Outsourcing sustainability: a gametheoretic. Alvaro J. Mendoza & Robert T. Clemen. Environment Systems and Decisions Formerly The Environmentalist

Transcription

1 Outsourcing sustainaility: a gametheoretic modeling approach Alvaro J. Mendoza & Roert T. Clemen Environment Systems and Decisions Formerly The Environmentalist ISSN Volume 33 Numer 2 Environ Syst Decis (213) 33: DOI 1.17/s

2 Your article is protected y copyright and all rights are held exclusively y Springer Science +Business Media New York. This e-offprint is for personal use only and shall not e selfarchived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own wesite. You may further deposit the accepted manuscript version in any repository, provided it is only made pulicly availale 12 months after official pulication or later and provided acknowledgement is given to the original source of pulication and a link is inserted to the pulished article on Springer's wesite. The link must e accompanied y the following text: "The final pulication is availale at link.springer.com. 1 23

3 Environ Syst Decis (213) 33: DOI 1.17/s Outsourcing sustainaility: a game-theoretic modeling approach Alvaro J. Mendoza Roert T. Clemen Pulished online: 9 May 213 Ó Springer Science+Business Media New York 213 Astract As a response to stakeholders interest in sustainale products and services, an organization may change its approach to sustainaility issues, from isolated social and environmental projects to corporate sustainaility strategies and practices that are part of their core usiness. However, many of the efforts associated with these sustainaility strategies cannot e directly exerted y focal organizations. We consider the situation in which a focal organization (sustainaility uyer) outsources sustainaility efforts to another organization (sustainaility seller). While uyers cannot directly exert sustainaility efforts, they can provide economic or technical support to their sellers in order to incentivize these efforts. We investigate how the effort and support decisions change according to characteristics of stakeholders, uyers, and sellers. Additionally, the presence of sustainaility-minded stakeholders may lead to uyers competition on the sustainaility effort exerted y their sellers. Therefore, we extend our analysis of sustainaility efforts and incentives to the case of two competing uyers, and we determine conditions under which sharing a seller is preferred y the uyers to having a separate seller for each uyer. Keywords Corporate sustainaility Buyers sellers networks Supply chain Stakeholders Stackelerg game A. J. Mendoza (&) R. T. Clemen Fuqua School of Business, Duke University, Durham, NC, USA alvaro.mendoza@duke.edu R. T. Clemen roert.clemen@duke.edu 1 Introduction Organizations such as multinational rand companies, governments, and communities are facing pressure from their stakeholders to operate in a sustainale way, considering not only economic enefits ut also their environmental and social impacts. However, many of these organizations interested in leading sustainaility initiatives (i.e. uyers of sustainaility efforts) may not always have the capacity or control required to implement these initiatives directly. In these cases, uyers need to outsource sustainaility efforts from other organizations (sustainaility sellers) such as manufacturing companies, government agencies, or nongovernmental organizations (NGOs). As a first example, consider the case of Apple, which is incentivizing Foxconn, one of its largest suppliers, to improve working conditions in its suppliers factories. On January 25, 212, The New York Times pulished a detailed report 1 descriing the poor working conditions in a Chinese factory elonging to Foxconn. On Feruary 9, 212, CNNMoney 2 reported that aout 25, people asked Apple, oth online and at Apple stores, to improve working conditions in its suppliers factories. The same month, Apple partnered with the Fair Laor Association (FLA) to conduct a voluntary audit aout working and living conditions in three of the Foxconn factories in China. The results of the investigation, released on March 29, 212 and widely covered y US media, highlighted at least 5 issues related to the FLA Code and Chinese laor law, including in the following areas: health and safety, worker 1 (accessed April 5, 212). 2 tion/ (accessed April 5, 212).

4 Environ Syst Decis (213) 33: integration and communication, and wages and working hours (Fair Laor Association 212). FLA s report also descries the main points of a remediation plan prepared y Apple and Foxconn to address each of the issues identified. The Apple Foxconn example illustrates the importance of sustainaility performance for different parties. First, consumers protests and wide media coverage showed that Apple s stakeholders were concern aout the issues identified. Second, Apple s quick reaction to the prolem, partnering with the FLA to conduct voluntary audits to the factories and designing a remediation plan to address the identified issues, demonstrates its interest in the sustainaility practices of its suppliers. Finally, Foxconn s commitment to implement the remediation actions is a clear sign of its willingness to improve its sustainaility performance. Walmart, GE, Nike, and Adidas are other examples of large companies working to improve their sustainaility performance (Plameck et al. 212). Many of these strategies are motivated y increasing stakeholder pressure on the companies to implement sustainaility initiatives. The World Business Council for Sustainale Development (28) reported that consumer awareness and willingness to act on environmental concerns rose in most countries over the time period studied. In the US, for example, it increased from 57 % in 27 to 8 % in 28. As a response to this increasing pressure, many companies are changing their approaches to sustainaility, from isolated social and environmental projects to corporate sustainaility strategies and practices that are part of the core usiness. Goals, strategies, actions, and results on sustainaility performance are often pulished on companies wesites. Not only companies ut also governments and communities may e interested in leading sustainaility initiatives. For example, several municipalities in North Carolina work with Clean Energy Durham, a non-profit organization, to help community memers learn and implement energy-saving techniques. The program, known as Pete Street TM, consists of manuals, training programs, and consulting that municipalities, counties, utilities, or a coalition of community agencies can use to launch and run energy-saving initiatives. 