Poverty alleviation ecosystem evolutionary game on smart supply chain platform under the government financial platform incentive mechanism

Journal Pre-proof Poverty alleviation ecosystem evolutionary game on smart supply chain platform under the government financial platform incentive mechanism Xiaole Wan, Xiaoqian Qie

PII: DOI: Reference:

S0377-0427(19)30600-4 https://doi.org/10.1016/j.cam.2019.112595 CAM 112595

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Journal of Computational and Applied Mathematics

Received date : 25 February 2019 Revised date : 14 September 2019 Please cite this article as: X. Wan and X. Qie, Poverty alleviation ecosystem evolutionary game on smart supply chain platform under the government financial platform incentive mechanism, Journal of Computational and Applied Mathematics (2019), doi: https://doi.org/10.1016/j.cam.2019.112595. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

© 2019 Published by Elsevier B.V.

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Xiaole Wan1*, Xiaoqian Qie1

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Poverty Alleviation Ecosystem Evolutionary Game on Smart Supply Chain Platform under The Government Financial Platform Incentive Mechanism

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School of Management, Ocean University of China, Qingdao 266100, China

* Corresponding author. E-mail addresses: [email protected] (X. Wan), [email protected] (X. Qie).

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Abstract：Artificial intelligence, machine learning and big data computing promote the development of smart supply chain. The cooperative poverty alleviation model with multi-subject participation composed of cooperative, smart supply chain platform and the government was constructed. The evolutionary game method was used to explore the behavioral strategies of cooperative poverty alleviation ecosystem between the smart supply chain platform and the cooperative under the government financial platform subsidy mechanism. Particularly, the game equilibrium in the cooperation between the smart supply chain platform and the cooperative under the subsidy and non-subsidy mechanisms of the government was analyzed. Finally, numerical simulation was implemented to analyze the effects of risks, intelligence degree, consumer preference and price on game equilibrium. The study results demonstrate: (1) In the range allowed by technology and cost, increasing the intelligence degree of the smart supply chain platform will benefit the cooperation between the smart supply chain platform and the cooperative; (2) Under high unsalable risks and unsalable losses, the cooperative will cooperate with the smart supply chain platform; (3) consumer preference influences not only the cooperative game between smart supply chain and cooperative, but also product demand and product price; and (4) under constant conditions, dependence on government subsidies is inversely proportional to the intelligence degree. In other words, enhancing the intelligence degree of the smart supply chain platform helps to transform the "blood transfusion" poverty alleviation to “hematopoietic” poverty alleviation, and decreases the dependence of poverty alleviation on government financial platform subsidies.

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Keywords：smart supply chain；poverty alleviation ecosystem；government financial platform incentive mechanism；evolutionary game

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1. Introduction

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As the development of machine learning and artificial intelligence techniques, more researchers regard them as the effective ways to development algorithms and solve the problems. For instance, Ordóñez et al. (2019) developed an algorithm combines time series analysis methods to forecast the values of the predictor variables with machine learning techniques to predict RUL from those variables. Applied machine learning based regression methods to predict the errors of reduced-order models, Stefanescu et al. (2018) discussed the multivariate predictions of local reduced-order-models (MP-LROM) methodology. As companies conceive a more predictable and automated future for logistics and distribution, they are increasingly interested in the application of machine learning and artificial intelligence in smart supply chain (IT Word, 2018). The popularity of smart manufacturing leads to the formation of more data. Some studies begin to explore how to use such data in an effective manner (Sharp et al., 2018 & Wang et al., 2018). For the past few years, with the growing application of machine learning model in smart supply chain (Priore et al. 2018；Bousqaoui et al. 2017), more and more in-depth studies have been conducted in this field .(García Nieto et al.,2018；García Nieto et al.,2019). For instance, Wan et al. (2016&2017) conducted the research on consumer electronics supply chain from the perspective of least squares support vector machine and random forest theory. High attention of the society on poverty relief makes the research on poverty relief supply chain a hot research topic now (Rodríguez et al., 2016). As a great power devoted to poverty relief, China advocates that “the success or failure of poverty relief and development lies in precision”, and advocated the government financial platform, society and market to jointly promote the construction of a large-scale poverty development pattern. The smart supply chain platform has become an important means of transforming “transfusion-type” poverty alleviation to “hematopoiesis-type” poverty alleviation. For example, JD recommends special products from poverty-stricken counties in China Special Product Poverty Alleviation Center on JD platform, and promotes poverty alleviation products on the smart supply chain platform. However, due to the backward agricultural production technology and infrastructure construction in poverty-stricken areas, most smart platforms cooperate with cooperatives to build a poverty alleviation model which composed of smart supply chain platform (poverty alleviation center), cooperatives and farmers, which is conducive to improving the scale efficiency and market competitiveness of agricultural products. Therefore, the decision-making research under the poverty alleviation model with multi-subject participation composed of cooperative, smart supply chain platform and the government is of great importance. Compared with the traditional static equilibrium analysis method, evolutionary game explores the rules of management decision-making through a dynamic and evolutionary method, which helps decision-makers to make scientific and effective decisions. At present, evolutionary game theory has achieved substantial achievement in supply chain management: some scholars use evolutionary game to analyze the behavioral strategies of supply chain members under carbon emission policies. Barari et al. (2012) looked for a synergetic alliance between the environmental and commercial benefits by establishing coordination between the producer and the retailer to adjudicate their strategies to trigger green practices with the focus on maximizing economic profits by leveraging upon the product’s greenness and solved it by using two players evolutionary game. In order to establish long-term green purchasing relationships between multi-stakeholders (suppliers and manufacturers), Ji 2

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et al. (2015) developed an evolutionary game model. Wu et al. (2017) constructed a low-carbon strategic evolution model based on the game between government financial platform and enterprises in complex network environment. Babu & Mohan (2018) built a strong theoretical framework to integrate, explain, and predict sustainability for supply chains using evolutionary game theory. In accordance with the two-population evolutionary game model, Reza et al. (2018) established a model for the relation between government goal and producer goal under three different scenarios. As proved by the research findings, customs collection was the most effective means to minimize the influence of environment. Chen and Hu (2018) built an evolutionary game theory model between government financial platforms and manufacturers based on static carbon taxes and subsidies, and explored the evolutionary stability strategies of government financial platforms and manufacturers under different constraints. In addition, they analyzed the optimal carbon tax and subsidy mechanisms under three models of dynamic tax and static subsidy, static tax and dynamic subsidy, and dynamic tax and dynamic subsidy. Some scholars used evolutionary games to study remanufacturing supply chain members’ fulfillment of corporate social responsibility through the game strategy. For example, Li et al. (2013) examined the evolutionary stable strategy (ESS) of the producer and retailer in the reproduction industry by reference to the preset evolutionary game model applicable for two-echelon closed-loop supply chain. In a research on the evolutionary game model applicable for two-echelon closed-loop supply chain, Li et al. (2014) discovered the great significance of price and government subsidy to the progress of the reproduction industry. Under the evolutionary game theory model, Shu et al. (2018) pointed out that the producer and retailer might compete or not compete for the dominance over the market in the changing process of supply chain or market. It was up to their willingness for new and reproduced products. In recent years, evolutionary game has been widely used in dynamic supply chain network systems. Throughout the study on individual collaboration network, Jesús et al. (2011) investigated that the bipartite graph approach might be employed to survey the mesoscopic information of real group structure. Li et al. (2012) adopted the prisoner’s dilemma game model to go into the evolutionary game of random growth network. The research results proved that fast growth speed made for the improvement of the average earnings of cooperators and defectors. By analyzing the evolutionary dynamics of actions in social network, Scatà et al. (2016) discussed the evolutionary process of cooperation in which the node could either select cooperation or defection in classical social dilemma scenarios like prisoner’s dilemma and snowdrift game. On the basis of the evolutionary game model, Gemeda et al. (2017) raised a new evolutionary cluster-head algorithm to solve the resource trouble in wireless sensor network. Yi et al. (2017) analyzed the evolutionary stability strategy of network externality for retailers' marketing objectives by constructing retailer group evolutionary game and optimization decision model. Wang et al. (2019) established a low-carbon diffusion model based on evolutionary game theory and complex network theory, and explored the game of low-carbon strategies and the learning strategies between network neighbors. With a view of expediting the diffusion of electric vehicle, Li et al (2019) followed a sophisticated network evolutionary game model to examine the dynamic influence of government policy on the diffusion of electric vehicle in various networks. Smart supply chain platforms have become an important means for precise poverty alleviation. For example, Zhu et al. (2017) explored the feasible path of 3

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“Internet + rural e-commerce” suitable for poverty alleviation in poor areas by combining the platforms and rural economic development. Qin (2018) studied the innovation of e-commerce participation in poverty alleviation mode under the background of “Internet + precise poverty alleviation”. Some achievements have been made in the participation of government financial platforms in poverty alleviation. For example, Fu et al. (2018) constructed an evolutionary game model of industrial poverty alleviation under the government financial platform reward and punishment mechanism. Yu et al. (2018) established an evolutionary game model between government financial platforms and low-income families and a dynamic game model under imperfect information conditions between low-income families and cooperatives. Moreover, the plight of financial poverty alleviation in precise poverty alleviation was analyzed. However, no achievement has been achieved in the multi-agent evolutionary game under the model with multi-subject participation composed of cooperative, smart supply chain platform and the government. The behavioral strategies of cooperative poverty alleviation of smart supply chain platforms and cooperatives under the government financial platform subsidy mechanism are explored. The game equilibrium between smart supply chain platforms and cooperatives under the government financial platform subsidy mechanism and non-subsidy mechanism was analyzed. To this end, this paper constructs a cooperative financial poverty alleviation ecosystem involving multi-agents of government financial platforms, cooperatives and smart supply chain platforms. The influence of wisdom degree, wisdom cost, cooperative risks and consumer preference on the agent interests is discussed. In the meanwhile, the evolutionary game is used to study the decision equilibrium between the supply chain agents.

