Monitoring And Implementation: A Bargaining Game

Monitoring And Implementation: A Bargaining Game Model between Government and Core Enterprise in Greening Supply Chain Reza Mahmoudi

Ashkan Hafezalkotob

Department of Industrial engineering Islamic Azad University, South Tehran Branch, Tehran, Iran [email protected]

Department of Industrial engineering Islamic Azad University, South Tehran Branch, Tehran, Iran [email protected]

Abstract—The overwhelming growth in the struggle between economy and ecology has led managerial research to promote methodologies to reap profits ensuring sustainability of the ecosystem thus venturing into the novel domain incorporating sustainability with green supply chain management and coordination. In order to investigate the game between government and core enterprise in greening supply chains, this article analyzes their respective costs and benefits and equilibrium points of the game on the basis of Nash Bargaining game theory. We propose a game theoretical framework that will help the government and the core enterprise to determine the optimal strategy. Game analysis shows that core-enterprise's costs and benefits to implement green supply chain management as well as subsidies and penalties from governments directly affect the game results. Keywords: green supply chain; government; game theory; bargaining game;

I.

INTRODUCTION

Pollution and environmental protection in the present century are extremely significant global problems. Due to this fact, governments have transformed environmental policies gradually from only focusing on end-of-pipe control to concerning environmental requirements of production and products through the whole product life cycles [1]. For example in china, some local development and reform committees have encouraged enterprises to adopt the strategy of circular economy and cleaner production; some local economic committees have evaluated energy consumption for local heavy industrial enterprises; local finance bureaus also have initiated programs such as green public procurement. Therefore, Chinese governments have increasingly required enterprises to green their supply chains, that is, to

implement green supply chain management (GSCM) [2]. Core enterprises play an important role in greening supply chains [3, 4]. The motivation and capability of core enterprises are two key elements to successfully green supply chains [5]. Environmental regulations and policies by governments are key drivers for enterprises to implement GSCM [6, 7]. Hence, this article studies the game between the government and core enterprise during greening supply chains. Some authors have studied the relationships between the two players, namely, government and enterprise. Through a case study, Zhu and Cote argue that the support of government improves the economic and environmental performance of the enterprise, and then the enterprise further integrates and greens the entire supply chains [8]. Wang analyzes the reasons why enterprises unscrupulously discharge pollution and develops a game model to explain the relationships between governments and enterprises [9]. The studies' results show that, to green supply chains successfully, it is crucial to put forward win-win measures between governments and core enterprises according to different phases of government environmental policies and enterprise environment management. By using game theoretical approaches, some studies have been done in GSCM. To investigate the problem of negotiations between producers and reverse-logistics suppliers for cooperative agreements under government intervention, utilizing the asymmetrical Nash bargaining game with uncertainties, Sheu [10] proposed a Bargaining framework for competitive green supply chains under governmental financial intervention. Their results indicate that financial intervention by a government generates a significant effect on the relative bargaining power of green supply chain members in

Corresponding Author: Reza Mahmoudi E-mail: [email protected] Telephone Number: +98-914-1586380.

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negotiations. Ghosh and Shah [11] used game theory to a comparative analysis of greening policies across supply chain structures. By considering situations in which the players cooperate or act individually, they examined an apparel serial supply chain whose players initiate product ‘‘greening’’. They built game theoretic models and showed how greening levels, prices and profits are influenced by channel structures. They also studied the impact of greening costs and consumer sensitivity towards green apparels. Zhao, Neighbour, Han, McGuire and Deutz [12] provided an approach in the context of green supply chain management, using game theory to analyze the strategies selected by manufacturers to reduce life cycle environmental risk of materials and carbon emissions. To looking 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, Barari, Agarwal, Zhang, Mahanty and Tiwari [13] developed an evolutionary game approach. Sheu and Chen [14] analyzed the impacts of government financial intervention on competition among green supply chains using a three-stage game-theoretic model. Their results suggest that the government should adopt green taxation and subsidization to ensure that green profit attributed to green-product production is nonnegative. Due to the gaps in the literature, there are two main contributions in this research. First, the monitoring implement problem in a green supply chain, as an important subject, is regarded as the game subject. Second, although some research has focused on the game theoretical models in green supply chain, but there are few studies that have used the bargaining game model in the green supply chain. Specially, in the green supply chain management, there is no study that used Bargaining game to analysis the game between government and core enterprise in monitoring and implementation subject. Therefore, in this paper, to analyze the game between government and core enterprise and discuss the factors influencing the equilibrium strategy, the Bargaining game theory has been used and a game theoretical model is proposed for such decision making framework. Game theory is an important research method. Game theory models, also called equilibrium models, optimize the bidding strategies by investigating players’ interactions and analyzing economic equilibria of the system. Typically, in a game, each player chooses the strategy from its own strategy set; then a payoff will be assigned to each player by the payoff function; as a result the optimal solution can be reached via Nash equilibrium. Nash equilibrium is a strategy combination of all players in which no player can increase its payoff by changing its own strategy alone so that every player will finally