3 Note that neighorhoods (the uyer) may not have the technical knowledge to develop and implement energy-saving programs, ut they can contract with Clean Energy Durham (the seller) to help them accomplish their goals. In this paper, we develop a framework to study the role of organizations in the implementation of sustainaility initiatives. We consider a uyer (e.g. Apple or a North Carolina municipality) who outsources sustainaility efforts (e.g. improving working conditions or implementing energysaving programs) to a seller (e.g. Foxconn or Clean Energy 3 (accessed Novemer 2, 212). Durham). Buyer s stakeholders (e.g. customers, financial institutions, governments, residents) value the sustainaility initiatives led y the uyer. Although the uyer cannot directly exert any sustainaility effort, she can provide support to the seller in the form of money, knowledge, equipment, information, etc. We descrie the model in detail in Sect. 3, and in Sect. 4, we study the impact on effort and support decisions of key uyer s and seller s characteristics such as the seller s enefit and cost of effort, and the cost and efficiency of uyer s support. We also investigate how stakeholders pressure for sustainaility efforts impact effort and support decisions. Buyer s and seller s decisions may have an impact on competing uyers and sellers. In the Apple Foxconn example, Apple s competing uyers may face stronger stakeholder pressure to lead similar sustainaility initiatives. In addition, other Foxconn uyers might free ride on Apple s support to Foxconn. In the Clean Energy Durham example, the sustainaility strategy of a particular municipality may increase the pressure on neary communities to support similar sustainaility initiatives that make them equally or more attractive to current and potential usinesses and residents. To capture the impact on other uyers and sellers, in Sect. 5, we extend our asic uyer seller model to consider the case of two uyers who compete on sustainaility performance in two possile network structures. In the first structure, the two uyers share the same seller, while in the second structure, the two uyers have separate sellers. We determine conditions on stakeholder, uyer, and seller characteristics that may lead uyers and sellers to prefer one network structure over the other. 2 Literature review A significant amount of literature recognizes the importance to companies of addressing sustainaility issues in their operations. Seuring and Müller (28) surveyed 191 papers pulished etween 1994 and 27 addressing sustainaility issues in supply chain management. They point out that aout 74 % of the papers focus on the environmental dimension of sustainaility, 11 % address the social dimension, and the remaining 15 % incorporate oth dimensions into the analysis. Regarding the research methodology used, they notice that more than 6 % of the papers are cases or surveys, while only aout 1 % of the papers use mathematical models. Most of these modeling papers focus on the construction of metrics to quantify the environmental and social performance of the companies (e.g. Clift 23; Foran et al. 25; Noci 1997; Sarkis23). Our paper contriutes to the small ut growing literature that uses mathematical models to address sustainaility

5 226 Environ Syst Decis (213) 33: decisions. Our modeling approach has similarities with that used in several papers addressing process improvement and quality decisions in the supply chain. Gupta and Loulou (1998) develop a model to determine the optimal channel structure, transfer and retail prices, and R&D levels in a four-stage game where manufacturers can reduce their production cost through process improvements. Bernstein and Kök (29) also study cost reduction through process improvement efforts, considering the case where efforts are made y suppliers over the life cycle of a product. These two papers consider process improvements made y only one of the parties in the supply chain. Similar to ours, there are a numer of papers that consider settings where oth uyers and suppliers can impact improvement efforts. Harhoff (1996) examines the case of a monopolistic supplier who can contriute to improve product quality y creating knowledge spillovers that manufacturers (i.e. uyers) use as a sustitute for their own R&D effort. Zhu et al. (27) propose a model where oth the uyer and the supplier can invest in quality improvement efforts. Finally, Kim and Nettesine (212) consider a setting where the manufacturer and the supplier engage in a collaorative effort to reduce uncertainty aout component production cost. Their focus is on the impact of information asymmetry and contracting strategies on parties incentives to collaorate. There are some key differences etween our framework and models from the process and quality improvement literature. Instead of focusing on the supply chain per se, our framework applies to the case of a generic uyer that outsources sustainaility efforts to a generic seller. The uyer and seller could e companies, government agencies, NGOs, or any other type of organization. Additionally, while papers studying quality and process improvement efforts usually focus on the enefits generated either through cost reduction (e.g. Bernstein and Kök 29; Zhu et al. 27; Gupta and Loulou 1998) or through price or demand increase (e.g. Harhoff 1996), our paper considers multiple enefits of sustainaility efforts simultaneously. For example, consider a supplier implementing energy-efficiency initiatives. On the one hand, the supplier will otain a direct enefit through electricity cost savings. On the other hand, the uyer contracting with that supplier may also otain a enefit (e.g. increase on demand, lower taxes, access to green investors, etc.) for having a greener supplier. Kleindorfer et al. (25) mention corporate image improvement, regulatory compliance, liaility limitation, community relations improvement, employee health and safety improvement, and customer relations enhancement as additional drivers of sustainaility efforts. Haanaes et al. (211) report the results of a survey of over 3, managers aout sustainaility and innovation. Nearly half of the respondents ranked improved rand reputation as the most important sustainaility enefit ahead of reduced cost due to energy efficiency, increased competitive advantage, and reduced cost through materials and waste efficiencies. Other sustainaility enefits ranked in the survey were access to new markets, increased market share, improved perception of management of the company, improved regulatory compliance, and improved aility to attract top talent. Finally, a numer of papers discuss conceptual or empirical evidence of the impact of stakeholders, seller, and uyer characteristics on the adoption of particular sustainaility initiatives. Brun and Gereffi (211) use gloal value chain (GVC) analysis to study the adoption of energy-efficiency practices in companies. They conclude that firms in consumer-products supply chains, operating in energyintensive industries, are most likely to adopt energy-efficiency improvements ecause of the associated cost savings and marketing value. Jira and Toffel (212) review several papers that study how the adoption of environmental practices among suppliers is influenced y factors such as environmental regulations, suppliers resources and assets, numer of uyers, uyers technical assistance and training to suppliers, and duration of the supplier uyer relationship. The impact of several of these factors can e captured in our model. 