2. Basic models and hypotheses 2.1. Model hypotheses

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The “Farmers + Cooperative + Smart supply chain platform + government financial platform” poverty alleviation ecosystem composed of cooperatives, smart supply chain platforms, government financial platforms is considered, as shown in Figure 1: Government Financial Platform

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(subsidy， non-subsidy）

Farmers

Cooperatives

(subsidy， non-subsidy）

Smart supply chain platforms

(subsidy, non-subsidy）

Consumers

Fig. 1. Smart supply chain structure under the government financial platform subsidy mechanism 4

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The cooperation game occurs between cooperatives and smart supply chain platforms, and the government financial platform implements cooperation games with cooperatives and smart supply chain platforms. Therefore, cooperatives and smart supply chain platforms are bounded and rational, and it is difficult to make optimal choices in a game. Therefore, each agent has a long-term game until the evolution is stable. Hypothesis 1: With the goal of smart poverty alleviation, the poverty alleviation policy of the government financial platform subsidizes cooperatives and smart supply chain platforms. The game strategy is “subsidy” and “non-subsidy”. At the same time, there are two strategies of “cooperation” and “non-cooperation” between cooperatives and smart supply chain platforms. Refer to the references of Zhu & Dou (2007) as well as Wu & Xiong (2012), assumed that the probability of subsidy by the government financial platform is z , and the probability of “non-subsidy” is (1- z ) . The probability that cooperatives cooperative with smart supply chain platforms is x , and the probability that smart supply chain platforms cooperate with cooperatives is y. Hypothesis 2: Under the supply chain cooperation poverty alleviation model of “Plants + Cooperatives + Smart Supply Chain Platform”, products are sold through the “Poverty Alleviation Center (Smart Supply Chain Platform)”. Consumers have preferences for poverty alleviation products. Consumers’ preference for poverty alleviation is assumed to be  （ 0    1 ), and consumers’ poverty alleviation preferences will affect market demands. At the same time, this paper believes that smart degree will influence the poor sales risk of products ( L p ), and the smart degree

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of the smart supply chain is  （ 0    1). Therefore, the smart degree  is inversely proportional to the poor sales risks of cooperative products L p . Hypothesis 3: When cooperatives cooperate with smart supply chain platforms, the government financial platform will differentiates the subsidy mechanisms for them (The State Council Bulletin of China, 2011). The subsidy a for cooperatives is calculated according to the proportion of volume. The subsidy of the government financial platform for the smart supply chain platform is directly used as the platform construction cost cz .

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2.2. Market demand function

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Based on the above hypotheses, when consumers do not cooperate with smart supply chain platforms, consumers will regard poverty alleviation products as common products.  is assumed to be consumers’ willingness to pay, which obeys the uniform distribution on [0, Q ] . When cooperatives do not cooperate with smart supply chain platforms, the utility of purchasing unit products is U t    pt , where pt is the unit sales price. On the contrary, if cooperatives operate with smart supply chain platforms, consumers will purchase poverty alleviation products on smart supply chain cooperation platforms, and the utility of purchasing unit products is U f    p f , where p f is unit sales price ( pt  p f ) for cooperation between cooperatives and smart supply chain platforms. Moreover, when U t  U f  0 , consumers will not buy products in the case of non-cooperation; when U f  U t  0 , consumers will purchase products in the case of cooperation. If U f  U t , there is no difference between the two situations. Obviously, 5

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consumers’ choices face three critical conditions: (1)Let U t  0 , and 1  pt can be obtained (subscript I represents the value of  when U t  0 ); (2) let U f  0 , and

 II  pt (subscript II represents the value of  when U f  0 ); (3) let U f  U t , and p f  pt

(subscript III represents the value  of when U f  U t ).  Therefore, two situations can be obtained: (1) When  I   II ,  III   I   II . consumers in [0, II ] do not buy the products, consumers in [ I ,  II ] will purchase the products for cooperation, consumers in [ II , Q] buy products in the case of non-cooperation; (2) When  II   I , consumers will not consider the products at the time of cooperation. Obviously, consumers may choose either ordinary products or poverty alleviation products. Therefore, this paper only considers Situation (1). In summary, the market demand functions in different situations where cooperatives do not cooperate or cooperate with smart supply chain platforms can be obtained, and Conclusion 1 can be drawn: Conclusion 1: When cooperatives do not cooperate with smart supply chain p f   pt platforms, the market demand function is qt  . In the case of cooperation,  1 p f  pt the market demand function is q f  Q  .  1

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 III 

3. Solution of the evolution model of without government financial platform subsidy 3.1. Income function without government financial platform subsidy

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There are two strategies of cooperation (C) and non-cooperation (N) for both cooperatives s and smart supply chain platforms e .When government financial platforms do not provide subsidy, the game strategies of both parties are as follows: (1) Both cooperatives and smart supply chain platforms choose the cooperation strategy. In this case, the benefits of both parties can be expressed as  s and  e . Since the smart degree of the platform can reduce the risk for cooperatives, the income function is:  s  p f q f  cs q f  cg  (1   ) Lp   p f q f , where cs is the unit cost of cooperative products, cg is the commission paid by cooperatives to smart supply chain platforms, which can be regarded as a fixed cost, and  p f q f is the dynamic

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cost paid by cooperatives to smart supply chain platforms.  is the probability of a product being unsalable, 0    1 . The benefit of smart supply chain platforms is 1 expressed as  e   0  Te  cg   p f q f  (c0   2 ) , where Te is additional 2 benefits for smart supply chain platforms in the poverty alleviation cooperation model, ce is the total cost of establishing a poverty alleviation center for smart supply chain platforms. It is assumed that there is a quadratic function relationship between the smart degree of supply chain platforms and the smart degree cost, which can be 1 2 expressed as ce  c0   , where c0 is the common cost,  is the smart cost 2 6

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coefficient, cg   p f q f  ce . (2) If the cooperative chooses to cooperate with the smart supply chain platform, but the smart supply chain platform chooses the non-cooperative strategy, the former will faces uncertainty of demand, leading to slow sales risks. Therefore, the cooperative's income function can be expressed as:  s  p f q f  cs q f  cg   Lp   p f q f . However, although the smart supply chain platform does not participate in cooperation, its benefits will change under the free rider effect. The benefit function of the smart supply chain platform can be expressed as:  e   0  e , where  0 is the benefit when there is no poverty alleviation center in

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the smart supply chain platform, and  e is the increased profits for the smart supply chain platform under the free rider effect. In general, the commission of the smart supply chain platform to the cooperative is definitely greater than the benefit earned through the free rider. cg   p f q f   e And Te   e . (3) When the cooperative does not cooperate with the smart supply chain platform, the cooperative’s income function is:  s  pt qt  cs qt   Lp . The benefit

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function of the smart supply chain platform is:  e   0 。 (4) If the cooperative chooses the non-cooperation strategy, and the smart supply chain platform chooses the cooperation strategy, the former still have a free rider effect on the cooperation strategy of the smart supply chain platform. Therefore, the cooperative’s income function is:  s  pt qt  cs qt   L p   s , where  s is the increased profits for the cooperative's free rider effect. The benefit function of the smart supply chain platform is expressed as:  e   0  Te  ce 。 According to the above analysis, the payment matrix of the cooperative and the smart supply chain platform when the government financial platform does not provide subsidy can be obtained, as shown in Table 1:

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Table 1 Payment matrix of cooperatives and smart supply chain platforms when government financial platform does not provide subsidy. Smart supply chain platform

Cooper ation （C） Non-co operati on （N）

Non-cooperation（N）

 s  p f q f  cs q f  cg   p f q f  (1   ) Lp     T  c   p q  ( c  e

0

e

g

f

f

0

1

 )

