Bargaining framework for competitive green supply chains under governmental financial intervention

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Bargaining framework for competitive green supply chains under

governmental ﬁnancial intervention

Jiuh-Biing Sheu

Institute of Trafﬁc and Transportation, National Chiao Tung University, 4F, 118 Chung Hsiao W. Rd., Sec. 1, Taipei 10012, Taiwan, ROC

a r t i c l e

i n f o

Article history: Received 5 July 2010

Received in revised form 12 September 2010 Accepted 27 December 2010

Keywords:

Green supply chain cooperation Bilateral negotiation

Nash bargaining game

Government’s ﬁnancial instruments

a b s t r a c t

This work investigates the problem of negotiations between producers and reverse-logis-tics (RL) suppliers for cooperative agreements under government intervention. Utilizing the asymmetrical Nash bargaining game with uncertainties, this work seeks equilibrium negotiation solutions to player agendas. Analytical results indicate that financial interven-tion by a government generates a significant effect on the relative bargaining power of green supply chain members in negotiations. Over intervention by a government may result in adverse effects on chain members’ profits and social welfare. Furthermore, a bar-gaining framework underlying the duopoly–oligopoly context may contribute to a negoti-ation outcome most profitable for green supply chain members.

1. Introduction

As global environmental issues emerge along with the involvement of governments via green legislation and ﬁnancial instruments (e.g., green taxation and subsidies), interaction between a producer1_{and reverse-logistics (RL) suppliers}2 _is

unavoidable in a green supply chain before the condition of cooperative synergism is attained. For example, the impact of the European Waste Electrical and Electronic Equipment (WEEE) and Restriction on Hazardous Substances (RoHS) directives

increased costs by 3% for branded ﬁrms and 5–10% for manufacturers of consumer electronics (Ho and Kretz, 2005). Such

WEEE-induced extra expenses and responsibilities have increased producer awareness of the need to cooperate with RL-suppliers. A producer selling consumer electronics products to the European Union (EU) is required to collect and recycle used-products to comply with WEEE directives. One can then postulate an interaction process in which the producer negotiates with its RL-supplier before achieving a cooperative supply chain relationship for WEEE compliance. When a government’s ﬁnan-cial instruments are involved, the relative power of producers and RL suppliers is likely to be altered, which may complicate the interaction among chain members and solutions for green supply chain coordination. A typical example is green taxation, where governments levy green taxes on producers and subsidize the recycling industry using the money raised to promote ecologically sustainable activities (Luk, 2005). Additionally, numerous practical cases have indicated that producers used to be deﬁned as powerful supply chain members need help from RL-suppliers to comply with take-back directives; otherwise, producers may take on considerable risk of violating WEEE directives and losing EU markets (Deffree, 2007). Accordingly, adopting a bargaining theory that addresses issues of vertical integration in green supply chains is indispensable, particularly in global operation contexts.

E-mail address:jbsheu@mail.nctu.edu.tw

1

‘‘Producers’’ refers to manufacturers and ﬁrms that sell products under their own brands.

2

An RL-supplier is deﬁned as a member that provides RL-related services, including used-product collection and recycling, to the producer in a green supply chain.

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Transportation Research Part E

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Despite the importance of understanding how green supply chain members interact through the bargaining process to move toward green supply chain coordination, previous studies of such member interactions are limited in the ﬁeld of green

supply chain management (GSCM) and related areas.Nagarajan and Bassok (2008)noted that research modeling

relation-ships between agents in a supply chain using economic bargaining theory is limited in operations management literature

(van Mieghem, 1999;Gurnani and Shi, 2006; Plambeck and Taylor, 2007a,b;Taylor, 2007).van Mieghem (1999)applied a

two-stage stochastic game to address issues associated with outsourcing between a producer and its subcontractor, which build capacity before realizing demand. The role of bargaining power was introduced to analyze the scenario with incom-plete contracts.Gurnani and Shi (2006)utilized a Nash bargaining (NB) game to compute optimal contract price and quantity of trade in a supplier–buyer distribution channel under asymmetrical beliefs held by dyadic channel members of supply

reli-ability.Plambeck and Taylor (2007a,b)recently investigated several issues such as investments in innovation and capacity

allocation in supply chains, and renegotiation effects on supply contract design.Taylor (2007)addressed the impact of re-peated interactions on capacity investment and procurement in a supplier–buyer supply chain, where rere-peated game theory is applied to generate an optimal relational contract for a long-term supply chain relationship.Nagarajan and Bassok (2008) developed a sequential bargaining framework to address the assembly problem in a decentralized supply chain, where a sin-gle assembler buys complementary components from multiple suppliers that form coalitions to negotiate with the assem-bler on proﬁt allocations in the supply chain. Relative to existing literature, this work focuses on negotiation between producers and RL-suppliers in competitive green supply chains under oligopoly competition and governmental green strat-egies. Thus, the negotiation issue addressed is extended in this work, where intra-chain cooperation and inter-chain compe-tition in green supply chains are driven by governmental take-back legislation and ﬁnancial instruments.

Additionally, a vast amount of supply chain contract literature focuses on design of coordinating mechanisms that are generally tied to specific structures of supply chains by assuming asymmetrical bargaining power between supply chain members. The supply chain coordination problems are then solved by allocating the first-best profit among chain members

using cooperative game theory. Typical among these are buy-back contracts (Pasternack, 1985), quantity–ﬂexibility

con-tracts (Tsay, 1999), price–discount contracts (Bernstein and Federgruen, 2005), and revenue-sharing contracts (Cachon

and Lariviere, 2005; Koulamas, 2006). For instance,Cachon and Lariviere (2005)discussed in-depth the strengths and

lim-itations of revenue-sharing contracts. They demonstrated that revenue-sharing mechanisms are very promising in

coordi-nating dyadic members of supplier–retailer supply chains. A comprehensive review can also be found inCachon (2003).

Furthermore, some efforts have focused on other coordination mechanisms such as two-part tariffs and vender-managed

inventory (VMI) when retailers are dominant (Mishra and Raghunathan, 2004; Raju and Zhang, 2005; Kurata, 2006).

Although notable advances in cooperative contracts have been made by scholars, literature is generally limited to the scope of typical supply chain coordination, and does not discuss the inﬂuence of bargaining power in green supply chains or address the issue of interaction between forward and reverse supply chain members under governmental green legisla-tion and ﬁnancial intervenlegisla-tion. These shortcomings provide a research opportunity. In reality, evidence from practical cases spanning diverse industries has indicated that negotiation is the antecedent of cooperative contracts in which the relative

power of chain members underlies the negotiation process for green supply chains. Conversely, according to Wilson

(2006), global recycling industries are attempting to increase awareness of the effects green legislation will have on

produc-ers, leaving room to increase beneﬁts when negotiating with producers. Issues such as bargaining power and its inﬂuence on green supply chain coordination (e.g., coordination between producers and RL-suppliers) warrant further investigation.

Rooted in the conceptual framework proposed bySheu et al. (2005), this work focuses on the negotiations between

pro-ducers and RL-suppliers in competitive green supply chains under the influence of governmental take-back legislation and financial intervention. Specifically, this work addresses the following research questions.

1. How do producers and RL-suppliers interact in bilateral negotiations for cooperative agreements?

2. What are the major concerns of producers and RL-suppliers in bilateral negotiations under governmental intervention, and how do they adapt to these inﬂuences while moving toward equilibrium bargaining solutions?

3. How does bargaining power inﬂuence the negotiation decisions of dyadic players for a cooperative agreement in a green supply chain contingent on governmental ﬁnancial intervention?

4. If governmental financial intervention via green taxation and subsidies is indispensable to holding producers responsible for environmental impact, what are the equilibrium solutions of a unit green tax and subsidy? Additionally, how do finan-cial instruments influence the decisions of producers and RL-suppliers in negotiations for green supply chain cooperation?

