晴读（39）：精读期刊论文

摘要：Today, the editor will present the Recycling Channel Competitive Relationship Incentive Model (Model SN) from the paper "Design of

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“晴读（39）：精读复刻论文《基于委托代理理论的逆向供应链激励机制设计与回收模式选择》的回收渠道合作关系激励模型（模型SC）”

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"Qing Du (39): The incentive model for cooperative relationships in recycling channels (Model SC) from the in-depth reprinted paper "Design of Incentive Mechanism and Selection of Recycling Mode in Reverse Supply Chain Based on Principal-Agent Theory"

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今天小编将从思维导图、精读内容、知识补充三个板块为大家带来《基于委托代理理论的逆向供应链激励机制设计与回收模式选择》的回收渠道竞争关系激励模型（模型SN）。

Today, the editor will present the Recycling Channel Competitive Relationship Incentive Model (Model SN) from the paper "Design of Incentive Mechanism and Selection of Recovery Mode for Reverse Supply Chain Based on Principal-Agent Theory" to everyone through three sections: mind map, intensive reading content, and knowledge supplement.

一、思维导图（Mind Mapping）

二、精读内容（Conduct in-depth reading of the material）

1.模型背景与目标

该模型（P2）旨在解决制造商与回收商合作关系下的契约设计问题，核心是制造商通过设计最优契约（包含固定支付和收益分成），激励两个回收商（i和j，i=1,2）付出最优努力，最终最大化制造商自身的期望效用。

1. Model Background and Objectives

This model (P2) aims to solve the contract design problem in the cooperative relationship between manufacturers and recyclers. Its core lies in that manufacturers, by designing optimal contracts (including fixed payments and revenue sharing), incentivize two recyclers (i and j, where i=1,2) to exert optimal efforts, ultimately maximizing the manufacturers' own expected utility.

2.目标函数（制造商效用最大化）

(1)制造商的期望效用USCM表达式为：

2. Objective Function (Maximization of Manufacturer's Utility)

(1) The expression for the manufacturer's expected utility, denoted as USCM, is:

(2)制造商的效用来自两部分——保留的收益分成（扣除给回收商的部分），减去支付给回收商的固定费用。

(2) The manufacturer's utility comes from two parts: the retained revenue share (after deducting the portion given to recyclers) minus the fixed fees paid to recyclers.

(3)变量含义：

αiSC：制造商给回收商i的固定支付（契约中的固定部分）；

βiSC：回收商i获得的收益分成比例（契约中的浮动部分，1-βiSC为制造商保留的比例）；

eiSC：回收商i的努力水平（决策变量，影响回收收益）；

θi：回收商i的基础收益（外生参数）；

b:自身努力对收益的边际贡献；

t:回收商间的努力溢出效应（i的努力对j的收益有正向影响，体现“合作关系”）。

(3) Definitions of Variables:

αiSC: Fixed payment from the manufacturer to recycler \( i \) (the fixed part of the contract);

βiSC: Revenue sharing ratio obtained by recycler i (the floating part of the contract, where 1-βiSC is the ratio retained by the manufacturer);

eiSC: Effort level of recycler i (a decision variable that affects recycling revenue);

θi: Basic revenue of recycler i (an exogenous parameter);

b: Marginal contribution of one's own effort to revenue;

t: Effort spillover effect among recyclers (the effort of i has a positive impact on the revenue of j, reflecting the "cooperative relationship").

3.约束条件（回收商参与与激励兼容）

3. Constraints (Recycler Participation and Incentive Compatibility)

模型包含两个约束，确保回收商愿意参与且付出最优努力：

（1）参与约束（IR）：回收商i的期望效用不低于其保留效用-Ω，可理解为不参与时的最低收益）：

The model includes two constraints to ensure recyclers are willing to participate and exert optimal efforts:

(1) Participation Constraint (IR): The expected utility of recycler i is not lower than its reservation utility -Ω, which can be understood as the minimum benefit when not participating.

其中，a（eiSC）2/2是回收商的努力成本（a为成本系数），ρ（βiSC）2/2是回收商承担的风险成本（ρ为风险厌恶系数，σ2为收益波动方差）。Among them, a（eiSC）2/2 is the recycler's effort cost (where a is the cost coefficient), and ρ（βiSC）2/2 is the risk cost borne by the recycler (where ρ is the risk aversion coefficient and σ2 is the revenue fluctuation variance).