2

 s  pt qt  cs qt   Lp   s 1

 e   0  Te  (c0   ) 2 2

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Cooperatives

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Cooperation（C） 2

 s  p f q f  cs q f  cg   Lp   p f q f

 e   0  e  s  pt qt  cs qt   Lp

e  0

3.2. Model stability analysis In the evolutionary game, Replicator Dynamic and Evolutionary Stable Strategy (ESS) represent the convergence process and steady state of the evolutionary game, respectively. According to the hypotheses the proportion of cooperatives adopting the cooperation strategy is x(0  x  1) , the proportion of adopting non-cooperation 7

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strategy is 1  x . The proportion of the smart supply chain platform adopting the cooperation strategy is y (0  y  1) , and the proportion of adopting the non-cooperation strategy is 1  y . The expected benefits of cooperatives when they choose cooperation and non-cooperation are: U sc  y[ p f q f  cs q f  cg   p f q f  (1   ) L p ]  (1  y )[ p f q f  cs q f  c g   L p   p f q f ]

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U sn  y[ pt qt  cs qt   Lp   s ]  (1  y )[ pt qt  cs qt   L p ] The average expected return of the cooperatives is: 

U s  xU sc  (1  x)U sn

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The expected benefits of platforms choosing cooperation and non-cooperation are:

1

U ec  x[ 0  Te  cg   p f q f  (c0   2 )]  (1  x)[ 0  Te  (c0   2 )]

2 U en  x[ 0  e ]  (1  x) 0 The average expected return of the platforms is: 

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U e  yU ec  (1  y )U en

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The core idea of replication dynamics is that if fitness or payoff of a strategy is higher than the population’s payment, the strategy will be adopted by more participants in the population. Therefore, according to the replication dynamic formula of the evolutionary game, the replication dynamic equations of cooperatives and smart supply chain platforms can be obtained as follows:  dx F ( x)   x(U sc  U s )  x(1  x)[( p f  cs   p f )q f  cg  ( pt  cs )qt  y ( L p   s )] dt  dy 1 F ( y)   y (U ec  U e )  y (1  y )[ x(cg   p f q f   e )  (c0   2 )  Te ] dt 2 The core idea of the evolutionary stability strategy (ESS) is that if the payment of adopting the strategy is higher than the payment of the variant using the strategy, the variant will gradually disappear in the group over time. A two-dimensional dynamic system is established from the above-mentioned replication dynamic equation ( I ) ：

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 dx  dt  x(1  x)[( p f  cs   p f )q f  cg  ( pt  cs )qt  y ( LP   S )]  dy 1   y (1  y )[ x(cg   p f q f   e )  (c0   2 )  Te ] 2  dt The solution of the available dynamical system is： （0，0） ，（0，1） ，（1，0），

（ 1 ， 0 ） and ( xu , yu ) ,

where yu 

p f q f  cs q f  cg   p f q f  ( pt  cs )qt

 s   Lp

and

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1 (c0   2 )  Te 2 xu  . Therefore, it can be known that points（0，0）,（0，1）,（1， cg   p f q f   e

0） and（1，0）are local equilibrium points of the system. However, ( xu , yu ) is the local equilibrium point of the system under certain conditions. Proposition 1 can be obtained. Proposition 3.1. If ( xu , yu ) is the local equilibrium points of the system, 8

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 s  p f q f  cs q f  cg   p f q f  ( pt  cs )qt   Lp   Lp  0

 Lp   s 

p f q f  cs q f  c g   p f q f

or

 ( pt  cs )qt   Lp

,

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cg   p f q f   e  (c0   2 )  Te   e .

2 Proof If ( xu , yu ) is the local equilibrium points of the system, 0  xu  1 and

,

and

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cg   p f q f   e  0

1

cg   p f q f   e  (c0   2 )   e 2

1

cg   p f q f  (c0   2 )   e . 2

Similarly, yu 

p f q f  cs q f  cg   p f q f  ( pt  cs )qt

 s   Lp p f q f  cs q f  cg   p f q f  ( pt  cs )qt

,

 ap f q f  ( pt  cs )qt  cz   s   Lp

 s  p f q f  cs q f  cg   p f q f  ( pt  cs )qt   Lp   Lp  0

.

.

If

That

， is

 s   Lp

，

p f q f  cs q f  cg   p f q f  ( pt  cs )qt p f q f  cs q f  c g   p f q f

 Lp   s 

 ap f q f  ( pt  cs )qt  cz   s   Lp

p f q f  cs q f  c g   p f q f

namely,

, 0  yu  1 . If  s   Lp ，

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p f q f  cs q f  c g   p f q f

If 0  xu  1 ，

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0  yu  1 ,

1 (c0   2 )  Te 2 where xu  ， cg   p f q f  ce . cg   p f q f   e

， .

That

is

 ( pt  cs )qt   Lp 。

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Partial equilibrium points exist only if the above conditions are met. ( xu , yu ) The proposition is proved. In summary, the local equilibrium points of the system are (0,0), (0,1), (1,0), (1,0) and ( xu , yu ) .

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3.3. Stability Analysis of Evolutionary equilibrium Point of Jacobi Matrix According to the computational differential equations proposed by Friedman, the group dynamics of the dynamic system is formed. By analyzing the local stability of the Jacobi matrix of the system, the Jacobi matrix can be obtained.  X X   x y   a a    11 12  J  ,where ：  Y Y   a21 a22   x y   

dF ( x)  (1  2 x)[( p f  cs   p f )q f  y L p  y s  cg  ( pt  cs )qt ] ， dx

a12 

dF ( x)  x(1  x)[ Lp   s ] ， dy

a21 

dF ( y )  y (1  y )[cg   p f q f   e ] ， dx

a22 

dF ( y ) 1  (1  2 y )[ xcg  x p f q f  (c0   2 )  Te  x e ] 。 dy 2

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a11 

9

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Its trace condition ( trJ ) and the determinant value ( det J ) are calculated: 1 2 trJ  (1  2 x )[( p f  cs   p f ) q f  y L p  y  s  c g  ( pt  cs )qt ]  (1  2 y )[ xc g  x  p f q f  (c0   )  Te  x e ] 2 1

det J  (1  2 x )[( p f  cs   p f ) q f  y L p  y  s  c g  ( pt  cs ) qt ](1  2 y )[ xc g  x  p f q f  (c0 

2

 )  Te  x e ] 2

 x (1  x )[ L p   s ] y (1  y )[c g   p f q f   e ]

of

Substitute（0，0）,（0，1）,（1，0）,（1，0）and ( xu , yu ) into the above formula, and Table 2 can be obtained:

trJ

det J

 ( pt  cs )qt

p f q f  cs q f  c g   p f q f

（0，0）

1

1

2

0

2

 ( pt  cs )qt

p f q f  cs q f  c g   p f q f 1

  L    (c   )  T p

（1，0）

s

0

2

2

[ c g   p f q f   e  ( c0 

[  c g   p f q f   e  ( c0 

f

1

2

 )  Te ]  2

1

 )  T ] 

p

s

1

 )  T ][ p q  c q  c  2

e

2

f

t

s

f

t

f

s

e

p

[ c g   p f q f   e  ( c0 

f

g

1 2

s

 )  Te ][ 2

p f q f  c s q f  c g   p f q f  ( pt  c s ) qt ]

2

2

[( p f  cs   p f ) q f  c g  ( pt  cs ) qt 

 L   ]

[  ( c0 

 p q  ( p  c ) q   L   ]

e

[ p f q f  c s q f  c g   p f q f  ( pt  c s ) qt ]

（1，1）

2

2

Pr e-

（0，1）

 ( pt  cs )qt ][

[ p f q f  cs q f  c g   p f q f (c   )  Te ]

(c   )  Te 0

p ro

Table 2 Balance point analysis of System ( I )

[ c g   p f q f   e  ( c0 

1 2

 )  Te ][( p f  2

cs   p f ) q f  cg  ( pt  cs ) qt   L p   s ] [( p f  c s   p f ) q f  c g  ( pt  c s ) qt ]{[  s 

al

( xu , yu )

p

the

sake

f

s

f

f

cs ) qt ]}[ c g   p f q f  ( c0 

0

urn

For

 L ]  [( p  c   p ) q  c  ( p 

T ][( c  e

0

1 2

g

1

t

 )    2

2

e

 )  T ] 2

e

(  s   L p )( c g   p f q f   e )

of

discussion,

b  s

，

c  p f q f  cs q f  cg   p f q f  ( pt  cs )qt   Lp ， d   L p ， e  cg   p f q f ，

1

f   e  (c0   2 )  Te ， g   e .Therefore, only when e  f  g , b  c  d 、 2

Jo

e  f  g , d  c  b , ( xu , yu ) is the effective equilibrium point. Proposition 3.2. When e  f  g ， b  d  c 、 f  e  g , b  d  c 、 f  e  g , d  b  c 、 e  f  g , d  b  c 、 f  e  g , d  c  b , the evolutionary stability strategy of the system is (N, N). Proposition 3.3. When e  g  f , b  c  d 、 e  g  f , b  d  c 、 e  g  f , d  b  c , the evolutionary stability strategy of the system is (N, C). 10

Journal Pre-proof

e  f  g, c  b  d 、 e  g  f , c  b  d 、 e  g  f , c  d  b 、 e  f  g , c  d  b 、 e  g  f , d  c  b , the evolutionary Proposition

3.4.