Compared with typical problems associated with supply chain cooperation, the issue addressed in this work has the fol-lowing different features. First, this work aims at the green supply chain cooperation case under governmental intervention by means of take-back legislations and financial measures. Although economic incentives (e.g., cost minimization and profit maximization) remain important in any supply chain, cooperation between a producer and RL-supplier in a green supply chain is based on the need for extended producer responsibility (EPR). Therefore, it is logically agreed that a producer needs to seek for an appropriate RL-supplier to form a cooperative green supply chain for take-back legislation compliance in ad-vance of making production decisions. For example, regardless of the reliability and efficiency of virgin-complements (VC) supply provided by VC suppliers in the high-tech industry, producers often require collaboration from RL-suppliers to collect and recycle products in the EU to comply with WEEE directives. Global benchmark branded firms, such as IBM,

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Hewlett-Packard, Xerox, Sony, and ASUS are increasingly focusing on their core competencies while contracting out their EPR via

sophisticated negotiation mechanisms to gain sustainable competitive advantage (Ho and Kretz, 2005; Lee, 2008; Weber,

2008). Second, under governmental inﬂuence and strategic threats from competitors, negotiation between a producer and

RL-supplier is indispensable before reaching cooperative green supply and take-back agreements. This is followed by deter-mination of green production for competition. Therein, a producer must consider the response of an RL supplier in negoti-ation and the bidding effect of its competitors, which may provide alternatives (called outside options inMuthoo, 2002) to the RL-supplier, on the negotiated decision of the RL-supplier and vice versa. Additionally, government involvement via green legislation and ﬁnancial intervention (e.g., green taxes and subsidies) is increasingly recognized as a major coercive inﬂuence

promoting EPR (Hammond and Beullens, 2007; Atasu et al., 2009). Consequently, the relative bargaining power of producers

and RL-suppliers may change, increasing the complexity of interactions between producers and RL suppliers. This is also why this work accounts for relative bargaining power and formulates this power as a function dependent on governmental ﬁnan-cial instruments in the proposed producer-RL-supplier bargaining framework. Incorporating bargaining power into a pro-ducer and RL supplier bargaining framework to characterize the factors inﬂuencing player solutions in negotiations

differs from existing models that focused on closed-loop supply chain network equilibrium (Nagurney and Toyasaki,

2005; Hammond and Beullens, 2007).

From a methodological perspective, the proposed model has the following features. First, this model incorporates the influences of governmental take-back directives and financial intervention into the bargaining framework of competing green supply chains to approximate the equilibrium bargaining solutions of producers and RL-suppliers for used-product collection, recycling, and final product production. To the best of our knowledge, such a bargaining framework characterizing the problem of negotiations between producers and RL-suppliers under the influence of governmental green strategies is limited in previous GSCM studies. Second, this work formulates the aforementioned problem of negotiation between a pro-ducer and RL-supplier using a novel asymmetrical NB game model. Thus, several uncertainty issues existing in reservation prices of dyadic negotiators, expected profits and breakdown risks from outside options (i.e., cooperating with other part-ners) are considered in model formulation. Some bargaining theories have recently been proposed to deal with uncertainty

issues such as random disagreement points in NB solutions (Chun and Thompson, 1990; Smorodinsky, 2005) and bargaining

over alternatives with Markov processes (Merlo and Wilson, 1995; Herings and Predtetchinski, 2009). Unlike those theoret-ical works, model development in this work is focused on problem solving for green supply chain cooperation. Nevertheless, the proposed treatments in dealing with the aforementioned uncertainty issues are novel applications of NB game theory. Moreover, we assume the relative bargaining power of producers and RL-suppliers is affected by governmental green tax and subsidy policies rather than a given value, as did in literature using asymmetrical NB solutions (Muthoo, 2002). There-fore, the proposed model speciﬁes the respective bargaining-power functions to characterize the effect of governmental ﬁnancial intervention on bargaining solutions of producers and RL suppliers during negotiations.

Notably, in this work, take-back legislation is treated as a prerequisite to model formulation and analysis, even though this legislation is one of the government’s primary instruments to keep production green and manage product lifecycles. Fur-thermore, the issue of efﬁcient take-back legislation was addressed byAtasu et al. (2009), and may provide insights in the

government’s use of legislation as a coercive strategy complementing this work. Drawing from the work byAtasu et al.

(2009), we assume target collection and recycling rates are adjustable on a case-by-case basis and are given. Nevertheless,

differing fromAtasu et al. (2009), who considered the potential of subsidizing producers for recycling, this work considers

another taxation subsidy scenario in which governments levy green taxes on producers and subsidize RL-suppliers (Luk,

2005). Furthermore, the aim and scope of this work are not limited to the interaction between government and producers.

Rather, the main purpose is to develop a bargaining framework that considers the potential problems and solutions in inter-actions between producers and RL suppliers moving toward green supply chain coordination under governmental take-back legislation and the ﬁnancial instruments mentioned.

The remainder of this paper is organized as follows. Section2deﬁnes the producer and RL-supplier negotiation problem

through a bargaining framework characterizing problem scope, assumptions, and bargaining structure. In Section3, a three-stage game-based model is formulated and solved using the asymmetrical NB game and backward induction approaches.

Based on the derived equilibrium solutions, Section4presents qualitative and quantitative analyses to gain insight into

the influence of governmental financial intervention in the specified bargaining framework for a producer and RL-supplier.

Section5gives conclusions and recommendations.

2. Bargaining framework

This section describes a bargaining framework for negotiation problems for producers and RL-suppliers in competitive green supply chains under the inﬂuence of governmental take-back legislation and ﬁnancial instruments. This work

pro-poses a bargaining framework based on NB game theory (Muthoo, 2002;Brams, 2003) (Fig. 1). This work characterizes

the aforementioned negotiation problem in terms of (1) problem scope, (2) assumptions, and (3) bargaining structure. The problem scope is negotiations between producers and RL-suppliers in competitive green supply chains under govern-mental inﬂuence via take-back legislation and ﬁnancial instruments. The problem background is such that ‘‘I’’ producers with their respective brands compete while selling their products in a demand market subject to governmental take-back

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(de-noted by f for producing each product unit) on producers and provides subsidies (de(de-noted by s for recycling each end-of-life (EOL) product unit) to those in charge of recycling EOL-products (i.e., RL suppliers in this work). Furthermore, drawing from

Atasu et al. (2009), we assume unit collection and recycling rates (denoted by c and r) are given and predetermined by the

government. Under governmental involvement via the aforementioned green strategies, producers may contract out EOL-product collection and recycling responsibilities with ‘‘J’’ RL providers that are also in competition. Notably, the problem scope is limited to the case in which each given producer cooperates with only one RL-supplier to form a green supply chain. Based on these prerequisites, one can speculate that a producer may negotiate with any given RL-supplier before reaching a cooperative contract, thus leading to a bargaining situation in which both a producer and RL-supplier have a common inter-est to cooperate (e.g., forming a green supply chain to increase mutual beneﬁts) but have conﬂicting interinter-ests (e.g., the price a producer will pay and that an RL-supplier will sell recycled components to the producer over how to cooperate during negotiations.

It is noteworthy that in most practical cases, a cooperative agreement/contract is needed between green supply chain members (especially for the producer and (green) supplier), such that the original isolated members can be cooperative members collectively working as a team for a green supply chain. According to our preliminary analysis using interview sur-vey data collected from industries including notebook computers, textiles, iron and steel, such cooperative agreements are indispensable, especially to make sure that a producer can obtain reliable recycled materials/components at appropriate prices without concerns of material shortage and unusual variability of procurement prices. Under such a cooperative agree-ment, both the producer and RL-supplier then go for their proﬁts contingent on the signed contract agenda such as the price

and supply of recycled components. Moreover, according toChen and Sheu (2009), more and more producers take into

ac-count the factor of recyclability in product design (Chen and Sheu, 2009), and thus it is inferred that a green producer usually intends to obtain the recycled components processed from its own products for quality and cost control of recycling. Accord-ingly, it is reasonably agreed that a cooperative RL-supplier sells the corresponding recycled components/materials to the cooperative producer under a green supply chain cooperative agreement, which is also the case primarily investigated in this study.