3 Model description We consider a uyer that supports a seller to implement sustainaility initiatives. The seller decides to exert a level of sustainaility effort, x, for which she pays a cost, c(x), and receives a direct enefit, r(x). The function r(x) may include a wide range of sustainaility enefits that the seller may receive as a result of the effort. In the Apple Foxconn example from the first section, the direct enefit for Foxconn may include cost reduction due to energy efficiency or waste management, operational risk reduction, and greater employee productivity. In the Clean Energy Durham example, enefits for Clean Energy Durham eyond payment for its services may include reputation enhancement and more effective fundraising. We assume the seller pays a cost c for every unit of effort, while rðþ is an increasing and concave function. The logic ehind this assumption is that the seller will undertake projects in a ang-per-uck order until all profitale projects have een implemented and a maximum level of internal enefit has een achieved. The idea that sustainaility projects with a higher direct enefit per unit of effort should e done first is not only intuitive ut also consistent with widely used approaches such as the McKinsey Aatement Curve (Enkvist et al. 27). To otain closed-form solutions and discuss the implication of different parameters on the effort and support decisions, we use specific functional forms. This is a

6 Environ Syst Decis (213) 33: common approach in papers from the process and quality improvement literature such as Gupta and Loulou (1998), Bernstein and Kök (29), Harhoff (1996), and Zhu et al. (27). Specifically, we define rx ðþ¼rð1 e ax Þ. In this function, r [ represents the maximum enefit that the seller can otain through sustainaility efforts. This parameter depends on factors such as the size of the seller and the type of activities that she does. For example, larger firms operating in energy-intensive industries may e expected to have a higher r ecause of opportunities for energy efficiency. Parameter a can e seen as a measure of the seller s efficiency with which she otains direct enefits from sustainaility efforts. We assume a [, which means that every project will have a positive internal enefit. This parameter depends on the portfolio of sustainaility projects that the seller can implement. On the one hand, initiatives such as energy efficiency and recycling may produce a high direct enefit to the seller through cost reduction. On the other hand, projects such as improving education may generate a lower direct enefit to the seller. All else eing equal, we would expect that a seller with a portfolio dominated y the first type of sustainaility project would have a higher a than a seller with a portfolio dominated y the second type of project. Note that a higher a implies that a higher enefit can e achieved with a given amount of effort or, equivalently, that a lower effort is required to achieve a given enefit. Although the uyer can exert no sustainaility effort, she can provide support to her seller to decrease the cost of the seller s effort. We denote the uyer s support y u and assume it decreases the marginal cost of the seller s effort from c to c S ðuþ. Specifically, we define c S ðuþ ¼ c e u, which is a decreasing and convex function. Similar models of cost reduction can e found in Bernstein and Kök(29) and Kim and Nettesine (212). If the uyer provides no support, the seller s cost of effort does not change from its original level, c. If the uyer provides support u, the seller s cost decreases according to efficiency rate [. Furthermore, we assume the uyer pays a cost c for every unit of support provided to her seller. The uyer s stakeholders can oserve the sustainaility effort exerted y the uyer s seller. We think this is a reasonale assumption. The numer of companies willing to measure, monitor, and report their sustainaility performance increases every day. According to the Gloal Reporting Initiative (GRI), 95 % of the world s 25 iggest companies now report their sustainaility performance. 4 In the specific case of rand-owning companies, these 4 Source: (press release of March 8, 212). GRI is a non-net enefit organization that provides companies and organizations with a comprehensive sustainaility reporting framework that is widely used around the world. companies typically monitor and report the sustainaility performance of their suppliers. For example, Apple leads auditing programs across their entire supply chain to evaluate its supplier s performance in sustainaility aspects such as laor and human rights, worker health and safety, environmental impact, and worker education and development. The results for the last 6 years are availale at Apple s wesite. 5 In addition to companies own reporting, there exist agencies such as FTSE and the Dow Jones Sustainaility Indexes that evaluate and report companies sustainaility performance. The participation of these organizations generally adds transparency and crediility to the reported results. Under the assumption that the uyer s stakeholders can oserve sustainaility efforts, we represent the price that they are willing to pay for every unit of effort as p(x). This price for sustainaility efforts includes a wide range of incentives provided y stakeholders to uyers such as increase in demand, the price premium paid y consumers, tax enefits, greater access to capital and etter financing sources, and risk reduction. Our uyer seller network can e seen as a monopoly producing sustainaility efforts. Similarly to Gupta and Loulou (1998), we follow a common assumption in the asic monopoly literature and define the inverse demand function (i.e. price) for sustainaility efforts as a linear function. This assumption will also simplify our analysis in Sect. 5, where uyers compete on sustainaility efforts, similarly to Cournot 6 quantity competition. (As noted y Talluri and van Ryzin 24, a Cournot equilirium need not exist for general inverse demand functions.) Specifically, we define px ðþ¼a x, where a; [. In this function, a represents the initial stakeholder s willingness to pay for sustainaility efforts, while determines the rate at which this willingness to pay decreases as the effort increases. We want to note that even though we use a linear price function, our analysis in Sect. 4 could also e done using other decreasing and convex willingness to pay functions. In the appendix, we present the one uyer one seller analysis for the case in which px ð Þ ¼ a=ð1 þ xþ and show that the structure of the results has some similarities with those otained with a linear price function. Within this setting, we model uyer and seller decision prolems as a Stackelerg game, with the uyer as the leader. The uyer moves first and offers a support u to the seller. After oserving the uyer s decision, the seller chooses the level of sustainaility effort x. Our goal is to 5 (accessed March 27, 212). 6 In Cournot competition, two firms simultaneously decide how much to produce. These quantity choices have an impact on the market price. See Mas-Colell et al. (1995) for a detailed description.