When

stability strategy of the system is (C, C). Proposition 3.5. When f  e  g , b  c  d

、

f  e  g, c  b  d 、

of

f  e  g , c  d  b , the evolutionary stability strategy of the system is (C, N). Proposition 3.6. When e  f  g , b  c  d , the system does not have stability. Proposition 3.7. When e  f  g , d  c  b , the evolutionary stability strategy

Table 3 Stable points in different situations

det J

Stability

(0, 0)

uncertainty

（-）

saddle point saddle point saddle point saddle point saddle point saddle point unstable point saddle point stable point stable point saddle point unstable point saddle point unstable point stable point saddle point

(0,1)

uncertainty

（-）

(1, 0)

uncertainty

（-）

(1,1)

uncertainty

（-）

( xu , yu )

0

（-）

(0, 0)

uncertainty

（-）

(0,1)

（+）

（+）

(1, 0)

uncertainty

（-）

(1,1) (0, 0)

（-） （-）

（+） （+）

(0,1)

uncertainty

（-）

(1, 0)

（+）

（+）

(1,1)

uncertainty

（-）

(0, 0)

（+）

（+）

(0,1)

（-）

（+）

(1, 0)

uncertainty

（-）

urn

e  f  g, c  b  d e  f  g, c  d  b

trJ

Pr e-

e  f  g, b  c  d

Stable points

al

Situations

Jo

e  f  g, b  d  c e  f  g, d  b  c

e  g  f ,b  c  d

p ro

of the system is (C, C), (N, N). Proof: According to Table 2, the symbols of trJ and detJ at each equilibrium point in the Jacobian matrix J can be obtained to judge the local stability. The stability analysis in the above propositions and situations is shown in Table 3.

11

Journal Pre-proof

f  e  g, b  d  c f  e  g, d  b  c

(0, 0)

（+）

（+）

(0,1)

uncertainty

（-）

(1, 0)

uncertainty

（-）

(1,1)

（-）

(0, 0)

uncertainty

(0,1)

（-）

（+）

(1, 0)

（+）

（+）

(1,1)

uncertainty

（-）

(0, 0)

（-）

（+）

unstable point saddle point saddle point stable point saddle point stable point unstable point saddle point stable point saddle point saddle point unstable point saddle point saddle point stable point unstable point saddle point unstable point stable point saddle point stable point unstable point saddle point saddle point saddle point

f  e  g, d  c  b

e  g  f ,d  c  b

（+） （-）

(0,1)

uncertainty

（-）

(1, 0)

uncertainty

（-）

(1,1)

（+）

（+）

(0, 0)

uncertainty

（-）

(0,1)

uncertainty

（-）

(1, 0) (1,1)

（-） （+）

（+） （+）

(0, 0)

uncertainty

（-）

(0,1)

（+）

（+）

(1, 0)

（-）

（+）

(1,1)

uncertainty

（-）

(0, 0)

（-）

（+）

(0,1)

（+）

（+）

(1, 0)

uncertainty

（-）

(1,1)

uncertainty

（-）

(0, 0)

uncertainty

（-）

urn

Jo

f  e  g, c  b  d f  e  g, c  d  b

of

saddle point

al

f  e  g, b  c  d

（-）

p ro

e  g  f ,b  d  c e  g  f ,d  b  c

uncertainty

Pr e-

e  g  f ,c  b  d e  g  f ,c  d  b

(1,1)

12

Journal Pre-proof

（-）

(1, 0)

（+）

（+）

(1,1) (0, 0)

（-）

（+）

（-）

（+）

(0,1)

（+）

（+）

(1, 0)

（+）

(1,1)

（-）

( xu , yu )

0

3.4 Analysis of evolution results

saddle point unstable point stable point stable point unstable point unstable point stable point saddle point

of

uncertainty

（+） （+）

p ro

e  f  g, d  c  b

(0,1)

（-）

al

Pr e-

From Proposition 3.2. to Proposition 3.6., the evolutionary game process of cooperatives and smart supply chain poverty alleviation platforms in various situations can be obtained. Based on the stability of the equilibrium points, the evolution path diagrams of the 11 cases (Fig. 2.(a)-(k)) and the corresponding results are analyzed.

（b）

Jo

urn

（a）

（c）

（d）

13

of

Journal Pre-proof

（f）

（h）

al

（g）

Pr e-

p ro

（e）

（j）

Jo

urn

（i）

（k） Fig. 2. Evolution path diagram of system 1 in 11 cases

According to the phase diagram of the system dynamic evolution in Figure 2, the following analysis results can be obtained: 14

Journal Pre-proof

(1) From Proposition 2, when f  e  g , b  d  c and f  e  g , or  s   Lp  p f q f  cs q f  cg   p f q f  ( pt  cs )qt   Lp  Lp   s  p f q f  cs q f  cg   p f q f  ( pt  cs )qt   Lp

,

1  e  (c0   2 )  Te  cg   p f q f   e .Therefore, whether the smart supply chain 2

p ro

of

platforms choose to cooperate or not, the benefits of cooperatives participating in cooperation are lower compared with that when they choose non-cooperation. Therefore, cooperatives prefer the non-cooperation strategy. Whether the cooperative chooses cooperation or non-cooperation, the benefits of the smart supply chain platforms choosing cooperation are lower than those choosing non-cooperation. The platforms prefer the non-cooperation strategy. As shown in Fig. 2(a), the stability point of the system evolution strategy is (0,0), the instability point is (1,1), and the saddle points are (0,1) and (1,0). In this case,  s and  L p do not influence the final game outcome. (2) From Proposition 3.2, when e  f  g , b  d  c , e  f  g , d  b  c , or  s   Lp  p f q f  cs q f  cg   p f q f  ( pt  cs )qt   Lp ,

Pr e-

 Lp   s  p f q f  cs q f  cg   p f q f  ( pt  cs )qt   Lp 1

cg   p f q f   e  (c0   2 )  Te   e .Therefore, whether the smart supply chain

urn

al

2 platforms choose to cooperate or not, the benefits of cooperatives participating in cooperation are lower compared with that when they choose non-cooperation. Cooperatives prefer the non-cooperation strategy. When cooperatives choose cooperation strategy, the benefits of the smart supply chain platform are greater than the benefits of the non-cooperation. When the cooperative chooses non-cooperation strategy, the benefit of the smart supply chain platform is lower. Since the cooperatives tend to non-cooperation, the smart supply chain platforms will also choose the non-cooperation strategy. As shown in Fig. 2(b), the stability point of the system evolution strategy is (0,0), the instability point is (1,0), and the saddle points are (0,1) and (1,1). f  e  g, d  c  b (3) From Proposition 3.2, when , ,  Lp  p f q f  cs q f  cg   p f q f  ( pt  cs )qt   Lp   s 1  e  (c0   2 )  Te  cg   p f q f   e . Therefore, when smart supply chain 2

Jo

platforms choose cooperation, cooperatives also prefer cooperation strategy. If smart supply chain platforms choose non-cooperation, cooperatives prefer non-cooperation strategies. Whether the cooperative chooses cooperation or non-cooperation, the benefits of the smart supply chain platform are lower in the case of cooperation. Therefore, both the smart supply chain platforms and the cooperatives are more inclined to non-cooperation. As shown in Fig. 2(c), the stability point of the system evolution strategy is (0,0), the instability point is (0,1), and the saddle points are (1,1) and (1,0). (4) From Proposition 3.3, it can be found when e  g  f , b  c  d , ,  s  p f q f  cs q f  cg   p f q f  ( pt  cs )qt   L p   L p 1

cg   p f q f   e   e  (c0   2 )  Te . When the smart supply chain platform 2

15

Journal Pre-proof

,

p ro

 Lp   s  p f q f  cs q f  cg   p f q f  ( pt  cs )qt   Lp

of

chooses cooperation, the benefit of cooperatives in cooperation is less than that of non-cooperation. When the smart supply chain platform chooses non-cooperation, the benefit of cooperatives in the case of cooperation is higher. No matter the smart supply chain platforms choose cooperation or non-cooperation, the benefit of cooperation is higher than that of non-cooperation. Since the platforms will choose to cooperate, they are more inclined to choose non-cooperation strategy. As shown in Fig. 2(d), the stability point of the system evolution strategy is (0, 1), and the unstable point is (0, 0), and the saddle points are (1, 0) and (1, 1). (5) From Proposition 3.3, when e  g  f , b  d  c , e  g  f , d  b  c , or  s   Lp  p f q f  cs q f  cg   p f q f  ( pt  cs )qt   Lp 1

cg   p f q f   e   e  (c0   2 )  Te . Therefore, whether the smart supply chain

Pr e-

2 platforms choose to cooperate or not, the benefits of cooperatives participating in cooperation are lower compared with that when they choose non-cooperation. Therefore, cooperatives prefer the non-cooperation strategy. Whether the cooperative chooses cooperation or non-cooperation, the benefits of the smart supply chain platforms choosing cooperation are higher than those choosing non-cooperation. As shown in Fig. 2(e), the stability point of the system evolution strategy is (0,1), the instability point is (1,0), and the saddle points are (0,0) and (1,1). (6) From Proposition 3.4, it can be found when e  f  g , c  b  d ,

e  f  g , c  d  b , p f q f  cs q f  cg   p f q f  ( pt  cs )qt   Lp   s   Lp or p f q f  cs q f  cg   p f q f  ( pt  cs )qt   L p   L p   s