Compared with a typical bilateral negotiation framework, which involves only two-players in a bargaining process, the proposed negotiation framework for a producer and RL-supplier can be more intricate in the following two perspectives. First, involvement of government via green legislation and ﬁnancial intervention likely alters the relative power of producers and RL-suppliers while bargaining. This point is drawn from evidence of several practical cases in Europe, indicating that a

recycler inﬂuences producer market share and costs for WEEE compliance (Clean Production Action, 2003; Stevels and

Huis-man, 2005). Thereby, we further assume that the relative bargaining power of producers and RL suppliers are functions of f

and s, denoted by

a

(f, s) and b(f, s), respectively, where 0 6

a

(f, s) 6 1, 0 6 b(f, s) 6 1, and, moreover, the conditions

a

ðf ; sÞ þ bðf ; sÞ ¼ 1;@aðf ;sÞ @f <0; @aðf ;sÞ @s <0; @bðf ;sÞ @f >0, and @bðf ;sÞ

@s >0 must hold. Second, under competition, any producer i must

consider the negotiations with RL-suppliers and the bargaining strategies of competing producers i0(" i0, i0–i) that seek coop-eration with RL suppliers before constructing a green supply chain. Therefore, if a producer fails to reach a negotiated agree-ment with an RL-supplier, the producer will incur transaction costs spent during negotiation and risk of counterattack from competing green supply chains formed by competing producers and the RL-supplier. Similar phenomena also apply to RL suppliers. Government influence Producer 1 Producer i Reverse logistics supplier 1 Reverse logistics supplier j Production decision of producer 1 Production decision of producer i Negotiation mechanism

Tack-back directives Financial instruments

1,2,..i,,,,I

1,2,...j,...J

1,2,..i,,,,I

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To facilitate problem formulation, we make the following six assumptions.

Assumption 1. Market competition environments in which both producers and RL-suppliers exist are oligopoly competition, where ‘‘I’’ competing producers proceed with Cournot oligopoly competition in production. Furthermore, we assume each producer sources out its take-back responsibility to one of ‘‘J’’ competing RL providers, which also exist in the oligopoly competition contexts.

Assumption 2. The unit cost of ﬁnal product manufacturing (cm) is the same for all producers; similarly, the unit cost for

recycled component procurement (cy) is assumed the same for all RL-suppliers.

Assumption 3. All competing green supply chains fully comply with green legislation, and have the capability of producing a homogeneous product, where production of a unit product requires

s

xand

s

yquantities of virgin and recycled components

(denoted by x and y, respectively), which are complementary.

Assumption 4. For sake of analytical tractability, the ﬁnal product price (P(Q)) is assumed to be a simple Cournot inverse demand (Q) function in which the ﬁnal product demand market density is normalized to 1. Therefore, P(Q) = 1 Q, where Q ¼PIi¼1qi, where qiis the amount of product sold by producer i.

Assumption 5. All producers have the same bargaining power

a

(f, s) relative to the bargaining power b(f, s) of RL-suppliers, which is also identically for all RL-suppliers.

Assumption 6. Governmental financial instruments are subject to the balanced budget condition (i.e., the total amount of green taxes equals that of green subsidies), meaning that the government would not benefit financially.

Based on the problem scope and assumptions, this work speciﬁes a three-tier bargaining structure (Fig. 1). Drawing

fromUlph (1996), this work treats the government as the primary source of coercive power holding producers responsible

for collecting and recycling the EOL products they produce. Thus, the first tier deals with the government’s financial influ-ence strategies, including green taxation levied on producers and subsidies offered to RL supplies, where f and s are treated as the two primary governmental decision variables. The second tier specifies the main bargaining structure that contains I competing producers negotiating with J competing RL-suppliers for cooperative contracts. The unit price (pyj;iÞ and

guaran-teed quantities (yj,i) of recycled components ordered by producer i (" i 2 I) and supplied by RL-supplier j (" j 2 J) are

con-sidered the two primary agendas during negotiation. If the cooperative agreement is achieved by a given pair of producer i and RL-supplier j, a green supply chain will be formed, where the cooperative RL-supplier j must collect and recycle EOL-products consistent with the amounts requested by take-back directives for cooperative producer i. Meanwhile,

coop-erative producer i must purchase these recycled components with p_y

j;i. Conversely, if the cooperative agreement is not

achieved, producer i and RL supplier j incur costs associated with negotiation breakdown (termed breakdown costs); more-over, producer i must search for another RL supplier for negotiation until a cooperative agreement is achieved. The third tier determines producers’ production (qi, " i 2 I) based on governmental strategies and output of negotiations in the ﬁrst

and second tiers. 3. Model

A three-stage game-based model is constructed in this section to formulate the aforementioned bargaining problem in competitive green supply chains. Stage 1 conceptualizes the government’s objective by maximizing social welfare (SW) to derive the equilibrium solutions for f and s. In Stage 2, this work applies the asymmetrical NB game with uncertain reser-vation prices, expected proﬁts and breakdown risks to seek negotiation solutions (i.e., pyj;iand yj,i) for cooperative agreements

between producers and RL suppliers given f and s. Based on the government’s inﬂuence via f and s as well as the output of cooperative agreements, producer production quantities are determined in Stage 3. To approximate equilibrium solutions of

the three-stage game-based model, this work adopts backward induction (Kreps, 1990) starting from Stage 3 under the goal

of producer proﬁt maximization, ending with Stage 1 for the solutions of the government’s ﬁnancial intervention. The details of model formulation associated with these three-stages are presented in the following subsections.

3.1. Production solutions of competing producers (Stage 3)

In this stage (Stage 3), this work formulates the problem of producer competition in ﬁnal product production given gov-ernmental inﬂuential strategies and agreements with cooperative RL-suppliers. To facilitate model formulation, we assume unit price (px) for virgin-components (x) is the same for all producers. ByAssumptions 1–4, we infer that any given producer i

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Max qi

p

i¼ 1 XI i0 ¼1 qi0Þ " # qi px

s

xqi pyj;i

s

yqi cmqi fqi;

8

i ð1Þ where cmis the marginal cost for producing a ﬁnal product unit. Notably, in Eq.(1), qirepresents the decision of producer i for

production quantities, which must be determined at this stage; pyj;iis a negotiation agenda determined in Stage 2; and f is the

unit green tax associated with a ﬁnal product unit, and is determined by the government in Stage 1. The derivations of pyj;i

and f are shown in the following subsections.

To ensure the existence of equilibrium solutions of qi(" i), the ﬁrst-order condition in Eq.(1)with respect to qi("i) must

be satisﬁed as 1 X I i0 ¼1 qi0 q_i p_x

s

_x p_y j;i

s

y cm f ¼ 0;

8

i ð2Þ

Based on Eq.(2), one can further prove that the objective function of producer i, as represented by Eq.(1), is concave on qi

as the corresponding second-order condition is satisﬁed (i.e.,@2pi

@2qi¼ 2 < 0;8iÞ. Since all competitive producers involved in

the oligopoly competing context adopt Cournot competition, as stated inAssumption 1, one can derive the reaction function (^qiÞ of producer i with respect to qias

^ qi¼

1 px

s

x pyj;i

s

y cm f

I þ 1 ;

8

i ð3Þ

Notably, ^qi can be regarded as antecedent of the equilibrium solution of qias this work must backwardly input such a

function in to Stages 2 and 1 to approximate the equilibrium solutions of pyj;i and yj,i(i.e., the negotiation agendas deﬁned

in Stage 2) as well as those of f and s (i.e., the governmental ﬁnancial instruments deﬁned in Stage 1), such that the equilib-rium solution of qican then be derived.

3.2. Negotiation between a producer and RL-supplier (Stage 2)

This stage deals with the negotiation problem between I competing producers and J competing RL-suppliers using the

asymmetrical NB solutions, where the uncertainties of reservation prices with respect to p_y

j;i associated with producers

and RL-suppliers as well as expected proﬁts and breakdown risks from outside options are considered. According toMuthoo

(2002), a generalized form of a two-player (A and B) asymmetrical NB game can be expressed as MaxðuA;uBÞ2HðuA dAÞ

g

ðuB dBÞ1g, where uAand uBrepresent the utilities of players A and B, respectively, from obtaining possible shares of a

com-mon interestH(e.g., a pie) under the achievement of an agreement subject to uA+ uB 6H; dAand dBrepresent the utilities of

players A and B, respectively, when they fail to reach an agreement subject to dA6uAand dB6uB; and

g

represents the

bar-gaining power of player A relative to that of player B subject to 0 <

g

< 1. The asymmetrical NB solutions (u

Aand uBÞ can then be

derived to characterize the equilibrium solutions of players A and B in the bargaining game.