choose its strategy exactly as the equilibrium strategy combination. Game theory models provide analytical rationale and explanation on how market power can be exercised via strategic behavior, but the assumption that all players are rational usually does not hold in practice [15]. Also, it is limited by the requirement of common knowledge on all generation companies actual production costs [16]. However, the research conclusions that exist are reached based on the hypothesis that the participants are fully rational. Therefore, this paper analyzes the game between rational government and core enterprise in greening supply chain with the Bargaining game theory and discusses the factors influencing selected strategies. The rest of the paper is organized as follows. In the following section, the assumptions, elements of the proposed model and the benefit matrix are presented. Section III, briefly discusses the Bargaining game and its application. A breakdown point has been introduced and the algorithm of game procedure is presented in section IV. In section V, a numerical example is presented. Then in section VI, the results have been analyzed. Eventually, concluding remarks and suggestions for the future research are given in section VII. II.

THE MODEL

This paper studies the relationship between a government and a core enterprise in a green supply chain. The enterprise has two different strategies. The enterprise might adopts strategy of implementing GSCM (hereafter referred to as “implement”) or chooses not to implement GSCM (“not implement”). Correspondingly, government has two strategies to choose. One is to monitor enterprise (“monitor”) such as monitoring whether or not dangerous elements have been marked; the other is not to monitor enterprise (“not monitor”). The game strategies are shown in Table I. TABLE I.

GOVERNMENT-ENTERPRISE GAME STRATEGIES Enterprise

government

Monitor Not monitor

Implement

Not Implement

(Monitor, Implement) (Not monitor, Implement)

(Monitor, Not Implement) (Not monitor, Not Implement)

To establish the model, the parameters and variables used in the model formulae are as follows:

C IE

Increased cost of “implement” enterprise

CM

Monitoring cost of “monitor” government

R IE

Increased benefit of “implement” enterprise

FG

Community pollution treatment fee

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A IE

Allowance for “implement” enterprise

PNE

Penalty for “not implement” enterprise

UbGC The upper bound of government cost, where C M  FG  AIE  UbGC The proposed models are established upon the following assumptions: 1) “Government” refers to local government, which can be considered as a joint local environment improvement committee. 2) GSCM implementation in an enterprise will increase investments and inputs to meet the environmental requirements while at the same time bring benefits by improving product price and increasing market share. 3) If a government monitors an enterprise, the government will provide supports such as preferential loan policies and product procurement for enterprise that implement GSCM. The profit function for the enterprise is formulated as follows:  E  k E (C IE  A IE  R IE )  l E (PNE ) (1)  u E ( C IE  R IE )  v E (0) where

k E , l E ,u E ,v E 0,1

and

k E  l E  u E v E  1 . If the government chooses to monitor and enterprise chooses to implement, k E  1, lE  u E  v E  0 , if the government chooses to monitor but the enterprise does not implement, l E  1, k E  u E  v E  0 . When the government is not willing to monitor and the enterprise implements the GSCM, u E  1, k E  l E  v E  0 . If the government is not willing to monitor and the enterprise does not implement, v E  1, k E  l E  u E  0 . Similarly, the profit function for the government is formulated as follows: G  k G (C M  A IE )  lG ( FG  C M  PNE )  uG (0)  v G (C IE  R IE )

procurement costs; 2) reduction of resource and energy consumption; 3) decreased waste disposal fee; 4) less waste discharge costs. A “monitor” government needs to pay the monitoring cost of C M , including cost of collecting, assessing, and reporting relevant information. If the government monitors an enterprise, an enterprise implementing GSCM will be provided the subsidy of A IE ; on the contrary, an enterprise without implementing GSCM would be fined by the penalty of PNE . If an enterprise does not implement GSCM, a government needs to pay community pollution treatment fee of FG . Therefore, the benefit matrix of this game between the government and enterprise, pertaining to various combinations of strategies that the players may play, is presented in Table II. TABLE II.

Enterprise

government

Implement

Not Implement

Monitor

(A, B)

(C, D)

Not monitor

(E, F)

(G, H)

Where

A  C M  AIE

(3)

B  C IE  AIE  R IE

(4)

C  FG  C M  PNE

(5)

D  PNE

(6)

E 0

(7)

F  C IE  R IE

(8)

G  FG

(9)

H 0

(10) III.

