双重效应影响下疫苗供应链的区块链引入与定价决策

doi:10.6040/j.issn.1671-9352.0.2025.006

Abstract

Abstract: To solve the problem of traceability in the vaccine supply chain, a dual effect of blockchain-enabled in monitoring vaccine flow and affecting consumers’ risk perception is considered and the Stackelberg game is used to compare and analyze the blockchain introduction decision of vaccine manufacturer and the pricing decision of vaccine supply chain. The research shows that:(1)The harm of the vaccine gray market is reflected in disrupting the market price order and reducing the profits of vaccine manufacturer and vaccine supply chain.(2)Vaccine manufacturer is always willing to introduce blockchain to suppress the vaccine gray market. However, vaccine manufacturer refuses to build blockchain to the extent required to completely suppress the vaccine gray market, which explains why the introduction of blockchain still cannot completely suppress the gray market in reality.(3)The introduction of blockchain by vaccine manufacturer helps to increase immunization coverage and rebuilt vaccine trust, but contrary to the intuitive feeling, it will reduce consumer surplus and social welfare in some cases.

Key words: vaccine supply chain, blockchain, dual effect, pricing, game theory

CLC Number:

F224

LI Shiyang, CHEN Keyu, ZHOU Nan. Blockchain introduction and pricing decision of vaccine supply chain under the influence of dual effects[J].JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2026, 61(8): 39-51.