Utilizing the above NB game concept, this work formulates the green supply chain cooperation problem as an asymmet-rical NB game in which uncertainties of reservation prices of pyj;i, breakdown risks and expected proﬁts obtained from

out-side options (i.e., cooperating with other partners) are conout-sidered. The proposed asymmetrical NB product is given by

Max ðpA;pjÞ2H ^

p

i ^di h iaðf ;sÞ ^

p

j ^dj h ibðf ;sÞ ;

8

ði; jÞ ð4Þ

where ^

p

iand ^

p

jrepresent the proﬁts of producer i and RL-supplier j, respectively, obtained under a cooperative agreement

obtained during a given negotiation event; ^diand ^djrepresent the expected value of net proﬁt associated with producer i and

RL-supplier j, respectively, when they cannot reach agreement, but rather cooperate with other players in any the subse-quent negotiation events. Moreover, conditions ^di6

p

^iand ^dj6

p

^jmust hold.

Consider the probabilities under both agreement and disagreement conditions for both producer i and RL-supplier j in any given negotiation event. Therein, this work introduces the concept of reservation price for pyj;i to characterize the potential

outcome of negotiation and breakdown probabilities in a given negotiation event. This work deﬁnes pyj;i and pyj;i as the

res-ervation prices of producer i and RL-supplier j, respectively, to represent the maximum price producer i is willing to pay and the minimum price RL-supplier j is willing to sell a unit of recycled components, respectively. We assume both producer i and RL-supplier j do not know the other’s reservation price; furthermore, pyj;iand pyj;iare drawn from a uniform distribution

bounded by the range [p0, ptop], where p0and ptopare lower and upper bounds speciﬁed for the random variables of the

uni-form distribution. Accordingly, pyj;iand pyj;i are independent and identically distributed (IID) random variables.

Theorem 3.1. Under asymmetrical information conditions for reservation price of pyj;i, any given pair of negotiators composed of a

producer and an RL-supplier has a 1/6 probability of achieving a cooperative agreement, and a 5/6 probability of negotiation breakdown in any given negotiation event.

The proof ofTheorem 3.1is straightforward. Notably, the equilibrium solution of pyj;i(denoted by p

yj;iÞ exists only when

pyj;i6p

yj;i

6pyj;i. By order statistics (Ross, 1993), the probability Uðpyj;i6pyj;iÞ can be derived by Uðpyj;i6pyj;iÞ ¼

Rptop

p0

Ry p0

/ðy; yÞdydy ¼Rptop

p0

Ry

p0/ðyÞ/ðyÞdydy ¼

1

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respec-tively. Furthermore,Uðpyj;i6p

yj;i6pyj;iÞ ¼Uðp

yj;i6pyj;i6pyj;iÞ ¼Uðpyj;i6pyj;i6p

yj;iÞ ¼

1

3under the conditionUðpyj;i6pyj;iÞ. We

then infer the probability for the achievement of a cooperative agreement byU ðpyj;i6p

yj;i

6pyj;iÞ \ ðpyj;i6pyj;iÞ

¼Uðpyj;i6 pyj;iÞ 1 3¼ 1

6, and the probability of negotiation breakdown is 5 6.

The next step is to specify ^

p

i; ^

p

j; ^diand ^djembedded in Eq.(4). As mentioned, ^

p

iand ^

p

jare the proﬁts of producer i and

RL-supplier j obtained under cooperative agreement in the present negotiation event. By combining Eqs.(1) and (3), we infer ^

p

i

and ^

p

jgiven by ^

p

i¼ 1 XI i0 ¼1 ð^qi0Þ " # cm ( ) ^ qi ½px

s

xq^iþ pyj;i

s

y^qi f ^qi;

8

i ð5Þ ^

p

j¼ ½pyj;i

s

yq^i cyð

s

y crÞ^qi ccolðc^qiÞ cproðcrqiÞ þ sðcr^qiÞ;

8

j ð6Þ where ^qi¼

1pxsxp_yj;isycmf

Iþ1 which is approximated previously (Stage 3); ccoland cprorepresent unit costs of collecting and

pro-cessing EOL-products for recycling, respectively. In terms of ^

p

i(Eq.(5)), this work mainly accounts for revenues of selling

ﬁnal products, production costs, and component procurement and green taxes charged by the government. In terms of ^

p

j

(Eq.(6)), this work considers the revenues obtained by the RL-supplier from selling recycled components to producers

and the costs in recycled component replenishment, EOL product collection and processing for recycling as well as green subsidies from the government. However, ^qi¼

yj;i

sy(Assumption 3); thus, under equilibrium conditions one can determine that

yj,iis a function of pyj;iand is given by yj;i¼

s

yð1 px

s

x pyj;i

s

y cm f Þ

I þ 1 ;

8

i; j ð7Þ

Furthermore, using Eqs.(3), (5) and (6)can be rewritten as

^

p

i¼ ð1 px

s

x pyj;i

s

y cm f Þ 2 ðI þ 1Þ2 ;

8

i ð8Þ ^

p

j¼

ðpyj;i

s

yþ ðs þ cy cproÞcr cy

s

y ccolcÞð1 px

s

x pyj;i

s

y cm f Þ

I þ 1 ;

8

j ð9Þ

To formulate ^diand ^dj, this work mainly considers: (1) the expected proﬁts (Eið^

p

ijj0Þ and E_jð^

p

_jji0ÞÞ earned by producer i and

RL supplier j when cooperating with other players, and (2) the expected values (Ei(cbre) and Ej(cbre)) of breakdown cost (cbre)

associated with producer i and RL-supplier j in any given negotiation event. Consider the case in which producer i fails to achieve an agreement with RL-supplier j in the present negotiation event, but searches for another RL-supplier from the J 1 RL-supplier pool until a cooperative agreement is obtained. Therein, Eið^

p

ijj0Þ is deﬁned as the expected value of proﬁt

associated with producer i when cooperating with RL supplier j0(j0–j) in another negotiation event. According toTheorem 3.1, the probability of negotiation breakdown is5

6in a given negotiation event, and thus, Eið^

p

ijj0Þ can be computed by Eið^

p

ijj0Þ ¼1 6

p

^ijj0 XJ1 e¼1 5 6 e1 ;

8

i ð10Þ where ^

p

ijj0¼ ð1pxsxpy j0 ;isycmf Þ 2 ðIþ1Þ2 ðj 0

–jÞ. Similarly, let Ejð^

p

jji0Þ be the expected value of proﬁt associated with RL-supplier j when

cooperating with producer i (i0–i) in another negotiation event. Then, Ejð^

p

jji0Þ can be derived as Ejð^

p

jji0Þ ¼1 6

p

^jji0 XI1 e¼1 5 6 e1 ;

8

j ð11Þ where ^

p

jji0¼ ½p_y

j;i0

s

yþ ðs þ cy cproÞcr cy

s

y ccolc

1pxsxpy j;i0sycmf

Iþ1 (i

0

–i). By contrast, breakdown cost (cbre) is the additional

cost dyadic negotiators pay when a negotiation event breaks down in disagreement, and is assumed a constant to facilitate analysis. Therefore, this work introduces expected values (Ei(cbre) and Ej(cbre)) of breakdown costs to characterize potential

risks of breakdown associated with producer i and RL-supplier j and, thus, approximate Ei(cbre) and Ej(cbre) by EiðcbreÞ ¼ cbre XJ1 e¼1 5 6 e1 " # ;

8

i ð12Þ EjðcbreÞ ¼ cbre XI1 e¼1 5 6 e1 " # ;

8

j ð13Þ

Using Eqs.(10)–(13), one can approximate ^diand ^dj by ^

di¼ Eið^

p

ijj0Þ E_iðc_breÞ;

8

i and j0–j ð14Þ

^

(8)

By combining Eqs.(8), (9), (14), and (15)with Eq.(4), the proposed asymmetrical NB product can then be reformulated as Max ðpA;pjÞ2H ^

p

i Eið^

p

ijj0Þ E_iðc_breÞ h iaðf ;sÞ ^

p

j Ejð^

p

jji0Þ E_jðc_breÞ h ibðf ;sÞ ;

8

ði; jÞ ð16Þ

Theorem 3.2. Under equilibrium conditions, the proﬁt earned by any given player (either a producer or an RL-supplier) from a cooperative agreement at a given negotiation event is always greater than the expected value of net proﬁt earned by cooperating with any other players at any following negotiation event.