7 228 Environ Syst Decis (213) 33: determine the equilirium decisions and analyze how they depend on the key parameters of our model. We first present the results for the case of a monopolistic uyer and then study the case of two uyers that compete on the sustainaility performance of their sellers. We should point out that even though our motivation is to study effort and incentive decisions when a uyer outsources sustainaility efforts from a seller, our framework may also e used to study other situations when a uyer can incentivize a seller to engage in some activities that enefits one or oth of them. The following proposition presents the optimal decisions and the corresponding optimal net enefits. All proofs can e found in the Appendix. Proposition 1 The optimal effort and support decisions, x and u, vary for four different regions characterized y A, a, c, and c. 1. Let X 1 ¼ A ; a; c ; c : A [ ; a c =c [ 2A and X 2 ¼ A ; a; c ; c : A ; a c =c [ 4c A =cþ 1=2 g.if A ; a; c ; c 2 f X1 [ X 2 g; then 4 One uyer one seller We first consider the case of a monopolistic uyer who supports a single seller to implement sustainaility initiatives. We denote y p S ðxu j Þ the seller s net enefit given uyer s support u. Thus, seller s decision prolem is to choose the level of sustainaility effort x that maximizes her net enefit function p S ðxu j Þ ¼ rx ðþc s ðþx; u ð1þ where rx ðþ¼rð1 e ax Þ and c S ðuþ ¼ c e u. Note that p S ðjuþ is concave ecause a and r are positive constants. Let A ¼ 1 ar a ln c and c ¼ a. Solving the seller s maximization prolem, we find that the seller s est response function is given y the following: xu ð Þ ¼ A þ cu; if u [ A c ; : ð2þ ; otherwise Note that c represents the relative efficiency of uyer s support with respect to the efficiency of seller s effort, while A determines the effort that the seller would exert without uyer s support. If the maximum enefit she can otain, weighted y her efficiency, is greater than her marginal cost, then A is positive. In this case, the seller will exert an effort A even if the uyer does not provide any support. Additionally, every unit of uyer s support will e converted into effort according to the relative efficiency rate, c. Conversely, if A is negative, the seller will exert a positive effort only if the effective support is high enough to compensate for the loss resulting from providing effort with no support. Anticipating the seller s decision, the uyer chooses the level of support for the seller. We denote the uyer s net enefit y p B ðuþ. Thus, the uyer chooses the level of support u that maximizes her net enefit function p B ðuþ ¼ px ðþx c u; ð3þ where px ðþ¼a x and x is given y (2). x ¼ a c =c 2 ; u ¼ a c =c 2A : ð4þ 2c The corresponding optimal net enefits are given y h p S ¼ r 1 1 þ a 2 a i c =c e 2 a ð ac =cþ ; p B ¼ a 2 c =c þ c A ð5þ : 4 c 2. Let X 3 ¼ A ; a; c ; c : A [ ; a c =c 2A. If A ; a; c ; c 2 X3, then x ¼ A and u ¼. The corresponding optimal net enefits are given y p S ¼ r c =a c A ; p B ¼ A a A ð6þ 3. Let X 4 ¼ A ; a; c ; c : A ; a c =c 4c A =cþ 1=2 g. If A ; a; c ; c 2 X4, then x ¼ and u ¼. The corresponding optimal net enefits are p S ¼ and p B ¼. Figure 1 shows the four regions descried in Proposition 1. In regions X 1 and X 3, the seller has an incentive to exert an effort A, even without any support from the uyer. Moreover, in region X 1, stakeholders willingness to pay is high enough so the uyer will provide the support required to increase seller s effort up to the level x defined in (4). Conversely, in regions X 2 and X 4, the seller does not have any internal incentive to exert an effort. If stakeholders willingness to pay is high enough, as in region X 2, then the uyer will provide the support required to induce the effort x defined in (4). However, if the uyer does not provide any support, as in region X 4, then the seller does not exert any effort. Finally, note that the uyer s support required to induce an effort x is higher in X 2 than in X 1. Looking at the impact of possile changes in the parameters on the optimal decisions and optimal net enefits, we first note that the uyer s support and the seller s

8 Environ Syst Decis (213) 33: Fig. 1 Structure of the optimal effort and support decisions. A, seller s effort without uyer s support; a, intercept of sustainaility effort s price; c marginal support s cost; c, support s efficiency relative to seller s efficiency (=a) effort, as well as the uyer and seller net enefits, generally increase if the stakeholders price for efforts increase (higher a, lower ) or if the cost of the uyer s support decreases. The efficiency of the uyer s support,, only plays a role if the uyer s support is positive, that is, regions X 1 and X 2.As increases, the uyer s support is more efficient in reducing seller s cost of effort. Therefore, the seller s optimal effort increases. The uyer s optimal support is increasing in for \2ac =ða 2A Þ. After that point, the uyer s support needed to induce the optimal seller effort decreases as she ecomes more efficient. Consequently, oth the seller s and the uyer s net enefits are increasing in. Furthermore, the net enefits increase at a decreasing rate, ecause oth the seller s direct enefit and the stakeholder s price have upper ounds. Finally, we study the impact of the three parameters that characterize the seller, r, c, and a. In region X 3, where the uyer provides no support, increasing r or decreasing c increase oth the seller s optimal effort and optimal net enefit. In regions X 1 and X 2, r and c do not affect optimal effort ecause, in these two regions, the uyer will provide the support needed to achieve the optimal effort, regardless of the seller s characteristics. Therefore, decreasing r or increasing c (within X 1 and X 2 ) will increase the uyer s support and decrease the uyer s net enefit. To analyze the impact of changes in the seller s efficiency, a, let us start with region X 3, where the seller s optimal effort is equal to A. In this case, as a increases, the seller initially increases her optimal effort and then decreases it when a [ c e=r. In regions X 1 and X 2, not only the seller s optimal effort ut also the uyer s optimal support are affected y changes in a. As a increases, the seller is more efficient in otaining a direct enefit