References

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[27] 高鹏,聂佳佳,薛佳. 区块链下考虑消费者隐私关注的绿色产品研发创新及政府补贴策略[J]. 管理学报,2024,21(7):1097-1106. Gao Peng, Nie Jiajia, Xue Jia. Green product r&d innovation and government subsidy strategy considering consumer privacy concerns under blockchain[J]. Chinese Journal of Management, 2024, 21(7):1097-1106. 附录: 定理1证明采用逆向归纳法进行求解,首先求解疫苗供应商的决策,接着求解疫苗生产商的决策。求π^NN_R关于p^NN_L的二阶条件(ə²π^NN_R)/(ə(p^NN_L)²)=-2<0,因此π^NN_R存在极大值。求π^NN_R关于p^NN_L的一阶条件,得到p^NN_L的反应函数为p^NN_L=(w+1)/2,代入到疫苗生产商的决策中,求π^NN_M关于p^NN_H的二阶条件(ə²π^NN_M)/(ə(p^NN_H)²)=(-2)/ε<0,因此π^NN_M存在极大值。求π^NN_M关于p^NN_H的一阶条件,并代入到p^NN_L的反应函数中,得到定理1。为保证均衡解为正,需要满足w<1。定理2证明采用逆向归纳法进行求解,首先求解疫苗供应商的决策,接着求解疫苗生产商的决策。求π^A_R关于p^A_L和p^A_N的二阶条件 ((ə²π^A_R)/(ə(p^A_L)²)(ə²πA_R)/(əpA_Ləp^A_N) (ə²π^A_R)/(əp^A_Nəp^A_L)(ə²π^A_R)/(ə(p^A_N)²))=(-2 0 0(-2)/((1-θ)θε)), 其中,一阶顺序主子式-2<0,二阶顺序主子式4/((1-θ)θε)>0,因此π^A_R存在极大值。联立求解π^A_R关于p^A_L和p^A_N的一阶条件,得到p^A_L和p^A_N的反应函数为 p^A_L=(w+1)/2,p^A_N=(θpH+w)/2。将反应函数代入到疫苗生产商的决策中,求π^A_M关于p^A_H的二阶条件,得到(ə²π^A_M)/(ə(p^A_H)²)=-(2-θ)/((1-θ)ε)<0,因此π^A_M存在极大值。求解π^A_M关于pA_H的一阶条件,并代入到p^A_L和p^A_N的反应函数中,即可得到定理2。为保证均衡解为正,需要满足w1,其中w₁=(θε)/2。命题1证明 (1)(əd^A*_N)/(əw)=1/((θ-2)θε)<0; (2)(əπ^A*_M)/(əw)=((2θ²ε-4θε-4)w+(4-θ)θε)/((4-2 θ)θε),分子为关于w的一次函数。令(əπ^A*_M)/(əw)=0,得到阈值w₀,当00时,(əπ^A*_M)/(əw)>0;当w₀_A1时,(əπ^A*_M)/(əw)<0,其中w₀=(4θε-θ²ε)/(4θε+4-2θ²ε)。定理3证明采用逆向归纳法进行求解,首先求解疫苗供应商的决策,接着求解疫苗生产商的决策。求π^B_R关于p^B_L和p^B_N的二阶条件 ((ə²π^B_R)/(ə(p^B_L)²)(ə²π^B_R)/(əp^B_Ləp^B_N ) (ə²π^B_R)/(əp^B_Nəp^B_L)(ə²π^B_R)/(ə(p^B_N)²))=(-2 0 0(-2)/((1-θ)θε)), 其中,一阶顺序主子式-2<0,二阶顺序主子式4/((1-θ)θε)>0,因此π^B_R存在极大值。联立求解π^B_R关于p^B_L和p^B_N的一阶条件,得到p^B_L和p^B_N的反应函数为 p^B_L=(w+1)/2,p^B_N=(θpH+w)/2+((f-s)x)/2。将反应函数代入到疫苗生产商的决策中,求π^B_M关于p^B_H的二阶条件,得到(ə²π^B_M)/(ə(p^B_H)²)=-(2-θ)/((1-θ)ε)<0,因此π^B_M存在极大值。求解π^B_M关于p^B_H的一阶条件,并代入到π^B_M中,求π^B_M关于xB的二阶条件 (ə²π^B_M)/(ə(xB)²)=-((4θ²-12θ+8)θε+8f(1-θ)(f+s)-θs²)/(4(2-θ)(1-θ)θε)<0。求解π^B_M关于xB的一阶条件,并代回到pB_H、 pB_L和pB_N的反应函数中,即可得到定理3。为保证均衡解为正,需要满足f< f_B1且w>wB1,其中, fB1=w-(2(1-θ)θε+(4-3θ)s)/(4-4θ), w_B1=(2(1-θ)θε+(4-3θ)s)/(4-4θ)。为便于表示,记L=(4θ²-12θ+8)θε+8 f(1-θ)(f+s)-θs²>0。命题2证明 (1)(əd^B_H(x))/(əx)=s/(4ε(1-θ))>0,(əd^B_N(x))/(əx)=((4 f+3s)θ-4 f-4s)/(4θε(2-θ)(1-θ))<0; (2)见定理3。命题3证明 π^A*_M-π^NN*_M=-((θε-2w)²)/(4θε(2-θ))<0;π^B*_M-π^NN*_M=((s²+4θ²ε-4θε)(θε-2w))/(4Lθε)<0; π^B*_M-π^A*_M=((1-θ)(θε-2w)²(2 f+s)²)/(2(2-θ)Lθε)>0。因此,π^NN*_M>π^B*_M>π^A*_M。 π^A*_R-π^NN*_R=((θε-2w)²(1-θ))/(4θε(2-θ)²)>0;π^B*_R-π^NN*_R=((2θ²ε-2θε+s(s+f))²(θε-2w)(1-θ))/(θεL²)>0; π^B*_R-π^A*_R=T₁g₁(f),T₁=(((4 f+3s)θ-4 f-4s)(2 f+s)(θ-1)(θε-2w)²)/(4(2-θ)²L²θε)>0, g₁(f)=(θ-1)f ²+((3θs)/4-s/2)f-θ³ε+3θ²ε+(-(s²)/8-2ε)θ+(s²)/2<0。因此,π^B*_R-π^A*_R<0_, π^A*_R>π^B*_R>π^NN*_R。命题3证毕。命题4证明 π^A*_SC-π^NN*_SC=-((θε-2w)²)/(4(2-θ)²θε)<0; π^B*_SC-π^NN*_SC=T₂g₂(f),T₂=(-(θε-2w)²)/(4θεL²)<0, g₂(f)=4(θ-1)(8θ²ε+3s²-8θε)f ²+16s(θ-1)(3θ²ε+s²-3θε)f +(5θ-4)s⁴+(16θ³ε-24θ²ε+8θε)s²+16θ⁴ε²-32θ³ε²+16θ²ε²>0。因此,π^B*_SC<π^NN*_SC。 π^B*_SC-π^A*_SC=T₃g₃(f),T₃=-((1-θ)(θε-2w)²(2f+s))/(4θε(2-θ)²L²)<0, g₃(f)=32(θ-1)f ³+48s(θ-1)f ²+(-16εθ⁴-6s²θ²+48θ³ε+40θs²-32θ²ε-32s²)f -16εθ⁴s-5θ²s³+64εsθ³+20s³θ-80εsθ²-16s³+32εθ, g₃(f)单调递减且存在唯一零点,记f₁为g₃(f)=0的根。当f₁< f_B1时,在定义域内g₃(f)<0, π^B*_SC>π^A*_SC。此时需满足01, s₁为f₁=f_B1的根。当s₁_B1时, f₁在定义域内,故当f_B1< f< f₁时,g₃(f)>0, π^B*_SC<π^A*_SC,当f₁< f< f_B1时,g₃(f)<0, π^B*_SC>π^A*_SC。命题5证明 (1)μA=μ_NN, μB-μA=((θε-2w)(2 f+s)s)/(2εL)>0; (2)CS^A*-CS^NN*=(θε-2w)/(8-4θ)>0; CS^B*-CS^NN*=T₄g₄(f), T₄=(θε-2w)/(8εL²)>0, g₄(f)>0,因此CS^B*>CS^NN*, CS^B*-CS^A*=T₅g₅(f), T₅=-((θε-2w)(2f+s))/(8(2-θ)εL²)<0, g₅(f)<0,因此CS^B*A*。命题6证明 SW^A*-SW^NN*=((θε-2w)w)/(2θε(2-θ))>0;SW^B*-SW^A*=T₆g₆(f), T₆=-((θε-2w)(2f+s))/(8θε(2-θ)L²)<0,g₆(f)>0。因此SW^A*>SW^B*; SW^B*-SW^NN*=T₇g₇(f), T₇=-((θε-2w))/(8θεL²)<0, g₇(w)为单调递减的一次函数,记g₇(0)=0的根为f₂, g₇(w)=0的根为w₂。当f_B1< f< f₂时,SW^B*>SW^NN*;当f₂< f< fB2且w₂SW^B*>SW^NN*;当f₂< f< f_B2且w_B12时,SW^B*NN*。

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Blockchain introduction and pricing decision of vaccine supply chain under the influence of dual effects

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