(2)

The profit functions (1) and (2), show that each party's profit has a positive relation with incomes and a negative relation with costs. Following the previous studies [17−20], we assume the costs and benefits of governments and core enterprises. An enterprise implementing GSCM would bring cost of C IE including the cost of cooperation along supply chains and internal GSCM. Whereas the enterprise can also gain the added benefit of R IE , including: 1) saving of material

BENEFIT MATRIX

BARGAINING GAME

In this study, the equilibrium point of the game with the presented benefit matrix in Table II, is achieved using the Nash bargaining game. Therefore, we briefly introduce the Nash bargaining game approach. The goal of the Nash Bargaining game, as a cooperative game, is dividing the benefits or utility between two players based on their competition in the market place. The Nash bargaining game model [21] requires the feasible set to be compact and convex. It contains some payoff vectors, so that each individual payoff is greater than the individual breakdown payoff. Breakdown Payoffs or

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Breakdown points are the starting point for bargaining which represent the possible payoff pairs obtained if one player decides not to bargain with the other player.

distinctive according to the costs and incomes for each party. Data for this numerical example are presented in Table III.

If u and b are the payment (benefit) and breakdown payoffs vector for the individuals, respectively, they must 2

maximize



(u i - bi )

by

solving

the

following

i 1

TABLE III. NE

DATA FOR NUMERICAL EXAMPLE

(C IE ,C M , FG ,

NE

R IE , A IE , PNE ,UbGC )

(C IE ,C M , FG , R IE , A IE , PNE ,UbGC )

1

(40,70,200,70,100,80,510)

26

(40,70,200,170,100,80,510)

2

(60,70,200,70,100,80,510)

27

(40,70,200,190,100,80,510)

3 4 5

(80,70,200,70,100,80,510) (100,70,200,70,100,80,510) (120,70,200,70,100,80,510)

28 29 30

(40,70,200,210,100,80,510) (40,70,200,70,120,80,510) (40,70,200,70,140,80,510)

6

(180,70,200,70,100,80,510)

31

(40,70,200,70,160,80,510)

7

(200,70,200,70,100,80,510)

32

(40,70,200,70,180,80,510)

8

(40,90,200,70,100,80,510)

33

(40,70,200,70,200,80,510)

9 10 11

(40,110,200,70,100,80,510) (40,130,200,70,100,80,510) (40,150,200,70,100,80,510)

34 35 36

(40,70,200,70,220,80,510) (40,70,200,70,240,80,510) (40,70,200,70,100,100,510)

12

(40,170,200,70,100,80,510)

37

(40,70,200,70,100,120,510)

13

(40,190,200,70,100,80,510)

38

(40,70,200,70,100,140,510)

achievable benefit for enterprise. By considering UbGC , as the upper bound of government cost,  UbGC is lesser than the worst achievable benefit for the government, therefore  UbGC is the lower bound of the government profit. It is believed that a player does not stay in the business unless it can meet his minimum benefit; therefore, we use min and  UbGC as the breakdown points. It should be noted that we can use min  min A ,C , E ,G  as a breakdown point for the

14 15 16

(40,210,200,70,100,80,510) (40,70,220,70,100,80,510) (40,70,240,70,100,80,510)

39 40 41

(40,70,200,70,100,160,510) (40,70,200,70,100,180,510) (40,70,200,70,100,200,510)

17

(40,70,260,70,100,80,510)

42

(40,70,200,70,100,220,510)

18

(40,70,280,70,100,80,510)

43

(40,70,200,70,100,80,530)

19 20 21

(40,70,300,70,100,80,510) (40,70,320,70,100,80,510) (40,70,340,70,100,80,510)

44 45 46

(40,70,200,70,100,80,550) (40,70,200,70,100,80,570) (40,70,200,70,100,80,590)

22

(40,70,200,90,100,80,510)

47

(40,70,200,70,100,80,610)

23

(40,70,200,110,100,80,510)

48

(40,70,200,70,100,80,630)

government, too. But in this paper  UbGC is considered as the government breakdown point.

24

(40,70,200,130,100,80,510)

49

(40,70,200,70,100,80,650)

25

(40,70,200,150,100,80,510)

50

(140,170,20,20,20,80,300)

maximization problem:

max (u1 - b1 )(u 2 - b2 ) s .t

u1  b1

(11)

u 2  b2 where (u1,u 2 ) (A , B ),(C , D ),(E , F ),(G , H ) . IV.

BREAKDOWN POINTS

As mentioned in Binmore et al. [22], the choice of the breakdown point is a matter of modeling judgment. In the benefit matrix, presented in Table II, let min  min B , D , F , H  . Therefore, min is the worst

NE: Number of Example

The algorithm of the game procedure is as follows: according to the data of the government and the enterprise, first the benefit matrix is calculated. Then, the optimal strategies for this game are obtained from the Nash bargaining problem (11). V.

All the calculations are done with MATLAB 14. For 50 different levels of (C IE ,C M , FG , R IE , AIE , PNE ,UbGC ) , the model is solved and the results are summarized in Table IV. VI.