from her sustainaility effort. Therefore, the support required from the uyer to increase her effort level is greater. In other words, as a increases, support is transformed into effort at a lower rate. For low values of a, the uyer tries to compensate for the increase in a y increasing her support. After some point (specifically, 1=2 a ¼ a þ a ðc Þ 2 =4c ), increasing support costs the uyer too much, and she starts to decrease her support. Consequently, the uyer s optimal net enefit is h increasing in a for a a a 2 2 8c 1=2 i =2c and decreasing in a when a is greater than this critical value. Regarding the impact on the seller s decision, we can see that the seller s optimal effort decreases as a increases, as a consequence of the decrease on the relative effectiveness of the uyer s support. The seller s optimal net enefit initially increases as a increases, achieves a maximum at a ¼ a=2c, and then starts to decrease. This is a consequence of the decrease in the optimal uyer s support after some a. This result implies that eing too efficient in otaining enefit from sustainaility efforts may hurt the seller. Although this may seem a it counterintuitive, recall that eing more efficient in this context means that the seller has a portfolio of sustainaility initiatives that lead to the maximum direct enefit with less sustainaility effort. Because the uyer s stakeholders care aout sustainaility effort, not the seller s direct enefit, this decrease in the sustainaility effort hurts the uyer s net enefit. Consequently, the uyer provides less support, which in turn may also hurt the seller s net enefit. Tale 1 summarizes the general shape of the impacts of seller s and uyer s characteristics on the optimal decisions and optimal net enefits. For example, the tale shows that, in regions X 1 and X 2, when a increases, the optimal seller s effort x increases at a lineal rate while the optimal seller s net enefit p S also increases ut it does it at a decreasing rate. 5 Competing uyers In this section, we study the case of two uyers who compete for stakeholders payments ased on the sustainaility effort exerted y their sellers. Each uyer needs only one seller to implement sustainaility initiatives. Thus, we consider two cases. In the first case, oth uyers outsource from the same seller, whereas in the second case, the uyers outsource two different sellers. Buyer competition adds some new elements into our prolem. Particularly, we focus our attention on two types of spillovers that may have an impact on the optimal effort and support decisions. The first type of spillover, which we called support spillover, is generated when uyers shared a seller. Given the nature of the seller s sustainaility efforts,

9 23 Environ Syst Decis (213) 33: Tale 1 Optimal effort, support, and net enefits under one-at-a-time changes on key parameters a,, intercept and slope of sustainaility effort s price; c, marginal support s cost;, support s efficiency; a, seller s efficiency; r, seller s maximum enefit; c, marginal effort s cost without support it may e difficult to associate them with a particular uyer. For example, if a seller improves laor conditions, it is reasonale to assume that the improvement would affect all workers, not just those working in the initiatives associated with a specific uyer. Therefore, a uyer s support to induce a higher effort y her seller may also enefit other seller s uyers. The second type of spillover, which we called effort spillover, is generated when there are multiple sellers. In this case, the sustainaility effort exerted y one seller can affect other sellers. For example, if a seller improves laor conditions for her workers, the pressure on other sellers to do the same may increase, which in turn may represent an additional cost. In another example, consider a seller that creates a program to improve health and education in the community where she operates. Other sellers operating in the same community may enefit from operating in a etter social environment and having access to more qualified laor. We now descrie the model for the cases of sharedseller and separate-seller networks, and we compare the optimal support and effort decisions in these two cases. To simplify our analysis, we focus on the case of identical uyers and identical sellers. 5.1 Shared-seller network In this case, we consider two identical uyers that outsource sustainaility efforts from the same seller. We use the same functional forms as in the previous section. Thus, the seller chooses the level of sustainaility effort x that maximizes her net enefit p S ðxu j 1 ; u 2 Þ ¼ ^rð1 e ax Þc e ðu 1þu 2 Þ x; ð7þ where u 1 and u 2 represent the support received from uyers 1 and 2, respectively. Note that the support efficiency rate,, is the same for the two uyers. Also, we denote the maximum direct enefit that the seller can achieve in this case y ^r, which can e different from r, defined in the case of a monopolistic uyer. Solving the seller s maximization prolem in this case, we find that the seller s est response function is given y the following: xu ð 1 ; u 2 Þ ¼ ^A þ cðu 1 þ u 2 Þ; if u 1 þ u 2 [ ^A c ; ð8þ ; otherwise; with ^A ¼ 1 a^r a ln c. Note that the seller s est response function has a similar form to that in the previous section, ut now depends on the sum of the support received from the two uyers. Anticipating the seller s decision, the uyers simultaneously choose their levels of support u i, i ¼ 1; 2, that maximize their net enefit p B i ðu i ju i Þ ¼ ða xþ x 2 c u i ; ð9þ Note that, according to (9), each uyer receives a payment for half of the seller s sustainaility effort. The underlying assumption in this case is that, in addition to oserving the seller s sustainaility effort, stakeholders also know that the uyers share the same seller. Therefore, each uyer claims half of the seller s effort. To simplify our analysis and focus our attention on the comparison etween the shared-seller and different-sellers networks, we restrict our analysis to the case where ^A [. This implies that the seller exerts a positive effort even without any support from the uyers. Solving the uyers maximization prolem, we find that uyer i s est response function is given y u i ðu i Þ ¼ K u i; if K u i [ ; ð1þ ; otherwise; where K ¼ 1 2c a 2c =c 2 ^A.