（2）激励兼容约束（IC）：回收商i会选择自身努力水平eiSC最大化自身效用，即：

(2) Incentive Compatibility Constraint (IC): Recycler (i) will choose its own effort level eiSC to maximize its own utility, i.e.:

4.求解结果（命题2）的含义

通过求解上述规划问题（P2），得到最优契约参数、努力水平及效用结果，核心结论如下：

4. Implications of the Solution Results (Proposition 2)

By solving the aforementioned programming problem (P2), the optimal contract parameters, effort levels, and utility results are obtained, with the core conclusions as follows:

（1）最优分成比例βiSC*：分成比例由努力的边际贡献（b+t、b+2t）、风险成本（ρaα2）共同决定；努力的边际贡献越大（b、t越大），分成比例越高（激励回收商付出更多努力）；风险成本越高（ρσ2越大），分成比例越低（回收商厌恶风险，需降低其承担的风险份额）。

(1) Optimal Revenue Sharing Ratio βiSC*: The revenue sharing ratio is jointly determined by the marginal contribution of effort ( b+t、b+2t) and the risk cost (ρaα2）the greater the marginal contribution of effort (the larger b and t are), the higher the revenue sharing ratio (to incentivize recyclers to exert more effort); the higher the risk cost (the larger ρσ2 is), the lower the revenue sharing ratio (since recyclers are risk-averse, it is necessary to reduce the risk share they bear).

（2）最优固定支付αiSC*：固定支付用于平衡回收商的参与约束，与保留效用（-Ω）、基础收益（θi）及努力成本相关。本质是制造商在分成比例确定后，通过固定支付确保回收商至少获得保留效用。

(2) Optimal Fixed Payment αiSC*: The fixed payment is used to balance the recycler's participation constraint and is related to the reservation utility -Ω, basic revenue θi, and effort cost. In essence, after the revenue sharing ratio is determined, the manufacturer ensures that the recycler obtains at least the reservation utility through the fixed payment.

（3）最优努力水平eiSC*：努力水平与努力的边际贡献（(b+t)、(b+2t)）正相关，与努力成本（a）和风险成本（ρσ2）负相关，符合“成本-收益”权衡逻辑。

(3) Optimal Effort Level eiSC*: The effort level is positively correlated with the marginal contribution of effort ((b+t), (b+2t) ), and negatively correlated with the effort cost ( a ) and risk cost ( ρσ2), which conforms to the "cost-benefit" trade-off logic.

（4）最优期望效用UiSC=-Ω：回收商i的效用（刚好满足参与约束，制造商榨取全部超额收益）；制造商的效用UMSC由总基础收益、努力带来的额外收益减去回收商的保留效用组成，体现合作关系下的整体收益分配。

(4) Optimal Expected Utility UiSC=-Ω: This is the utility of recycler i (which just satisfies the participation constraint, with the manufacturer extracting all excess benefits); the manufacturer's utility UMSC consists of the total basic revenue, the additional revenue brought by efforts, minus the recycler's reservation utility, reflecting the overall revenue distribution under the cooperative relationship.

5.核心结论

该模型揭示了合作关系下回收渠道的最优契约设计逻辑：制造商通过“固定支付+收益分成”的契约组合，在考虑回收商风险厌恶和努力溢出效应（合作的体现）的前提下，实现自身效用最大化。其中，分成比例主要用于激励努力和分担风险，固定支付用于确保回收商参与，最终结果体现了制造商对供应链剩余的主导分配权。

5. Core Conclusions

This model reveals the logic of optimal contract design for recycling channels under cooperative relationships: manufacturers achieve the maximization of their own utility by adopting a contract combination of "fixed payment + revenue sharing," while taking into account recyclers' risk aversion and the effort spillover effect (a reflection of cooperation). Among them, the revenue sharing ratio is mainly used to incentivize efforts and share risks, the fixed payment is used to ensure recyclers' participation, and the final result reflects the manufacturer's dominant right to distribute the supply chain surplus.

三、知识补充（Supplementary knowledge）

1.努力溢出效应：努力溢出效应是指在合作场景中，一个参与者（如回收商i）付出的努力，不仅会提升自身收益，还会对其他参与者（如回收商j）的收益产生正向影响的现象。

1. Effort Spillover Effect: The effort spillover effect refers to a phenomenon in cooperative scenarios where the effort exerted by one participant (e.g., recycler i) not only increases its own revenue but also has a positive impact on the revenue of other participants (e.g., recycler j).

2.努力的边际贡献：指参与者每额外多付出一单位努力，所能带来的收益（或效用）的增加量。

2. Marginal Contribution of Effort: It refers to the increase in revenue (or utility) that a participant can obtain for each additional unit of effort exerted.

3.外生参数：外生参数是模型中不受自身决策变量影响、由外部环境或系统设定好的固定参数。

3. Exogenous Parameters: Exogenous parameters are fixed parameters in the model that are not affected by the model's own decision variables and are determined by the external environment or system settings.

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