The proof ofTheorem 3.2is shown inAppendix B.1. In addition to supporting the existence of NB solutions by proving

^

di6

p

^_i and ^d_j6

p

^_j_ð8i; jÞ, the generalization ofTheorem 3.2also indicates that for any given player (either a producer or an RL-supplier) in the specified bargaining framework, profit obtained under a cooperative agreement is always greater than that obtained under disagreement even though the player is likely to reach agreement with another player in a subsequent negotiation event. Drawing fromTheorem 3.2, each player should devote their effort to achieving a cooperative agreement at the present negotiation event; waiting for a second chance to reach an agreement is never a good negotiation strategy in the specified bargaining framework.

UsingTheorem 3.2and Eq.(16)one can then derive the equilibrium solution of p_y

j;i(denoted by p

yj;iÞ by utilizing NB

solu-tions of ^

p

iand ^

p

j. Therefore, p yj;i¼ bðf ;sÞð1NiÞG2 ðIþ1Þ26½Njaðf ;sÞNibðf ;sÞcbreaðf ;sÞð1NjÞ GH Iþ1 ½2bðf ;sÞð1NiÞsy G ðIþ1Þ2þ½aðf ;sÞð1NjÞsy GH Iþ1 ;

8

ði; jÞ

s:t: bðf ; sÞð1 NiÞG2P6ðI þ 1Þ2½Nj

a

ðf ; sÞ Nibðf ; sÞcbreþ

a

ðf ; sÞð1 NjÞðI þ 1ÞGH

ð17Þ

where G ¼ 1 px

s

x cm f ; H ¼ ðs þ cy cproÞcr cy

s

y ccolc; Ni¼ 1 5₆ J1

ð8iÞ and Nj¼ 1 5₆ I1

ð8jÞ. Note that G, H, Ni

and Njare unnamed parameters speciﬁed only for model simpliﬁcation. The proof of pyj;i is given inAppendix A.1.

By inputting Eq.(17)into Eqs.(8) and (9), the proﬁts (^

p

iand ^

p

jÞ of producer i and RL-supplier j obtained from cooperative

agreement under equilibrium conditions can then be approximated. Furthermore, using Eqs.(7) and (17)one can also derive

the equilibrium solution of yj, i(yj;iÞ as

y j;i¼

s

y G

s

ypyj;i

I þ 1 ;

8

ði; jÞ ð18Þ

Theorem 3.3. The speciﬁed I J producer andRL-supplier bargaining framework has NB solutions for any given pair of a producer and RL-supplier at a bilateral negotiation event. Under NB equilibrium conditions, the following is true:

bðf ; sÞð1 NiÞ^

p

i ¼

a

ðf ; sÞð1 NjÞ^

p

jþ 6ð

a

ðf ; sÞNj bðf ; sÞNiÞcbre;

8

ði; jÞ ð19Þ

where ^

p

i and ^

p

j represent the proﬁts earned by producer i and RL-supplier j under NB equilibrium conditions. The proof of

Theorem 3.3is given inAppendix B.2.Theorem 3.3indicates that ^

p

i and ^

p

j are contingent upon the dyadic players’ relative

bargaining power and number of competitors under NB equilibrium conditions. Notably, b(f, s) = 1

a

(f, s), Ni¼ 1 5₆ J1

ð8iÞ, and Nj¼ 1 56

I1

ð8jÞ. Generally, the bargaining power of a producer exceeds that of an RL-supplier (i.e.,

a

(f, s) > b(f, s)) during negotiations as EOL product collection and recycling technology is not unique in the RL market. Moreover, the num-ber of producers is smaller than the numnum-ber of RL suppliers (i.e., I < J) in the specified bargaining framework, indicating that Ni> Nj. Therefore,Theorem 3.3implies that producer profit is greater than RL-supplier profit (i.e., ^

p

i > ^

p

jÞ under NB

equi-librium conditions.

Additionally, the generalization ofTheorem 3.3suggests the effects of bargaining power and number of competitors on

player proﬁts in negotiations. In this case, as the bargaining power of the RL-supplier (b(f, s)) decreases, the bargaining power of the producer (

a

(f, s)) increases, and thus, producer proﬁt (^

p

iÞ increases based on Eq.(19). From a producer perspective,

that many competitors (i.e., competing producers) exist in competing contexts suggests a great number of negotiation opportunities for RL-suppliers, thereby increasing the value of Njand decreasing producer proﬁt

p

^i

according to Eq. (19). A similar inference also applies to the case of RL-suppliers. Brieﬂy, bargaining power and the number of competitors adversely affect player proﬁts in the producer and RL-supplier bargaining framework. Such a generalization supports the rationalization of the form of coalitions observed in some negotiation cases, e.g., an assembler negotiating with supplier coalitions (Nagarajan and Bassok, 2008).

Proposition 3.1. Under NB equilibrium conditions of the speciﬁed I J producer and RL-supplier bargaining framework, the proﬁt of the producer is the same as that of the RL-supplier (i.e.,^

p

i ¼ ^

p

j;8i; j) if I = J and

a

ðf ; sÞ ¼ Ni

NiþNj.

The proof ofProposition 3.1is straightforward. Let I = J and

a

ðf ; sÞ ¼ Ni

NiþNj; thus, Ni¼ Nj¼ N)

a

ðf ; sÞ ¼ bðf ; sÞ ¼

1 2.

(9)

bðf ; sÞð1 NiÞ^

p

i ¼

a

ðf ; sÞð1 NjÞ^

p

j þ 6ð

a

ðf ; sÞNj bðf ; sÞNiÞcbre )1 2ð1 NÞ^

p

i ¼12ð1 NÞ^

p

jþ 612N12N cbre ) ^

p

i ¼ ^

p

j ;

8

ði; jÞ ð20Þ

Thus,Proposition 3.1is proved.Proposition 3.1is a special case of green supply chain cooperation, in which the producer and RL-supplier obtain the same proﬁt from a cooperative agreement under NB equilibrium conditions.

3.3. Government ﬁnancial instruments (Stage 1)

This stage investigates the effect of green taxes (f) and subsidies (s) on cooperative agreements (i.e., p yj;iand y

j;iÞ and

play-ers profits in the specified bargaining framework. Drawing from the concept of social welfare (SW) maximization, which is extensively used in literature for green policy determination (Dobbs, 1991;Walls and Palmer, 2001), this work proposes an objective function for the government that has the following four key elements: (1) consumer surplus (CS); (2) chain-based producer surplus (PS); (3) production-induced environmental costs (ECs); and, (4) recycling-induced environmental benefits (EBs). Therefore, the objective function of the government is given by

Max f ;s SW ¼ CS þ PS ECs þ EBs ¼ 1 2 XI i¼1 ^ q i !2 þ X I i¼1 ^

p

iþ ^

p

jji ! D X I i¼1 ^ q i þ V XI i¼1 cr^q i ð21Þ

where D and V represent unit green cost and beneﬁt induced by producing a unit product and recycling a unit EOL product,

respectively. Determining the values of D and V requires sophisticated economic approaches (Bovenberg and Goulder, 1996;

Kalimo, 2006). This work sets the ratio of D to V at 1:20 in Eq.(21)to facilitate further analysis (Stern, 2006). Therefore, Eq.

(21)can be rewritten as Max f ;s SW ¼ 1 2 XI i¼1 ^ q i !2 þ X I i¼1 ^

p

i þ ^

p

jji ! þ ð20cr 1ÞDX I i¼1 ^ q i ð22Þ

However, byAssumption 6, we speculate that the government may attempt to balance induced budget items, i.e., green

taxes and subsidies, to avoid additional ﬁnancial loading. Thus, the above objective function should be subject to the spec-iﬁed balanced budget condition given by

s X I i¼1 cr^q i ¼ f XI i¼1 ^ q i; f ; s P 0 ð23Þ

Notably, the involvement of ECs and EBs in the above objective function of the government is rooted in the concept of Green Gross Domestic Product (Green GDP), which was developed by the World Commission on Environment and Develop-ment in 1987. The basic idea underlying the Green GDP is that domestic ecological and environDevelop-mental damage should be regarded as a gross domestic cost and, thus, should be integrated into net GDP estimations. Furthermore, a growing number of environmental economists have argued for the importance of both environmental costs and savings when assessing the

environmental protection system performance (Bovenberg and Goulder, 1996; Mayers et al., 2005; Ruedenauer et al., 2005).