10 Environ Syst Decis (213) 33: Proposition 2 presents the optimal decisions and the corresponding optimal net enefits for the shared-seller network. Proposition 2 Assume that ^A [ and K [. The unique symmetric Nash equilirium of the shared-seller network game is given y x ¼ a 2c =c 2 ; u 1 ¼ u 2 ¼ a 2c =c 2 ^A : ð11þ 4c The corresponding optimal net enefits are given y h p S ¼ ^r 1 1 þ a 2 a i 2c =c e 2 a ð a2c =cþ ; p B 1 ¼ p B 2 ¼ aa 2c =c þ c ^A ð12þ 8 2c : As we oserve in (8), the seller decides aout the optimal effort ased on the sum of the uyers supports. This implies that the uyers supports are sustitutes for each other, which leads to multiple equiliria in the game. Specifically, the equiliria set consist of u 1 ; u 2 such that u 1 þ u 2 ¼ K. Proposition 2 presents the symmetric equilirium where u 1 ¼ u 2 ¼ K=2. To e ale to compare the results of this section with those otained in the case of a monopolistic uyer, we need to make some assumptions aout the value of the parameters in each case. Let us initially assume that the value of the parameters do not change from the monopolistic uyer case to the shared-seller case, in particular ^r ¼ r. In the shared-seller case, the uyers receive a payment for only half of the effort exerted y the seller. This leads to a decrease in the equilirium effort relative to the monopolistic uyer case, as we can see y comparing (4) and (11). Particularly, note that the optimal effort in (11) is equivalent to the solution in (4) ut with an equivalent cost equal to twice the cost of support, c. As a consequence, the sum of the supports that the seller receives from the two uyers is also lower. This reduction in the level of effort and supports leads to a decrease in the optimal net enefit for oth the uyers and the seller relative to the monopoly case, as we can see y comparing (5) and (12). We could alternatively assume that some parameters change in the shared-seller network. For example, it seems reasonale to assume that the total cost savings resulting from an energy-efficiency program are proportional to the size of the operations of the seller. If we additionally assume that the size of the operations is proportional to the numer of uyers served, then the maximum direct enefit that the seller can achieve is higher when she is working with two uyers, that is, ^r [ r. In this case, oth the seller and the uyer may e etter off in the shared-seller network relative to the monopolistic uyer case, as we can see y comparing Eqs. (5) and (12). 5.2 Separate-sellers network We now study a setting with two identical uyers that outsource sustainaility efforts from two separate ut identical sellers. Thus, uyer 1 outsources efforts from seller 1, and uyer 2 outsources from seller 2. As we previously mentioned, in this case, the effort exerted y one of the sellers may have an impact on the enefit of the other seller. We model this y introducing a parameter d 2ð1; 1Þ to reflect the fraction of the effort of a given seller that spills over to the other seller. A positive d means that one seller s effort enefits the other seller, while a negative d implies that it hurts the other seller. Therefore, in the second stage of the game, the sellers simultaneously choose their effort levels given the uyers support. An important assumption we make in this case is that the uyers supports are oservale y oth sellers. Thus, seller i s net enefit function in this case is given y ðx i jx i ; u i Þ ¼ ~r 1 e aðx iþdx i Þ c e u i x i : ð13þ p S i We denote the maximum direct enefit that each seller can achieve in this case y ~r, which can e different from r and ^r defined in the previous sections. Also note that the effort efficiency rate, a, is the same for oth sellers, given our assumption that they are identical. Solving seller i s maximization prolem in this case, we find that seller i s est response function is given y the following: x i ðx i ; u i Þ ¼ A ~ þ cu i dx i ; if u i [ ~A þdx i c ; ð14þ ; otherwise; where ~A ¼ 1 a~r a ln c. Thus, the equilirium of the effort game played y the sellers after knowing the uyers support is given y ( A ; if u i du i [ ~ ð1dþ c ; x i ðu 1 ; u 2 Þ ¼ ~A ð1þdþ þ cðu idu i Þ ð1d 2 Þ ; otherwise: ð15þ As in the shared-seller network, we focus on the case where sellers have an incentive to exert a positive effort even without uyers support, that is, ~A [. Anticipating the sellers decisions, the uyers simultaneously choose their levels of support u i, i = 1, 2, that maximize their net enefits p B i ðu i ju i Þ ¼ ða ðx 1 þ x 2 ÞÞx i c u i ; ð16þ Solving the uyers maximization prolem, we find that uyer i s est response function is given y u i ðu i Þ ¼ K ~ ð1dþ 2 u i ; if 2 ~K ð1 dþu i [ ; ; otherwise, ð17þ

11 232 Environ Syst Decis (213) 33: where ~K ¼ 1 2c ð1 þ dþa ð1 dþð1 þ dþ 2 c =c ð3 dþ ~A. Proposition 3 presents the optimal decisions and the corresponding optimal net enefits for the separate-sellers network. Proposition 3 Assume that ~A [ and ~K [. The Nash equilirium of the separate-sellers network game is given y x 1 ¼ x 2 ¼ a ð1 d2 Þc =c ; u 1 ð3 dþ ¼ u 2 ¼ ð1 þ dþa ð1 dþð1 þ dþ2 c =c ð3 dþ ~A : ð3 dþc ð18þ The corresponding optimal net enefits are given y p S 1 ¼ ps 2 ¼ ~r 1 1 þ a ð3 dþ a ð1 d2 Þc =c e að1þdþ ð3dþð að1d2 Þc =cþ i ; p B 1 ¼ p B 2 ¼ ð1 þ dþ a ð1 d2 Þc 2 =c ð1 dþð3 dþ 2 da½a 1 d2 c =cš ð1 dþð3 dþ þ c ~A : ð19þ c The results for the separate-sellers network have a structure similar to those that would arise in a typical Cournot competition. If we assume that all parameters of the model have the same value and, additionally, that there is no effort spillover, then the optimal sustainaility effort of each seller is lower than that in the original single uyer single seller case. However, the sum of the sellers efforts is higher than the optimal effort in the original case, as we can see y comparing Eqs. (4) and (18). Similarly, the uyer s support is also lower. This translates into lower optimal net enefit for oth uyers and sellers. Finally, we analyze the impact of the effort spillover parameter on the optimal decisions. First, note that a positive d, which represents a positive externality etween sellers efforts, decreases the level of effort that the seller exerts without uyer s support from ~A to ~A =ð1 þ dþ. Thus, each uyer needs to increase her optimal support in order to increase the optimal effort. Therefore, each seller s net enefit is increasing in d, while the uyer s net enefit is decreasing in d. A negative d has the opposite effects. Tale 2 summarizes the direction of the changes in the effort, the support, and the net enefits in the shared-seller and separate-sellers networks relative to the one uyer one seller case. Note that while uyers and sellers would generally prefer the monopolistic case, stakeholders would Tale 2 Competing uyers versus monopolistic uyer prefer the separate-sellers case ecause the total sustainaility effort is higher than in the other type of networks. 