1

,

cg   p f q f   e  (c0   2 )  Te   e . Therefore, whether the smart supply chain 2

urn

al

platforms choose to cooperate or not, the benefits of cooperatives in cooperation are higher are higher than that in non-cooperation. As shown in Fig. 2(f), the stability point of the system evolution strategy is (1,1), the instability point is (0,1), and the saddle points are (1,0) and (0,0). (7) From Proposition 3.4, when e  g  f , c  b  d , e  g  f , c  d  b , or p f q f  cs q f  cg   p f q f  ( pt  cs )qt   L p   s   Lp , p f q f  cs q f  cg   p f q f  ( pt  cs )qt   L p   L p   s 1

cg   p f q f   e   e  (c0   2 )  Te . No matter which strategy is chosen by the

Jo

2 smart supply chain platform, the benefits of cooperatives in cooperation are greater than those in non-cooperation. No matter which strategy the cooperatives choose, the smart supply chain platform is more profitable when the cooperation strategy is chosen. As shown in Fig. 2(g), the stability point of the system evolution strategy is (1,1), the instability point is (0,0), and the saddle points are (0,1) and (1,0). (8) From Proposition 3.4, it can be found when e  g  f , d  c  b , ,  Lp  p f q f  cs q f  cg   p f q f  ( pt  cs )qt   Lp   s 1

cg   p f q f   e   e  (c0   2 )  Te . When smart supply chain platforms choose

2 cooperation, cooperatives also prefer cooperation strategy. If smart supply chain platforms choose non-cooperation, cooperatives prefer non-cooperation strategies. 16

Journal Pre-proof

p f q f  cs q f  cg   p f q f  ( pt  cs )qt   L p   L p   s

of

Whether the cooperative chooses cooperation or non-cooperation, the benefits of the smart supply chain platform are higher in the case of cooperation. Therefore, both the smart supply chain platforms and the cooperatives are more inclined to the cooperation strategy. As shown in Fig. 2(h), the stability point of the system evolution strategy is (1,1), the instability point is (1,0), and the saddle points are (0,1) and (0,0). (9) From Proposition 3.4, when f  e  g , c  b  d 、 f  e  g , c  d  b , or p f q f  cs q f  cg   p f q f  ( pt  cs )qt   L p   s   Lp ,

1  e  (c0   2 )  Te  cg   p f q f   e .For cooperatives, no matter which strategy 2

Pr e-

p ro

is chosen by the smart supply chain platform, the benefits of cooperatives in cooperation are greater than those of non-cooperation. Whether the cooperative chooses cooperation or non-cooperation, the benefits of the smart supply chain platforms in cooperation are lower than that in non-cooperation. Therefore, the smart supply chain platform prefers the non-cooperation strategy. As shown in Fig. 2(i), the stability point of the system evolution strategy is (1,0), the instability point is (0,1), and the saddle points are (0,0) and (1,1). (10) From Proposition 3.5, it can be found when f  e  g , b  c  d , ,  s  p f q f  cs q f  cg   p f q f  ( pt  cs )qt   L p   L p 1  e  (c0   2 )  Te  cg   p f q f   e . When the smart supply chain platform 2

f

s

f

g

f

f

urn

f

al

chooses cooperation, the benefit of cooperatives in cooperation is less than that in non-cooperation. When the smart supply chain platforms choose non-cooperation, the benefit of the cooperatives in cooperation is greater than that in non-cooperative. Whether the cooperative chooses cooperation or non-cooperation, the benefits of the smart supply chain platform and the cooperative in cooperation are less than those in non-cooperation. Therefore, the smart supply chain platform is more inclined to the non-cooperation strategy. As shown in Fig. 2(j), the stability point of the system evolution strategy is (1,0), the instability point is (1,1), and the saddle points are (0,1) and (0,0). e  f  g, b  c  d (11) From Proposition 3.6, when , ,  s  p q  c q  c   p q  ( pt  cs )qt   Lp   Lp  0 1

cg   p f q f   e  (c0   2 )  Te   e . Based on the local stability analysis

Jo

2 method of the Jacobian matrix, according to the sign of the trace and determinant of the Jacobian matrix at the equilibrium point, Table 3 shows that the above five equilibrium points are saddle points. Therefore, there is no evolutionary stability strategy in the game model. In other words, there is no spontaneous evolutionary trend, which makes both cooperatives and smart supply chain platforms adopt a certain strategy without being invaded by the mutation strategy. This is also common in real-world situations. Incentives or reasonable arrangements are used to appropriately change the parameters in the payment matrix to obtain a stable strategy for the game. (12) From Proposition 3.7, it can be found when e  f  g , d  c  b , ,  Lp  p q  c q  c   p q  ( pt  cs )qt   Lp   s f

f

s

f

g

f

f

17

Journal Pre-proof

1

cg   p f q f   e  (c0   2 )  Te   e . For cooperatives, when smart supply chain

of

2 platforms choose cooperation, cooperatives also prefer cooperation strategies. If smart supply chain platforms choose non-cooperation, cooperatives prefer the non-cooperation strategies. When the cooperative chooses the cooperation strategy, the benefits of the smart supply chain platform in cooperation are greater than those in non-cooperation. When the cooperative chooses non-cooperation, the benefit of the smart supply chain platform in cooperation is smaller than those in non-cooperation. As shown in Fig. 2(k), the stability points of the system evolution strategy are (0,0) and (1,1), the unstable points are (1,0) and (0,1), and the saddle point is ( xu , yu ) .

f

f

s

f

g

f

p ro

3.5. Diversity Analysis of system evolution and equilibrium As stated in Proposition 3.7, when the parameters of the cooperative and the smart supply chain platforms meet the conditions of and  Lp  p q  c q  c   p q  ( pt  cs )qt   Lp   s f

1

cg   p f q f   e  (c0   2 )  Te   e , the stable points of the system evolution

Pr e-

2 strategy are (0,0) and (1,1), the unstable points are (1,0) and (0,1), and the saddle point is ( xu , yu ) . The evolutionary stability strategies of both parties are (c, c) (cooperatives participate in cooperation, platforms participate in cooperation) or (n, n) (cooperatives do not participate in cooperation, platforms do not participate in cooperation). Which state the system finally converges is determined by the area of I and II (as shown in Figure 2 (k)), which are expressed as s1 and s0 Said. When s1  s0 , the probability that the system converges to equilibrium point (1,1) is greater

urn

al

than that converging to equilibrium point (0, 0) . When s1  s0 , the probability that the system converges to equilibrium point (0, 0) is greater than that converges to equilibrium point (1,1) . When s1  s0 , the system has the same probability of converging to equilibrium points (1,1) and (0, 0) . By analyzing the areas of I and II , the factors that influence the evolutionary stability strategy of the system s0 in the cases of e  f  g and d  c  b can be obtained: 1   (c   2 )  Te p q  c q  c   p q  ( p  c )q  1 0 2 f f t s t s0    f f s f g  2  cg   p f q f   e  s   Lp    According to the above formula, the parameters influencing s0 include c0 , cg ,  ,

 , Te , L p , p f , pt and  . With the influence of the changes in these parameters on

Jo

s0 as an example, the probability that the system converges to the equilibrium point is calculated. Proposition 3.8. When the fixed costs c0 and cg increase, the costs of both the smart supply chain platforms and the cooperatives will increase. If the cooperative chooses non-cooperation, the probability that the smart supply chain platforms choose non-cooperation will increase. On the contrary, the probability that the cooperatives and the smart supply chain platforms choose to cooperate will increase. Proof: when other conditions are fixed, s0 is derived to c0 and cg , 18