Accordingly, this work considers both ECs and EBs in characterizing the objective function of the government with respect to environmental proﬁts obtained from intervention in the speciﬁed producer and RL-supplier bargaining framework.

Moreover, estimating the values of parameters D and V is theoretically feasible but beyond the scope and purpose of this work. Furthermore, some studies have suggested that the environmental impact of a product is from two main sources—(1)

hazardous wastes generated by the manufacturing process (Sheu, 2007), and (2) hazardous components in a product (

Huis-man et al., 2007; Mayers et al., 2005). Therefore, approximating the value of D based on ofﬁcial report by the governmental

environmental protection administration (EPA) with respect to aggregate external costs of hazardous wastes associated with the target product seems promising. Then, the value of V is estimated using the aforementioned V/D ratio.

To derive equilibrium solutions of f and s (f⁄_{and s}⁄_{), the effects of f and s on bargaining power should be speciﬁed in}

ad-vance. Thus, we assume that a linear form (Eq.(24)) characterizes the effects of f and s on the relative bargaining power of a producer (

a

(f, s)).

a

ðf ; sÞ ¼ a0 ðaf þ bsÞ ð24Þ

where a0is the initial bargaining power of a producer relative to the that of the RL-supplier without governmental ﬁnancial

intervention, and 0 6 a061; a and b represent the incremental effects of f and s on

a

(f, s), respectively, subject to a > 0, b > 0

and 0 6 a0 (af + bs) 6 1.

Using Eqs.(22)–(24), one can then derive the equilibrium solutions of f and s (denoted by f⁄_{and s}⁄_{, respectively) given by} f_¼½ð20cr 1ÞD þ Lða0K þ 2K 3a0LÞ þ ð1 a0ÞK2 3a0KL

½ð20cr 1ÞD þ Lð4a0 3

q

L þ

q

K þ 2Þ

q

Kð3L þ KÞ

ð25Þ s_¼f

(10)

where K = 1 px

s

x cm; L = (cy cpro)cr cy

s

y ccolc; and

q

¼acrþbcr . Note that K, L, and

q

are unnamed parameters speciﬁed

for model simpliﬁcation. The proof of f⁄

and s⁄

is given inAppendix A.2.

Proposition 3.2. Under the goal of SW maximization, the optimal solutions of the government for green taxes and subsidies are f⁄_{= s}⁄_{= 0 when the following conditions hold: (1) cr = 0.05, (2) a}

0= 0.5, and (3) K = L.

Proposition 3.2can be proved easily using Eqs.(25) and (26)subject to the aforementioned conditions. This proposition

suggests that the phenomenon in that without the aid of ﬁnancial instruments the government can achieve the goal of SW maximization only when (1) the product of collection and recycling rates equals 0.05, (2) the initial bargaining power of pro-ducers and RL-suppliers is the same, and (3) the ante-contract comparative proﬁts of a producer and RL-supplier are the same (i.e., 1 px

s

x cm= (cy cpro)cr cy

s

y ccolc).

Once f⁄_{and s}⁄_{are determined, one can feed their values back to Stage 2 to determine the values of p} yj;iand y

j;i, and then to

Stage 3 to determine the value of ^qias well as the proﬁts obtained by producers and RL suppliers in the proposed bargaining

framework. 4. Analysis

Based on the derived equilibrium solutions, qualitative and quantitative analyses are conducted as follows to provide additional insights into the correlations among government, producer, and RL-supplier decision variables in the speciﬁed producer and RL-supplier bargaining framework.

4.1. Qualitative analysis

Proposition 4.1. Financial instruments vs. bargaining power). For government use of ﬁnancial instruments, f⁄_{and s}⁄_determine

the relative bargaining power of dyadic players by

a

ðf_;_s_ÞTbðf_;_s_Þ; _{if f}_T2a0 1 2

q

i:e:; s _T 2a0 1 2ðacr þ bÞ :

The above proposition characterizes the relationship between government instruments and the relative bargaining power

of players in the speciﬁed producer and RL-supplier bargaining framework. To maximize SW, the government may adopt f⁄

and s⁄_{as ﬁnancial instruments, thereby changing the bargaining power of a producer from a}

0to a0

q

f⁄, and that of the RL

supplier from 1 a0to 1 a0+

q

f⁄. Consequently, government intervention using ﬁnancial instruments decreases producer

bargaining power and increases that of the RL-supplier in negotiations. The rule provided by this proposition can then be used to analyze the trade-off in relative bargaining power between producers and RL suppliers under government ﬁnancial intervention. The proof ofProposition 4.1is given inAppendix B.3.

Remark 4.1 (Financial instruments vs. negotiation agendas). Increases in green tax (f) or green subsidy (s) increases pyj;iand

decreases yj,i; conversely, a decrease to f or s decreases pyj;iand increases yj,i. This remark is based on the derivatives shown in

Eqs.(27)–(30). Under governmental intervention with ﬁnancial instruments, RL-suppliers are stimulated to bid up the unit

price (pyj;iÞ of recycled components sold to producers due to the increased bargaining power (b(f, s)). Conversely, green

taxation increases producer production cost and weakens their bargaining power in negotiations with RL-suppliers, thus

discouraging producer from obtaining additional recycled components (i.e., reduction of yj,i) in negotiations with

RL-suppliers that move toward cooperative agreements.

@p_yj;i @f ¼ 6qðNjþNiÞcbreþð1NjÞ q_GHða0qf ÞðGHÞ Iþ1 þð1NiÞ q_{G2 2ð1a0þ}qf ÞG ðIþ1Þ2 n o D n ½2ð1NiÞsyqGð1a0þqf Þ ðIþ1Þ2 ½ð1NjÞsy qðGHÞþ2ða0qf Þ Iþ1 n o D2 >0 ð27Þ where n ¼ ð1 a0þ

q

f Þð1 NiÞ G 2

ðIþ1Þ2 6½ða0

q

f ÞNj ð1 a0þ

q

f ÞNicbre ða0

q

f Þð1 NjÞIþ1GH; D¼ ½2ð1 a0þ

q

f Þð1 NiÞ

s

y_ðIþ1ÞG2þ ½ða0

q

f Þð1 NjÞ

s

yGH_Iþ1; both n andDare unnamed parameters speciﬁed only for model simpliﬁcation. @pyj;i @s ¼ @pyj;i @ ¼ cr_crf @pyj;i @f >0 ð28Þ @yj;i @f ¼

s

y 1 þ

s

y @p_yj;i @f I þ 1 <0 ð29Þ @yj;i @s ¼ cr

s

y 1 þ

s

y @p_yj;i @f I þ 1 <0 ð30Þ

(11)

Remark 4.2 (Bargaining power vs. negotiation agendas). Under governmental ﬁnancial intervention, the decrease in producer bargaining power (

a

(f, s)) corresponding to the increase in RL-supplier bargaining power (b(f, s)) increases pyj;i and decreases

yj,i. This remark is developed by taking the partial derivatives of pyj;iand yj,ibased on the bargaining power

a

(f, s) and b(f, s), as

in Eqs.(31)–(34). In reality,Remark 4.2reasons how the relative bargaining power of players influences negotiation agendas pyj;i and yj,iunder governmental financial intervention. As mentioned, governmental financial intervention via green taxes

and subsidies decreases in producer bargaining power and increase that of the RL-supplier. Therefore, an RL-supplier is prone to bid up the unit price of recycled components (pyj;iÞ during negotiation with a producer toward a cooperative agreement.

Additionally, producer bargaining power is adversely affected by green taxation in this case, such that a producer may com-promise with an RL-supplier on a higher value of pyj;i, leading to a lower demand for recycled components (yj,i) speciﬁed in

the negotiation agenda, compared with the case without government intervention.