5.3 Shared seller versus separate sellers We now compare the results otained in the previous two sections for the shared-seller and separate-seller networks. We focus our analysis on the performance variales relevant to the agents in the prolem. On the one hand, uyers and sellers want to maximize their net enefit. On the other hand, the uyers stakeholders care aout the total sustainaility effort exerted y all the sellers in the network. Proposition 4 presents the conditions under which these measures are higher in one network than in the other. We initially assume that all the corresponding parameters are equal in the two cases and that there is no effort spillover. Then, we discuss how the comparison is affected when the upper limit on the direct enefit of the sellers is different in the two cases and when there is an effort spillover in the separate-sellers case. Proposition 4 Let ^A ; ~A ; K; ~K [. Additionally, let ^A ¼ ~A and d ¼. Then: 1) The comined sustainaility effort exerted y sellers is always lower in the shared-seller network than in the separate-sellers network. 2) The seller s optimal net enefit is higher in the sharedseller network than in the separate-sellers network if a 4c c : 3) The uyer s optimal net enefit is higher in the sharedseller network than in the separate-sellers network if a 4c a~r c þ 36ln c : According to the first result of Proposition 4, the comined effort exerted y the two sellers in the separatesellers case is always higher than the effort exerted y the single seller in the shared-seller case. To understand why this is the case, note that, on the one hand, the equilirium effort in the shared-seller case has a structure similar to the Shared-seller Total support received ; ; y each seller Seller s effort ; ; Total effort in the network ; : Seller s net enefit ; ; Buyer s net enefit ; ; Separate-sellers (no effort spillover) Direction of the changes in the effort, the support, and the net enefits in the shared-seller and separate-sellers networks relative to the one uyer one seller case

12 Environ Syst Decis (213) 33: monopolistic uyer case, ut with each uyer receiving a payment for only half of the seller s effort. On the other hand, the uyers in the separate-sellers case play a Cournot effort game. Thus, as expected, competition increases the total effort expended in the network. Therefore, stakeholders always prefer the separate-sellers network over the shared-seller network. The second result of Proposition 4 presents a condition under which the seller in the shared-seller case is etter off compared to each of the sellers in the separate-sellers case. To understand this result, first note that ecause we are assuming that ^A ¼ ~A, the difference etween the seller s effort in the two cases depends on the total support that she receives from the uyer(s) in each case. From (11) and (18), we oserve that the total support received y the seller in the shared-seller network is a2c =c2 ^A 2c, while the support received y each seller in the separated-sellers case is ac =c3 ~A 3c. The first expression is greater than the second one when a 4c =c: Therefore, increasing stakeholders willingness to pay, increasing uyers relative efficiency, or decreasing uyers support cost all make the sharedseller network more attractive to the seller relative to the separate-sellers network. The third result of Proposition 4 shows that in addition to a, c, and c, the uyer s preference aout the network structure also depends on ~r and c. Lower values of ~r and higher values of c make the shared-seller network more attractive to the uyer relative to the separate-sellers network. Furthermore, note that the value of a required y the uyer to choose the shared-seller network is always higher than that required y the seller, ecause 36 ln a~r c [. This implies that if the uyers prefer the shared-seller network, then the seller does as well. Proposition 4 is illustrated in Fig. 2. We can see that the shared-seller network is more attractive to oth uyers and sellers when Fig. 2 Buyers and sellers network preferences. a,, intercept and slope of sustainaility effort s price; c marginal support s cost;, support s efficiency; a, seller s efficiency; c, support s efficiency relative to seller s efficiency (=a); ~r, seller s maximum enefit; c, marginal effort s cost without support stakeholders are willing to pay more for sustainaility efforts (i.e. " a; # ), uyers are more efficient in helping their sellers (i.e. " ; # c ), and sellers otain a lower direct enefit from efforts (# a; # ~r; " c ). Finally, we study how the results in Proposition 4 change if there is an effort spillover or if we allow ^A 6¼ ~A. First, we note that even though a negative d decreases, the comined effort exerted y the two sellers in the separateseller network, that comined effort is still greater than the effort exerted y the single seller in the shared-seller network, for any value of d. Regarding the second result of Proposition 4, we noted in the previous section that the seller s net enefit in the separate-seller network is increasing in d. Thus, the seller requires higher values of d, a, and c, and a lower value of c to prefer the shared-seller network. Conversely, the uyer s net enefit is decreasing in d. Therefore, higher values of d, c, and ~r and lower values of a, c, and c may lead the uyer to prefer the shared-seller network. We now assume that ^r 6¼ ~r, which implies that ^A 6¼ ~A. Particularly, we assume that ^r ~r, given that the seller is working with two uyers in the shared-seller network and only with one of them in the separate-sellers network. Assuming ^r ~r implies that oth seller and uyer net enefits in the shared-seller network are greater than the net enefits in the separate-seller network. Therefore, the higher the value of ^r relative to ~r, the lower the values of a, and c, and the higher the value of c that seller and uyer require to prefer the shared-seller network over the separate-sellers network. 