Journal Pre-proof

respectively: s0 1  0 c0 2(cg   p f q f  e ) 1

1

Pr e-

p ro

of

(c0   2 )  Te  (cg   p f q f   e ) 2 s0 2  0 cg 2(cg   p f q f   e ) 2 According to the analysis results, when other factors are fixed, the higher the fixed costs c0 and cg , the larger the area s0 , and the greater the probability that the system converges to the equilibrium point (0,0), that is, the probability that the cooperative and the smart supply chain platform choose non-cooperation is greater. Otherwise, the probability that the system converges to the equilibrium point (1,1) is greater, and the probability of cooperation between cooperatives and smart supply chain platforms increases. The proposition is proved. Proposition 3.9.  When  which can influence the variable cost of cooperatives increases, although the cost of cooperation between cooperatives and smart supply chain platforms will increase, the benefits of smart supply chain platforms will increase, the smart supply chain platforms and cooperatives are more likely to choose cooperation. Proof: when other conditions are fixed, s0 is derived to  :

urn

al

p f q f (c0   2 )  Te s0 2  0  2(cg   p f q f   e ) 2 When other factors are fixed, the higher the variable costs  , the larger the area s0 , and the greater the probability that the system converges to the equilibrium point (1,1), that is, the probability that the cooperative and the smart supply chain platform choose cooperation is greater. Otherwise, the probability that the system converges to the equilibrium point (0,0) is greater, and the probability of non-cooperation between cooperatives and smart supply chain platforms increases. The proposition is proved. Proposition 3.10.  When the smart degree changes, if  changes to a certain point, the cooperation probability between the cooperatives and the smart supply chain platforms is the highest. Proof: When other conditions are fixed, s0 is derived to   Lp [ p f q f  cs q f  cg   p f q f  ( pt  cs )qt ] s0   Te    2(cg   p f q f   e ) 2( s   Lp ) 2

Jo

The influence of  on the stability of the evolution strategy of the system is  2 s0 non-monotonous. The second-order partial derivative  0 of  from s0 is  2 obtained. When  is a specific value, the minimum value of s0 can be taken.  s0 0 ： Let , since the solution is: 0   1 , 

19

Journal Pre-proof



f

q f  cs q f  c g   p f q f

 ( pt  cs ) qt ](cg   p f q f   e ) 

 2 L2p 

 2s  2 s Lp  2 s Lp 2( L  2

2 p

Te



Te



Te



 2s

 2 L2p



(  2s  2 s L p  2 s L p 4( 2 L2p 

Te



Te



 2 L2p ) 2

Te



 L ) 2

2 p

of

0 

 Lp [ p

Because s0 only has one extreme point in 0    1, 0 is also the minimum point.

Pr e-

p ro

. In summary, when other parameter values are determined, there is the optimal smart degree  which makes the cooperation probability between the cooperatives and the smart supply chain platforms highest. The proposition is proved. Proposition 3.11. When the additional benefits Te brought by the poverty alleviation cooperation to the platforms increases, the probability of cooperation between cooperatives and smart supply chain platforms is higher. On the contrary, the cooperatives and smart supply chain platforms are more likely to choose non-cooperation. Proof: when other conditions are fixed, s0 is derived to Te s0   0 Te 2(cg   p f q f  e )

urn

al

Analysis results show that additional benefit Te will increase when other factors are fixed, and the area of s0 is smaller. Moreover, the probability that the system converges to the equilibrium point (1, 1) is greater. In other words, the probability that the cooperatives and the smart supply chain platforms choose cooperation is larger. Otherwise, the larger the probability that the system converges to the equilibrium point (0,0), cooperatives and smart supply chain platform are more likely to choose non-cooperation. The proposition is proved. Proposition 3.12. When the slow sales risk L p of cooperative products increases, the probability of cooperation between cooperatives and smart supply chain platforms will be higher. On the contrary, the probability that the cooperatives and the smart supply chain platforms choose non-cooperation will increase. Proof: when other factors are fixed, s0 is derived to L p .

Jo

s0  [ p f q f  cs q f  cg   p f q f  ( pt  cs )qt ]  0 Lp 2( s   Lp )2 According to the analysis results, when the other conditions are fixed, the slow sales risk L p of cooperative products increases, the area of s0 is smaller, and the probability that the system converges to the equilibrium point (1, 1) increases. In this case, the cooperatives and the smart supply chain platforms will more likely to choose cooperation. Otherwise, the probability that the system converges to the equilibrium point (0, 0) is greater, and the probability that the cooperatives and the smart supply chain platforms choose non-cooperation will increase. Proposition 3.13. When the product price p f increases, the probability of 20

)2

Journal Pre-proof

p f

2 p f  2cs  2  p f   pt 1 (c0   2  Te ) Q   Q   1 2  1  0 p f  pt  s   Lp 2 2(cg   p f (Q  )  e )  1

Q  

2  p f   pt

p ro

s0

of

cooperation between cooperatives and smart supply chain platforms will be higher. On the contrary, the probability that cooperatives and smart supply chain platforms choose non-cooperation will increases. p f   pt p f  pt Substitute qt  and q f  Q  to s0 , respectively.  1  1 p f  pt p f   pt 1 ( p f  cs   p f )(Q  )  cg  ( pt  cs ) (c0   2 )  Te 1  1  1 2 s0  [  ] p f  pt 2  s   Lp cg   p f (Q  )  e  1 Proof: when other conditions are fixed, s0 is derived to p f .

s0  pt

al

Pr e-

Analysis results show that when other conditions are fixed, with the increase of the product price p f in cooperation p f , the area of s0 will decrease, and the probability that the system converges to the equilibrium point (1, 1) will be greater, that is, the probability that the cooperatives and the smart supply chain platforms choose cooperation is larger. Otherwise, the probability that the system converges to the equilibrium point (0,0) will be greater, and probability of non-cooperation between the cooperatives and the smart supply chain platforms is greater. The proposition is proved. Proposition 3.14. If the product price pt changes in non-cooperation, when pt changes to a certain point, the cooperatives and the smart supply chain platforms have the greatest probability of non-cooperation. Proof: when other conditions are fixed, s0 is derived to pt .

 pf 1 (c0   2  Te )  1 2 2(cg   p f (Q 

p f  pt

cs   p f  2 pt   cs 

)  e )2

 1 2( s   Lp )

0

urn

 1 The influence of pt on the evolution strategy of the system is not monotonous. The second-order partial derivative

 2 s0  0 of s0 on pt is obtained. When pt is a pt2

Jo

specific value, the maximum value of s0 is available. Let

s0 *  0 , and pt  pt . When pt

pt  pt* , s0 takes the maximum value, and s0 only has one extreme point. Therefore, pt* is also the maximum point. In summary, when other parameter values are

determined, there is the optimal pt which makes the probability of non-cooperation between cooperatives and smart supply chain platforms greatest. The proposition is proved. Proposition 3.15. If consumers’ poverty alleviation preference  changes, when 21

Journal Pre-proof

 changes to a certain point, the cooperatives and the smart supply chain platforms have the greatest probability of cooperation. Proof: when other conditions are fixed, s0 is derived to  . 1 (  1)(c0   2  Te )  [(  1)(cg   p f   e )   p 2f   p f pt ] s0 2    2[(  1)(cg   p f   e )   p 2f   p f pt ]2 2( s   Lp )(  1) 2

of

p 2f  2 p f cs   p 2f  pt cs   p f pt   pt2   pt cs  ( pt cs  pt2 )(  1)

p ro

4. Evolutionary Game Analysis of Government Financial Platform Subsidy 4.1. Income function of government financial platform subsidy

urn

al

Pr e-

When the government financial platform provides subsidy, it is assumed that the product price of the cooperatives is unchanged, that is, p f  pt and q f  qt . (1) If both the cooperatives and the smart supply chain platforms choose the cooperation strategy, the benefit function of the cooperatives is:  s  p f q f  cs q f  cg   p f q f  (1   ) Lp  ap f q f , where a is the proportion of government financial platforms that subsidize cooperatives. The benefit of the smart 1 2 supply chain platform is:  e   0  Te  cg   p f q f  (c0   )  cz , where cz is 2 the subsidy directly paid by the government financial platform. (2) If the cooperatives choose to cooperate with the smart supply chain platforms, but the smart supply chain platforms choose a non-cooperation strategy, the income function of the cooperatives is:  s  p f q f  cs q f  cg   p f q f   Lp  ap f q f . Although the smart supply chain platforms do not participate in cooperation, their benefits will change under the free rider effect. Because the smart supply chain platform chooses non-cooperation and does not participate in poverty alleviation activities, there is no subsidy from the government financial platform. The benefit function of the smart supply chain platforms is:  e   0  e . (3) If both the cooperatives and the smart supply chain platforms choose non-cooperation, the government financial platform will provide direct subsidies to cooperatives. The income function of the cooperatives is:  s  pt qt  cs qt   Lp  cz .