@pyj;i @

a

¼ ð1 NiÞ G 2 ðIþ1Þ2þ 6ðNjþ NiÞcbreþ ð1 NjÞ GH Iþ1 h i

D

n ½2ð1 NiÞ

s

y_ðIþ1ÞG2þ ½ð1 NjÞ

s

yGH_Iþ1 n o

D

2 <0 ð31Þ @pyj;i @b ¼ @pyj;i @

a

>0 ð*b ¼ 1

a

) @b ¼ @

a

Þ ð32Þ @yj;i @

a

¼ @pj;i @

a

@yj;i @pyj;i ¼@pj;i @

a

ð

s

yÞ2 I þ 1 >0 ð33Þ @yyj;i @b ¼ @yyj;i @

a

<0 ð*b ¼ 1

a

) @b ¼ @

a

Þ ð34Þ

Remark 4.3 (Negotiation agendas vs. production quantities). Under governmental ﬁnancial intervention, the increase of recy-cled component unit price (pyj;i) decreases the guaranteed quantities of recycled components (yj,i) speciﬁed in a negotiation

agenda, thus decreasing the producer production (^qi). This remark is based on derived results by Eqs.(35) and (36), which

indicate how pyj;iand yj,ispeciﬁed in negotiation agendas affect the amount (^qiÞ of products produced. Under governmental

ﬁnancial intervention, an RL-supplier is likely to raise pyj;iduring negotiation with a producer. This may weaken producer

intention to develop a contract with an RL-supplier to acquire recycled components for production, thereby reducing yj,i

in negotiation agendas. Consequently, the amount of ﬁnal products produced ^qiis decreased. @^qi @pyj;i ¼

s

y I þ 1<0;

8

i ð35Þ @^qi @yj;i ¼

s

y @p_yj;i @yj;i I þ 1 ¼ 1

s

y >0;

8

i ð36Þ 4.2. Numerical illustration

In the subsequent quantitative analysis, the notebook computer manufacturing industry is utilized to demonstrate the effects of governmental ﬁnancial intervention on the speciﬁed green supply chain bargaining framework. Particularly, this work presets cost-related parameters needed in the proposed model using data obtained from interview surveys of

manag-ers of global logistics sectors of notebook computer producmanag-ers and recyclmanag-ers.Table 1summarizes the key preset parameters

Table 1

Preset values of parameters for quantitative analysis.

1. Government-related parameters 2. Number of competitors

Collection rate (%) Recycling rate r (%) Unit green cost D Number of competitive producers I Number of competitive RL-suppliers J

80 80 0.8 2 2 3. Producer-related parameters Initial bargaining power a0 Incremental effect of f on producer’s bargaining power (a)

Incremental effect of s on producer’s bargaining power (b) Unit price of virgin-components px Quantities of virgin-components for unit product productionsx

Quantities of recycled components for unit product productionsy

Unit cost of manufacturing cm

0.9 0.5 0.5 0.005 0.5 0.5 0.03

4. RL-supplier related parameters Others

Unit cost for recycled component procurement cy

Unit cost for EOL-product collectionccol

Unit cost for processing EOL product cpro

Breakdown cost in each negotiation event cbre

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in this study case. Sensitivity analysis was then conducted for unit green tax (f) starting from the value of 0.4–0.6 with an increment 0.01 to characterize changes to player bargaining power, negotiation decisions, and acquired proﬁts in the pro-posed bargaining framework. According to preliminary analysis, the aforementioned range of f values covers all feasible

do-mains of equilibrium solutions of decision variables, including f⁄_{, which equals 0.42, approximated using the preset}

parameters (Table 1). Thus, this work subjects the corresponding quantitative results to further analysis.Figs. 2–4present analytical results.

Fig. 2indicates that the bargaining power (

a

(f, s)) of a producer decreases as the unit green tax (f) increases, and that of the

RL-supplier increases as f increases within the feasible domain of 0.4–0.6. Such a generalization is consistent with the expec-tation of the trade-off relationship in bargaining power of a producer and RL supplier in the specified bargaining framework. Furthermore, under the influence of green taxation, producer bargaining power is less than that of an RL-supplier. Compared with 0.9 (i.e., the initial value of a0(Table 1)), such a decline in bargaining power is significant and coincides with the

pre-dicament global producer face in the EU market. This ﬁnding is also consistent with that obtained byWilson (2006), who

identiﬁed the increase in the inﬂuence of recyclers under green legislation.

An increase in unit green tax (f) increases pyj;i and decreases yiin negotiation agendas, thereby decreasing production

quantities (qi) (Fig. 3). This ﬁnding is consistent withRemark 4.3in qualitative analysis, suggesting that governmental

ﬁnan-cial intervention has a negative effect on negotiation agendas from a producer perspective. Furthermore, given the preset parameters (Table 1), the equilibrium solution of f is 0.42, which contributes to p

yj;iequaling 0.0026, which is the lowest

fea-sible solution of pyj;i compared with other solutions (Fig. 3). Therefore, we reason that under equilibrium conditions, unit

price of the recycled component supply (p

yj;iÞ obtained through negotiations is less than that of any other feasible solutions

in this work. Furthermore, we infer that a producer always intends to achieve a cooperative agreement under a low pyj;ivalue

regardless of whether governmental ﬁnancial instruments (f and s) intervene in the bargaining framework. Conversely, the bargaining power of an RL supplier is enhanced by governmental green subsidies and, thus, an RL supplier can adopt strat-egies such as increasing pyj;iand limiting yj,ito a guaranteed proﬁt value when entering into a cooperative agreement with a

producer.

Fig. 4provides the following three generalizations. First, under governmental ﬁnancial intervention, the proﬁt ^

p

j

of an RL-supplier is greater than that of a producer ^

p

i

in any scenario within the feasible domain. Such a generalization is

con-sistent with the fundamentals of the asymmetrical NB solutions (Muthoo, 2002), revealing that the player with relatively

greater bargaining power yields more remaining utility which refers to net aggregated proﬁts, i.e., ð^

p

iþ ^

p

jÞ

Eið^

p

ijj0Þ E_iðc_breÞ þ E_jð^

p

_jji0Þ E_jðc_breÞ

, in this work. Second, under equilibrium conditions in which f⁄_{= 0.42, the obtained}

sum of player profits is greater than that of others obtained within the feasible domain. Notably, the summed profits ob-tained at f = 0.4 and f = 0.41 are beyond the feasible domain (Fig. 3), even though they are greater than the summed profits obtained at f⁄_{= 0.42. Additionally, increasing the unit green tax (f) will likely increase producer production costs and weaken}

producer bargaining power when negotiating with RL-suppliers (Fig. 2). Therefore, the overall effect on ^

p

iis straightforward

and negative, as characterized by the ^

p

icurve (Fig. 4). Conversely, the effect of raising either f or s on RL-supplier proﬁts (^

p

jÞ

is arguable. The value of ^

p

j increases as f increases initially, and then declines when f > 0.45, implying the existence of a

counter-effect due excess governmental intervention on both ^

p

iand ^

p

j(Fig. 4).

(13)

Briefly, under governmental financial intervention, the bargaining power of a producer declines, whereas that of an RL-supplier increases. Such a trade-off effect further benefits an RL-RL-supplier when negotiating with a producer, thus leading to an increased unit price for recycled components an RL-supplier is willing to offer a producer, which in turn weakens pro-ducer demand for recycled components. Consequently, the outcome of the aforementioned negotiation agendas is unfavor-able for producer profits, and favorunfavor-able for RL-supplier profits under equilibrium conditions.Fig. 5presents the relationships among governmental financial intervention, bargaining power, negotiation agendas, and resulting profits of players. 4.3. Number of competitors and its impact in bargaining decisions

The following numerical study examines the impact of the number of competitors on bargaining solutions in the producer and RL-supplier bargaining framework. In addition to the basic scenario (I = J = 4), this work considers the following two

dif-Fig. 3. Quantitative analysis (II): unit green tax vs. negotiation agendas and production.

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ferent scenarios: (1) the number of producers is greater than the number of RL-suppliers (i.e., I > J); and (2) the number of producers is less than that of RL suppliers (i.e., I < J). All preset parameters (Table 1) remain the same except for the number of competitors (I and J).Figs. 6 and 7summarize analytical results for p

yj;i, y

j;i;qi, and player proﬁts.

Fig. 6indicates that the asymmetry in the number of producers and RL suppliers favors producers when bargaining in

negotiations. Given the number of RL-suppliers (J), few producers (i.e., I < J) existing in the bargaining framework represents few outside options to RL-suppliers, implying a reduced likelihood of achieving a agreement with another producer when current negotiations fail. Therefore, an RL supplier is likely to decrease pyj;iin the case I < J to facilitate achieving a cooperative

agreement with a producer. The case I > J implies that many competing producers exist and share a given product demand

market, where each competing producer is prone to increase its production amount qiunder Cournot competition. This may

lead to RL-supplier expectation of an increase in overall recycled component demand, and thus, an RL-supplier is willing to

reduce pyj;iwhen negotiating with a producer toward a cooperative agreement. Consequently, the amount of recycled

com-ponents (yj,i) and ﬁnal product production (qiÞ increase, as compared with those for the case in which I = J.

