 0$ ${\varPi _{{\rm{S3}}} } + (1 - \sigma )I > 0$ $ {E}_{4}\left(\mathrm{0,0},1\right) $ ${\varPi _{{\rm{G1}}} } - {\varPi _{{\rm{G2}}} } + {F_1} + {F_2} + \beta M{Q_2} - \gamma M{Q_2}$ ${\varPi _{{\rm{O4}}} } - {\varPi _{{\rm{O6}}} } + \beta M{Q_1} - \beta M{Q_2} + \sigma I$ $- {\varPi _{{\rm{S4}}} } < 0$ $ {E}_{5}\left(\mathrm{0,1},1\right) $ ${\varPi _{{\rm{G1}}} } - {\varPi _{{\rm{G2}}} } + U - \alpha M{Q_1} + \beta M{Q_1}$ $- ({\varPi _{{\rm{O4}}} } - {\varPi _{{\rm{O6}}} } + \beta M{Q_1} - \beta M{Q_2} + \sigma I)$ $- [{\varPi _{{\rm{S3}}} } + (1 - \sigma )I] < 0$ $ {E}_{6}\left(\mathrm{1,0},1\right) $ $- ({\varPi _{{\rm{G1}}} } - {\varPi _{{\rm{G2}}} } + {F_1} + {F_2} + \beta M{Q_2} - \gamma M{Q_2})$ ${\varPi _{{\rm{O1}}} } - {\varPi _{{\rm{O3}}} } + \alpha M{Q_1} - \gamma M{Q_2} + \sigma I + {F_1}$ $- ({\varPi _{{\rm{S2}}} } - {F_1} - {F_2})$ $ {E}_{7}\left(\mathrm{1,1},0\right) $ $- ({\varPi _{{\rm{G1}}} } - {\varPi _{{\rm{G2}}} })$ $- ({\varPi _{{\rm{O2}}} } + {F_1} + {F_2})$ ${\varPi _{{\rm{S1}}} } + (1 - \sigma )I + {F_2} > 0$ $ {E}_{8}\left(\mathrm{1,1},1\right) $ $- ({\varPi _{{\rm{G1}}} } - {\varPi _{{\rm{G2}}} } + U - \alpha M{Q_1} + \beta M{Q_1})$ $- ({\varPi _{{\rm{O1}}} } - {\varPi _{{\rm{O3}}} } + \alpha M{Q_1} - \gamma M{Q_2} + \sigma I + {F_1})$ $- [{\varPi _{{\rm{S1}}} } + (1 - \sigma )I + {F_2}] < 0$
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表 4 参数初始赋值
Table 4. Initial assignment of parameters
参数 初始值 单位 参数 初始值 单位 $ {R_1} $ 100 百万元 $ {C_{{\mathrm{t2}}}} $ 5 万元 $ {R_2} $ 50 百万元 $ \alpha $ 0.5 $ C $ 10 百万元 $ \beta $ 0.45 $ U $ 40 百万元 $ \gamma $ 0.4 $ M $ 3 万元 $ {c_1} $ 2 万元 $ {P_1} $ 10 万元 $ {c_2} $ 1 万元 $ {P_2} $ 15 万元 $ {c_3} $ 1 万元 $ {P_3} $ 13 万元 $ {Q_1} $ 1 百个 $ {P_4} $ 14 万元 $ {Q_2} $ 2 百个 $ {P_5} $ 12 万元 $ {r_1} $ 0.2 $ {P_6} $ 16 万元 $ {r_2} $ 0.3 $ I $ 1 万元 $ \sigma $ 0.5 $ {C_{{\mathrm{P1}}}} $ 5 万元 $ {F_1} $ 8.5 万元 $ {C_{{\mathrm{P2}}}} $ 6 万元 $ {F_2} $ 10 万元 $ {C_{{\mathrm{t1}}}} $ 4 万元
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