Jo

The benefit function of the smart supply chain platforms is:  e   0 。 (4) If the cooperatives choose the non-cooperative strategy, while the smart supply chain platforms choose the cooperation strategy, the cooperatives also have a free ride-in effect on the cooperation strategy of the smart supply chain platforms. Therefore, the benefit function of the cooperatives is:  s  pt qt  cs qt   Lp   s  cz . When the smart supply chain platforms choose cooperation, the government financial platform will provide subsidy. The benefit function of the smart supply chain 1 2 platforms is:  e   0  Te  (c0   )  cz 2 According to the above hypotheses, the payment matrix of cooperatives and smart supply chain platforms when the government financial platform provides subsidy is shown in Table 4: 22

Journal Pre-proof

Table 4 Payment matrix of cooperatives and smart supply chain platforms when the government financial platform provides subsidy Smart supply chain platform Cooperation（C） f

f

s

f

g

p q f

f

 (1   ) Lp  ap f q f

1

 s  p f q f  cs q f  cg   p f q f   Lp  ap f q f

 e   0  e

of

s

 e   0  Te  cg   p f q f  (c0   )  cz 2 2

 s  pt qt  cs qt   Lp   s  cz  e   0  Te  (c0   )  cz

 s  pt qt  cs qt   Lp  cz

e  0

2

2

p ro

1

Pr e-

According to the replication dynamic formula of the evolutionary game, the evolutionary game replication equation of the government financial platform subsidy can be obtained. The cooperative dynamic equation of the cooperatives is:  dx F ' ( x)   x(U sc  U s )  x(1  x)[( p f  cs   p f  ap f )q f  cg  ( pt  cs )qt  cz  y ( L p   s )] dt The replication dynamic equation of the smart supply chain platforms is:  dy 1 F ' ( y)   y (U ec  U e )  y (1  y )[Te  (c0   2 )  cz  x(cg   p f q f   e )] dt 2 A two-dimensional power system ( I1 ) can be obtained:

al

 dx  dt  x(1  x)[( p f  cs   p f  ap f )q f  cg  ( pt  cs )qt  cz  y ( L p   s )]  dy 1   y (1  y )[Te  (c0   2 )  cz  x(cg   p f q f   e )]  dt 2 The solution of the dynamical system is： （0，0） 、 （0，1） 、（1，0） 、（1，0）、 p q  c q  c   p f q f  ap f q f  ( pt  cs )qt  cz y 'u  f f s f g , where ， ( x 'u , y 'u )  s   Lp 1

urn

x 'u 

Te  (c0   2 )  cz 2  e  (cg   p f q f )

According

to

.

Proposition

3.1,

under

the

conditions

1

cg   p f q f  (c0   2 )  cz  Te   e   e

of and

2  s  ( p f  cs   p f  ap f )q f  cg  ( pt  cs )qt  cz   L p   L p ,（0，0）,（0，1）,

（1，0）,（1，0） and ( x 'u , y 'u ) are the equilibrium point of the system.

Jo

Cooperatives

  p q cq c

Coope ration （C） Non-c ooper ation （N）

Non-cooperation（N）

4.2. Model stability analysis According to the computational differential equations proposed by Friedman, the group dynamics of the dynamic system can be obtained. Moreover, the Jacobi matrix can be acquired by analyzing the local stability of the Jacobi matrix of the system: The trace trH and the determinant det H are expressed as: 23

Journal Pre-proof

 X  x H   Y  x 

X y Y y

  b b     11 12  ， Where   b21 b22    b11  (1  2 x)[( p f  cs   p f  ap f )q f  y L p  y s  cg  ( pt  cs )qt  cz ] ，

of

b12  x(1  x)[ L p   s ] ， b21  y (1  y )[cg   p f q f   e ] ，

1 b22  (1  2 y )[ x(cg   p f q f   e )  (c0   2 )  cz  Te ] 。 2 The trace trH and the determinant det H are expressed as: ( c0 

1 2

p ro

trH  (1  2 x )[( p f  cs   p f  ap f ) q f  y L p  y  s  c g  ( pt  cs ) qt  c z ]  (1  2 y )[ x (c g   p f q f   e ) 

 )  cz  Te ] 2

det H  (1  2 x )[( p f  cs   p f  ap f ) q f  y L p  y  s  c g  ( pt  cs ) qt  c z ](1  2 y )[ x (c g   p f q f   e )  ( c0 

1 2

 )  cz  Te ]  x (1  x )[ L p   s ] y (1  y )[cg   p f q f   e ] 2

（0，0）

Pr e-

Substitute（0，0）,（0，1）,（1，0）,（1，0）and ( x 'u , y 'u ) into the above formula, and Table 5 can be obtained. Table 5 Balance point analysis of System I1 trH

det H

[( p f  cs   p f  ap f ) q f  c g  ( pt  c s ) qt 

[( p f  cs   p f  ap f ) q f  c g  ( pt  cs ) qt

c z ]  [  ( c0 

1

 )  c  T ] 2

z

2

 c z ][  ( c0 

e

( p f  cs   p f  ap f ) q f   L p   s  c g  1

al

（0，1）

( pt  c s ) qt  c z  ( c0 

e

urn

c z ]  c g   p f q f   e  ( c0 

（1，1）

1

2

 )  c  T 2

z

z

e

1

 )  c  T ] 2

z

2

e

[( p f  cs   p f  ap f ) q f  c g  ( pt  cs ) qt 

[( p f  cs   p f  ap f ) q f  c g  ( pt  c s ) qt 

（1，0）

2

( pt  cs ) qt  c z ][ ( c0 

2

z

 )  c  T ]

2

[( p f  cs   p f  ap f ) q f   L p   s  c g 

 )  c  T

2

1

e

c z ][ c g   p f q f   e  ( c0 

1 2

 )  c  T ] 2

z

[( p f  c s   p f  ap f ) q f   L p   s 

[( p f  cs   p f  ap f ) q f   L p   s  c g

c g  ( pt  c s ) qt  c z ]  [ c g   p f q f   e

 ( pt  c s ) qt  c z ][ c g   p f q f   e 

2

 )  c  T ]

( c0 

2

z

e

Jo

 ( c0 

1

24

1 2

 )  c  T ] 2

z

e

e

Journal Pre-proof

[( p  c   p f

[ s

s

f

)q

c

f

  L p  ( p

 ap

g

f

c  p

f

s

q

f

f

 ( pt  c s ) q t  c z ]

) q  c  ap f

g

f

q

f

 ( pt  c s ) q t  c z ]

( x 'u , y 'u )

 s   L p

0

2

 )  c z ][( c  2

0

1

 ) 2

2

cz  cg   p f q f ]

(1   ) Te  ( c g   p f q f )

p ro



1

of

[(1   ) Te  ( c0 

According to Table 3， the necessary and sufficient condition that equilibrium point （ 1 ， 1 ） is the only ESS of System I1 is det H  0 , trH  0 ， [( p f  cs  ap f ) q f   L p   s  ( pt  cs ) qt   e  (c0 

1 2

 )  Te ]  0 2

namely, ap

f

Pr e-

[( p f  cs   p f  ap f ) q f   L p   s  c g  ( pt  cs ) qt  c z ][c g   p f q f   e  (c 0  q f   L p   s   e  ( c0 

c g   p f q f   e  ( c0 

1 2

1

2

2

 )  c z  Te ]  0 2

 )  Te  0 ， (   p f  ap f ) q f   Lp   s  cg  cz  0 ， 2

 )  c z  Te  0 . 2

1

and

Similarly, ap

f

q f   L p  Te  max(  s + e +c0 

ap f q f   Lp  max(  p f q f + s +cg +cz ) ， c g   p f q f  c z  Te  max(  e +c0 

1

1

 ) ， 2

2

 ) 。 2

2

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According to the above conditions, when other conditions are fixed, the risk that the government financial platform provides proportional subsidies and wisdom can be recovered is greater than the sum of the fixed costs of the cooperatives to the smart supply chain platform and the supply chain free-riding and fixed subsidies. As a result, the “free-riding” effect and the cost charged by the smart supply chain are no longer the factors that hinder the cooperative's choice of strategy. In addition, according to the relevant data, when the smart degree reaches a certain level, the risk cost of cooperatives can be decreased effectively, which helps to reduce the pressure on government financial platform subsidy. 5. Case analysis

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In order to verify the impact of the above-mentioned government financial platform subsidies and smart degree on cooperatives and smart supply chain platforms, the standardized data are used for case analysis under different game subsidies and different smart degrees in the government financial platform. The Cooperative in Sichuan province of China sells Mangoes on the poverty alleviation platform established by the Pinduoduo Smart Supply Chain Platform (The Chinanews online service, 2018). Pinduoduo smart supply chain platform applies machine learning and artificial intelligence techniques, therefore it has powerful information processing ability. The daily demand for mango in orchards is 600,000 kilograms, while the annual output of orchards is 2.2 billion kilograms, which basically balances supply and demand. The market price for direct mango sales is 1.2 yuan per kilogram, while the price for Pinduoduo Smart Supply Chain Platform sales is 0.8 yuan per kilogram, which generates a fixed cost of 0.16 yuan per kilogram of 25

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mango. Suppose the maximum selling price is 2.0 yuan/kg. In this case, the parameters are standardized. The total demand for Mangoes in the market is assumed to be Q  1 . The price of the product when the cooperative chooses the non-cooperative strategy is pt  0.6 , the price of the product when the cooperative chooses the cooperation strategy is p f  0.4 , the unit fixed cost of the product is

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cs  0.08 , consumers’ preferences for poverty alleviation products on smart supply chain platforms is   0.6 , the poor sales risk of cooperative products is Lp  0.7 ,and