In contrast withFig. 6, the analytical results ofFig. 7further indicate that asymmetry in the number of producers and RL-suppliers is proﬁtable to dyadic players in negotiations. Such a positive effect is particularly signiﬁcant as the number of competing producers decreases to 2 (i.e., duopoly competition) given that RL-suppliers compete in an oligopoly context, where J = 4 in this case. If one further compares the analytical results for two extreme cases—I = 2 and I = 7 (Figs. 6 and 7), one can determine that the value of pyj;iin the case when I = 2 is higher than that when I = 7. Nevertheless, the induced

promotional effect on qiwhen I = 2 is more signiﬁcant than that when I = 7.

Accordingly, we infer that a bargaining framework underlying the duopoly–oligopoly context where only two competing producers exist and negotiate with a few competing RL-suppliers may contribute to a negotiation outcome that is most prof-itable to dyadic players in bilateral negotiations.

Government's financial

instruments Bargaining power Negotiation agendas Production decision Players' profits

Fig. 5. Relationships between key variables in the speciﬁed bargaining framework.

I < J

I=J=4

I > J

(15)

5. Conclusions and recommendations 5.1. Conclusions

This work utilized a bargaining framework to analyze negotiations between producers and RL-suppliers toward cooper-ative agreements under governmental ﬁnancial intervention with the goal of SW maximization. With the proposed 3-stage game-based model, this work formulates governmental objective functions to approximate equilibrium solutions for green taxation and subsidization, followed by the use of the asymmetrical NB game with uncertainties to determine negotiation agendas and decisions of players in the speciﬁed bargaining framework.

Drawing from the proposed model and analytical results, the following summarizes several conclusions that help address the four research questions.

In the speciﬁed bargaining framework, each producer seeks a cooperative RL-supplier via sequential bilateral negotia-tions. During the negotiation process, dyadic players interact on the unit price of recycled component supply (pyj;iÞ and

guar-anteed supply (yj,i) toward a cooperative agreement. A cooperative agreement is achieved only when the equilibrium

solutions p yj;iand y

j;iexist, which can be derived by Eqs.(17) and (18), respectively. If negotiation fails, dyadic players seek

another player for negotiation.

In the aforementioned bilateral negotiation under governmental intervention, each player is concerned about (1) govern-mental ﬁnancial instruments, (2) potential threats from outside competitors (e.g., bidding and competing strategies), and (3) the reactions of dyadic players in negotiation. For instance, a producer will account for the unit green tax (f⁄_{) levied by the}

government and RL-supplier’s decisions in negotiation agendas (i.e., pyj;iand yj;iÞ to evaluate potential costs, and the potential

risks due to negotiation breakdown and potential beneﬁts from outside options (i.e., cooperating with another RL-supplier). Thus, this work formulates the aforementioned producer and RL-supplier bargaining problem as an asymmetrical NB prob-lem with uncertainties (Eq.(16)). The equilibrium solutions of p

yj;i and y

j;iare approximated based on asymmetrical NB

solutions.

In the work, we assume the relative bargaining power

a

(f, s) of a producer is a linear function of unit green tax and

sub-sidies (Eq.(24)), and embed such a function into the proposed asymmetrical NB product. Accordingly, the derived

asymmet-rical NB solutions, i.e., proﬁts shared by dyadic players through a cooperative agreement rely on equilibrium solutions of unit green tax and subsidies (f⁄_{and s}⁄_{) mediated by the effect of relative bargaining power.}

If governmental ﬁnancial intervention is indispensable to holding producers responsible for environmental impact, the

equilibrium solutions f⁄_{and s}⁄_{are recommended to governments as they help maximize SW and chain member proﬁts,}

com-pared with other feasible solutions. Notably, the method used to derive f⁄_{and s}⁄_{is a game-based approach and, thus, f}⁄_{and s}⁄

are equilibrium solutions rather than optimal solutions. Therein, governments should account for the factors inﬂuencing SW, proﬁt and reaction functions of chain members to determine f⁄_{and s}⁄_._{Proposition 4.1}_and_{Remarks 4.1 and 4.2}_{further clarify}

I < J I=J I > J

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

# of competing producers I (given J=4)

Pai-i Pai-j Sum of Pai

(16)

how governmental financial instruments influence the relative bargaining power and negotiation outcome of dyadic players in the specified bargaining framework. Nevertheless, analytical results obtained from numerical studies reveal the disadvan-tageous effect of governmental intervention on chain-based profits and SW in the case of excessive governmental interven-tion (e.g., levying a high unit green tax on producers). Addiinterven-tionally, the duopoly–oligopoly competing context in which only two competing producers and a few competing RL suppliers exist may contribute to negotiation outcomes that are most profitable to dyadic players in bilateral negotiations.

5.2. Recommendations

Although some ﬁndings and generalizations have been made to advance knowledge of negotiations among green supply chain members moving toward cooperative agreements under governmental intervention, several other directions are sug-gested for future research.

First, the characterization of bargaining power and corresponding power sources remain important to addressing nego-tiation issues of green supply chain members. To the best of our knowledge, the relative bargaining power of dyadic players in bilateral negotiations is typically treated as a parameter predetermined for simplicity in the bargaining game. Conversely, this work conceptualized the effect of green taxation and subsidization into a simplified linear function to characterize the influence of governmental financial intervention in the green supply chain bargaining framework. Nevertheless, we ague that additional power sources should be considered to rationalize such bargaining-power functions. For instance, in the field of channel relationship management (CRM) and related areas, diverse power sources, including coercive (e.g., legitimate power) and non-coercive power sources (e.g., rewards power and information power), and their derivatives, such as trust

and relationship commitment, have been extensively analyzed (Raven and Kruglanski, 1970; Frazier and Rody, 1991; Sheu

and Hu, 2009), but lack rationalization in quantitative approaches. Future research can focus on either methodological

devel-opment or quantitative analysis to bridge the gap between CRM and green supply chain cooperation.

Model extension to incorporate different bargaining frameworks and negotiation mechanisms in green supply chains are also noteworthy. For instance, issues associated with producer collusion to form an alliance with increased bargaining power for negotiating with RL-suppliers may need sophisticated bargaining game models, and vice versa. This can increase the ﬂex-ibility of extended models for analyzing practical cases. Additionally, issues of information asymmetry in negotiations among players may complicate the aforementioned bargaining problems, and thus warrant further investigation. Theoreti-cally, repeated games with uncertainties combined with Markov-based approaches seem promising for a bargaining frame-work in which dyadic players are pursuing long-term cooperative contracts through multiple negotiations.

Furthermore, diverse influential strategies adopted by a government and their influences on green supply chain cooper-ation and competition warrant further investigcooper-ation. Therein, different governmental financial instruments aimed at differ-ent chain members (e.g., retailers, virgin-compondiffer-ent suppliers, and even end-customers) and product categories may generate different effects on the performance of green supply chains. Strategically, green supply chain members may take different negotiation mechanisms and cooperative strategies into account in response to governmental intervention, which may raise additional critical issues that must be addressed.

In summary, this work made an incremental contribution to literature on green supply chain management by integrating governmental ﬁnancial intervention into the producer and RL-supplier bargaining framework to gain insights into the nego-tiation process and decisions of dyadic members moving toward green supply chain cooperation. We recommend that on the path leading to sustainable green supply chains, government involvement as a mediator is indispensable to facilitate inte-gration of supply and reverse supply chain members. Therein, these three parties should reach consensus on collectively addressing environmental impact issues, appropriate use of economic incentives and legislation as strategies that may gen-erate certain effects that facilitate GSCM and enrich SW.

Acknowledgements

This research was supported by Grant NSC 99-2410-H-009-031-MY3 from the National Science Council of Taiwan. The author also wishes to thank the referees for their helpful comments. The valuable suggestions of Professor Wayne K. Talley to improve this paper are also gratefully acknowledged. Any errors or omissions remain the sole responsibility of the authors.

Appendix A

A.1. Proof of equilibrium solution p

yj;i (Stage 2)

Using the proposed asymmetric Nash bargaining product (Eq.(16)), letW¼ ^