6 Summary and conclusions Companies and other type of organizations face growing pressure to improve their sustainaility performance. In this paper, we developed a model to study the situation in which a uyer provides support to her seller to increase the seller s sustainaility effort. We found that sustainaility efforts generally increase when stakeholders heighten their interest in sustainaility performance, when uyers are more efficient to provide support to their sellers, and when sellers manage a alanced portfolio of social and environmental projects, and not only projects with a high direct economic return. We then analyzed the situation of two uyers that compete on sustainaility performance, and compare the case where uyers share a seller against the case where uyers have separate sellers. We conclude that, while stakeholders generally prefer the separate-sellers network, uyers have more incentives to share a seller when stakeholders are willing to pay more for sustainaility efforts, when uyers are more efficient in helping

13 234 Environ Syst Decis (213) 33: their sellers, and when sellers otain a lower direct enefit from sustainaility efforts. Some of our findings are consistent with empirical evidence presented in some other papers investigating the impact of stakeholders, uyers and seller s characteristics on the adoption of sustainaility initiatives. Jira and Toffel (212) cite several papers that investigate the impact of some supply chain characteristics on the adoption of particular environmental practices. As noted y Jira and Toffel (212), Delmas and Montiel (29) and Locke et al. (27) found that adoption of environmental practices is more likely in countries with stronger regulatory requirements to pulicly disclose pollution data. This can e captured in our model as a greater stakeholders interest (government in this case) in sustainaility performance. Similarly, they mention that Lee (28) and Locke et al. (29) found that suppliers are more willing to adopt sustainaility practices when uyers provide technical assistance and training, engage in joint prolem solving, and share est practices with their sellers. This can e represented in our model as a greater efficiency in the support from uyers to sellers. Brun and Gereffi (211) use GVC analysis to study the adoption of energy-efficiency practices in companies. They found that firms in consumer-products supply chains, operating in energy-intensive industries, and closer to the consumers, are most likely to adopt energy-efficiency improvements ecause of the associated cost savings and marketing value. This can e incorporated into our model as a higher stakeholders willingness to pay for sustainaility efforts, and a higher seller s direct enefits from these efforts. We think that comining our model with the main elements of GVC analysis could help to etter understand the drivers of sustainaility efforts along the supply chain. A value chain represents the set of activities in which firms engage to produce goods and services. One of the most important characteristics of a GVC is the kind of governance used y leading firms in the chain to coordinate the relationship with other firms (Gereffi et al. 25; Bair 29). Gereffi et al. (25) identify five types of value chain ased on three factors: the complexity of the information and knowledge transfer required in the transactions; the aility to codify and efficiently transmit this knowledge along the chain; and the capailities of existing suppliers to meet the uyers requirements. We think that these three factors could e associated with some of the parameters in our model to determine which types of governance induce a etter sustainaility performance in the supply chain. Furthermore, empirical analyses from the GVC literature as well as those presented in the papers mentioned in the previous paragraph can e used to estimate some of the parameters in our framework. For example, information aout sellers capailities and the industry in which they operate can e helpful to estimate the potential direct enefit r as well as sellers efficiency a. Similarly, the complexity of transactions and the strength of the uyer seller relationship may e helpful to estimate uyer s support efficiency rate and the cost of support c. Finally, there are some possile extensions to our model that could e helpful to otain additional insights into our study of sustainaility efforts. First, we could study the impact of collaoration etween uyers to provide support to common sellers. According to Plameck et al. (212) companies such as Nike, Levi Strauss, and Adidas are working together in China to drive sustainaility efforts in their common sellers. Adding this collaoration to our model would create an interesting collaoration competition relationship etween uyers. Second, it may e interesting to examine the role of NGOs to drive sustainaility efforts in the supply chain. In addition to put pressure on rand uyers to improve the sustainaility performance of their supply chains, NGOs may also play a key role to actually increase sustainaility efforts along the chain. For example, they can facilitate monitoring and work with uyers and sellers to identify opportunities to improve their sustainaility performance. An example of this, discussed y Plameck et al. (212), is the collaorative relationship etween Timerland, Walmart, Nike, and other uyers with the Institute of Pulic and Environmental Affairs in China to encourage sellers to identify and fix air and water violations. Finally, it may e worthwhile to study the case where stakeholders, uyers, and sellers have incomplete information aout the network structure. This could have an impact on the payment schemes from stakeholders to uyers, as well as from uyers to sellers. Appendix Proof of Proposition 1 Anticipating the seller s response function given y (2), the uyer chooses the support level u C that maximizes her enefit function p B ðuþ ¼ A ða A Þþ a 2A c =c cu c 2 u 2 if u A =c c u if u\ A =c If A [, any positive u will increase seller s effort from A to A þ cu. Therefore, the uyer maximizes A ða A Þþ a 2A c =c cu c 2 u 2 suject to u C. The KKT conditions are given y c a 2A c =c 2c 2 u c a 2A c =c 2c 2 u u ¼ The second-order condition is 2c 2 \. Solving for u and replacing in the seller s est response function, we otain the optimal solution