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the poor sales probability is   0.7 . Under the free-riding effect, the cooperatives get the benefit  s  0.3 of free riders. When the cooperatives choose the cooperation strategy, the cost for the cooperatives is cg  0.1 and   0.8 , the cost for the smart supply chain platform is ce  0.1  0.52  2 , the original benefits of the smart supply

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chain platform is  0  . Under the free-riding effect, the benefits of the smart supply chain platform is  e  0.11 . The biggest benefit of the smart supply chain platform when choosing a cooperation strategy is Te  0.15 , and the smart degree of the smart supply chain platform is   0.8 。 According to the above parameter values, the simulation is carried out by matlab 2016a software, and the results are summarized in Fig. 3-6 and Table 6. The influence of different factors on the cooperative game equilibrium of cooperatives and smart supply chain platforms is analyzed. (1) Influence of fixed product cost cs and fixed cost of smart supply chain platform c0 on game equilibrium

Fig. 3. Influence of cs and c0 on equilibrium probability

As shown in Fig. 3., cs is in the interval of (0.1, 0.2). When c0 is 0.02, 0.04, 0.05, 26

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the changes of s0 have been described above. Therefore, when both costs decrease, the probability of cooperation between the cooperatives and the smart supply chain platforms is greater. When s0  0.5 , the cooperatives and the smart supply chain platforms are more inclined to non-cooperation strategies. The fixed costs of unit products tend to be decrease in practice, and the fixed costs of platforms will decrease with the development of technology. Therefore, cooperatives and smart supply chain platforms tend to choose the cooperation strategy. (2) Influence of the poor sales risk L p of cooperative products and the

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maximum benefit Te when smart supply chain platforms choosing the cooperation strategy on game equilibrium

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Fig. 4. Influence of L p and Te on equilibrium probability

As shown in Fig. 4, L p is in the interval of (0.67, 0.77). When Te is 0.12, 0.14, and 0.15, the change of s0 decreases with the increase of L p . When other conditions remain the same, the larger Te and L p , the more likely both parties choose the

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cooperation strategy. However, its relationship with s0 is not linear. With the decrease of Te and L p , the significance of the cooperation between the smart supply chain and the cooperative will be improved. Cooperatives tend to reduce their poor sales risk through cooperation, while smart supply chain platforms want to improve their benefits through cooperation. When Te and L p are small, there is no need to waste high costs to save a little bit of interest. (3) Influence of the smart degree  of the smart supply chain platform and the variable cost ratio on game equilibrium 27

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Fig. 5. Influence of  and  on equilibrium probability As shown in Fig. 5.,  is in the interval of (0.9,1). When  is 0.77, 0.79, and 0.81, the change of s0 decreases with the increase of  . When other conditions

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remain the same,   0.77 . The higher the smart degree  , the higher the cost of the smart chain supply platforms, but their benefits will increase. Therefore, there is a value of  which makes s0 the minimum, which is the best cooperation opportunity for cooperatives and smart supply chain platforms. (4) Influence of the unit product price p f and pt on game equilibrium

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Fig. 6. Influence of p f and pt on equilibrium probability As shown in Fig. 6, pt is in the interval of (0.57, 0.65). When p f is 0.38, 0.40 and 0.42, the change of s0 increase with pt . As can be seen from the figure, when pt is fixed, the larger the gap between p f and pt , the smaller s0 , and cooperatives and

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smart supply chain platforms tend to choose cooperation. There are also similar choices in real life. The price of the same products is lower on the Internet, and the sales volume of the products will rise. As a result, the total revenue of online stores is greater than that of offline stores. When p f is fixed, the situation will be different. The greater the difference between p f and pt , the larger the s0 . When the benefit gap of

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the unit product is too large, the sales gap cannot make up for the price gap. Only when the price of the online product is relatively reasonable can the best return be obtained. (5) Influence of consumers' preference  for poverty alleviation products on the smart supply chain platform on game equilibrium Table 6 Changes in consumer preference 0.56

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 s0

0.324455266

 and the area of s0

0.6

0.65

0.7875

0.81

0.471536232

0.711272245

5.089006

0.6454

As shown in Table 6, has influence on s0 in a certain interval: s0 increases with the increase of . However, when reaches the threshold, s0 will first decrease and then increase. The value of  is too small to provide sufficient demand to highlight the advantages of cooperation between cooperatives and smart supply chain 29

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platforms. After  reaches a certain value, the cooperative advantage gradually becomes apparent until a certain point where the cooperation probability between the cooperatives and the smart supply chain platforms is the largest. However, if  continuously increases, the cost paid by the cooperatives to the smart supply chain platforms will increase to a certain extent, and the advantages of cooperation will be further weakened. Therefore, consumers' preference for poverty alleviation products is also an important factor influencing the cooperative evolution game between cooperatives and smart supply chain platforms. 6. Conclusions

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This paper established a cooperative poverty alleviation model with multi-subject participation composed of cooperative, smart supply chain platform and the government. The evolutionary game method was used to explore the cooperative poverty alleviation strategy of smart supply chain platforms and cooperatives under the government financial platform subsidy mechanism. Particularly, the game equilibrium of the smart supply chain platform and cooperative in cooperation with and without the government financial platform subsidy was analyzed. Finally, through an example of cooperation between rural cooperatives and smart supply chain platform in Sichuan, China, shows the smart supply chain platform improves its smart degree by applying machine learning and artificial intelligence techniques. And numerical simulation was carried out to analyze the influence of machine learning ， artificial intelligence , risk, consumer preference and price on game equilibrium. The study results show that: (1) Within the scope of technology and cost, higher smart degree of the smart supply chain platforms will benefit both the smart supply chain platforms and the cooperatives; (2) in the face of higher poor sales risks and huge losses, the cooperatives tend to cooperate with the smart supply chain platforms; (3) consumer preferences influence not only the cooperative game between the smart supply chain platforms and the cooperatives, but also the product demand and product price; and (4) under the same condition, the higher the smart degree of the smart supply chain platform, and the lower the dependence on government financial platform subsidy. In other words, the smart degree of the smart supply chain platforms will help the government financial platform to transform poverty alleviation from a “transfusion” model to a “hematopoietic” model, thereby lowering the dependence on government financial platform subsidy in poverty alleviation. However, this paper only discussed the weakening effect of the smart supply chain platforms on the cooperation risks, while the positive effect of the smart degree on the precise marketing and prediction was neglected. With the development of technology and the popularity of the Internet, the accuracy and predictability of the smart supply chain platform will play an increasingly important role in the supply chain. Therefore, in the follow-up study, some factors such as precise marketing and prediction can be added to the poverty alleviation decision-making of the smart supply chain platform.

Disclosure None.

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Acknowledgements The authors would like to thank the anonymous reviewers for their valuable comments and suggestions to the manuscript. This study is supported by Supported by the Fundamental Research Funds for the Central Universities (No. 201913015)；

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Qingdao Postdoctoral Application Research Project; Shandong Social Science Planning Project (No. 19CHYJ10).

The authors would like to thank two anonymous referees and the Editor-in-Chief

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for their valuable comments and suggestions that help to improve the quality of the paper to its current standard.

Conflicts of Interest

7. References

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The authors declare that there are no conflicts of interest regarding the publication of this paper.

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Appendix

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Peng Yongyu, owner of "Tiemazhou Farm Shop" in Hongshilin Town, Guzhang County, Hunan Province, sells tea through e-commerce platforms (finance sina, 2019). The daily demand for tea is 900 kg, while the annual output of orchards is 310,000 kg, basically balancing supply and demand. The market price for mango direct sales is 600 yuan/kg, while the price for pin duo smart supply chain platform sales is 400 yuan/kg, and each kg of mango will generate a fixed cost for 100 yuan. Suppose the maximum sales price is 900 yuan/kg. In this case, the parameters are standardized. The total demand for tea in the market is assumed to be Q  1 . The price of the product when the cooperative chooses the non-cooperative strategy is pt  0.67 , the price of the product when the cooperative chooses the cooperation strategy is p f  0.44 , the unit fixed cost of the product is cs  0.11 , consumers’ preferences for poverty alleviation products on smart supply chain platforms is  0.6 , the poor sales risk of cooperative products is Lp  0.7 ,and the poor sales probability is   0.7 .

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Under the free-riding effect, the cooperatives get the benefit  s  0.3 of free riders. When the cooperatives choose the cooperation strategy, the cost for the cooperatives is cg  0.1 and   0.8 , According to the sequence of Case analysis in section 5, we will make the following figure for data test.

Fig. 7. Influence of cs and c0 on equilibrium probability

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Fig. 8. Influence of L p and Te on equilibrium probability

Fig. 9. Influence of  and  on equilibrium probability 36

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Fig. 10. Influence of p f and pt on equilibrium probability References

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Finance Sina, E-commerce poverty alleviation has increased her annual income by 50,000 yuan, https://finance.sina.com.cn/roll/2019-07-08/doc-ihytcitm0410385.shtml (accessed 7 September 2019).

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