NUMIRECAL EXAMPLE

In this section, we provide the numerical examples to discuss how the theoretical results in this paper can be applied in practice. It is supposed that there are a government and an enterprise in a supply chain. They both have two options: monitoring or not monitoring strategies for the government and implementation and non implementation for the enterprise. To demonstrate how the costs, C IE , C M and FG , and incomes, R IE , A IE and PNE , and the upper bound of government cost, UbGC , affect the equilibrium strategies of game , we consider 50 different examples. These examples are

NUMERICAL EXAMPLE ANALYSIS

In the numerical example, the Nash equilibrium strategy has been calculated for 50 different levels of (C IE ,C M , FG , R IE , AIE , PNE ,UbGC ) . By analyzing different equilibrium results, we can get several finding. When all parameters are constant: 1) With the increase of C M or R IE or PNE , the government will not be willing to monitoring but the enterprise will choose implementation strategy. Then (E,F) is the equilibrium strategy.

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TABLE IV.

NUMERICAL RESULTS FOR 20 DIFFERENT EXAMPLES

NE

Breakdown point

equilibrium strategy

NE

Breakdown point

equilibrium strategy

1

(-80,-510)

(A,B)

26

(-80,-510)

(E,F)

2

(-80,-510)

(A,B)

27

(-80,-510)

(E,F)

3 4 5

(-80,-510)

(A,B)

(-80,-510)

(E,F)

(-80,-510) (-80,-510)

(A,B) (A,B)

28 29 30

(-80,-510) (-80,-510)

(A,B) (A,B)

6

(-110,-510)

(G,H)

31

(-80,-510)

(A,B)

7

(-130,-510)

(G,H)

32

(-80,-510)

(A,B)

8

(-80,-510)

(A,B)

33

(-80,-510)

(A,B)

9 10 11

(-80,-510)

(A,B)

(-80,-510)

(A,B)

(-80,-510) (-80,-510)

(A,B) (E,F)

34 35 36

(-80,-510) (-100,-510)

(A,B) (A,B)

12

(-80,-510)

(E,F)

37

(-120,-510)

(A,B)

13

(-80,-510)

(E,F)

38

(-140,-510)

(A,B)

14 15 16

(-80,-510)

(E,F)

(A,B)

(-80,-510) (-80,-510)

(A,B) (A,B)

39 40 41

(-160,-510) (-180,-510) (-200,-510)

(E,F) (E,F)

17

(-80,-510)

(A,B)

42

(-220,-510)

(E,F)

18

(-80,-510)

(A,B)

43

(-80,-530)

(A,B)

19 20 21

(-80,-510)

(A,B)

(-80,-550)

(A,B)

(-80,-510) (-80,-510)

(A,B) (A,B)

44 45 46

(-80,-570) (-80,-590)

(A,B) (A,B)

22

(-80,-510)

(A,B)

47

(-80,-610)

(A,B)

23

(-80,-510)

(A,B)

48

(-80,-630)

(A,B)

24

(-80,-510)

(A,B)

49

(-80,-650)

(A,B)

25

(-80,-510)

(A,B)

50

(-120,-300)

(G,H)

NE: Number of Example and breakdown point is (min , UbGC )

2) In the high amount of FG or A IE , the equilibrium strategy is (A,B). It means, high cost of community pollution treatment or high profit level caused by implementation of green policies for enterprise, will encourage the government to monitoring and the enterprise to implementation. 3) When the government increase the upper bound of it's cost, it means that the government want to cost to implement the green policies by enterprise and monitoring. Therefore, with the increase in UbGC , the equilibrium strategy wil be (A,B). 4) When C IE has high amounts, the implementation will not be economical for enterprise and the equilibrium strategy is (G,H). VII. CONCLUSION To answer the question "Monitoring or not and Implementation or not?", the game between the government and the core enterprise is studied on the basis of Bargaining game. The proposed framework helps the

government and the core enterprise to determine the optimal strategies. To be more specific, the model, allows the government and the core enterprise to choose the optimal strategy regarding their costs and profits in each possible strategy. A numerical example was presented to illustrate the model's performance in 50 different levels of the costs and the incomes. The results show that the equilibrium strategies depend upon entirely on the costs and incomes level. With the increase of penalties for not implementation or allowance and benefit of implementation, the enterprise will be willing to implement the green policy. In the high level of environmental costs, the government will choose the monitoring strategy. There are several directions and suggestions for future research. First of all, to calculate the equilibrium strategy of the game, the Nash bargaining game model has been used, in the future research it can be calculated and analyzed by other game theory models. Secondly, the proposed model can be easily extended to the case where more than two government and core enterprise exist. Moreover, it would be very interesting but challenging to consider the uncertainty on model parameters. Eventually, the proposed framework can be used in other markets. REFERENCES [1]

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