1. Introduction
Industrial Symbiotic Networks (s) are collaborative networks of industries with the aim to reduce their materials and energy footprint by circulating reusable resources (e.g, physical waste material) among the network members Chertow (2000); Lombardi and Laybourn (2012); Yazan et al. (2016). Such a symbiosis leads to socioeconomic and environmental benefits for involved firms and the society. One barrier against stable implementations is the lack of frameworks able to secure such networks against unfair and unstable allocation of obtainable benefits among the involved firms. In other words, even if economic benefits are foreseeable, lack of stability and/or fairness may lead to noncooperative decisions and hence unimplementability of s ( implementation problem). Reviewing recent contributions in the field of industrial symbiosis research, we encounter studies focusing on the interrelations between industrial enterprises Yazan et al. (2016) and the role of contracts in the process of implementation Albino et al. (2016). We believe a missed element for shifting from theoretical design to practical implementation is to model, reason about, and support decisions in a dynamic way—and not by using snapshotbased modeling frameworks.
This abstract reports on extending the gametheoretic approach of Yazdanpanah and Yazan (2017) with regulative rules and normative socioeconomic policies—following the successful line of work on normative multiagent systems Shoham and Tennenholtz (1995); Grossi et al. (2013); Andrighetto et al. (2013). The extension provides a scalable solution to the implementation problem and enables enforcing desired industrial collaborations in a fair and stable manner.
1.1. Research Questions
The following questions guide the design of a gametheoretic framework and its normative coordination mechanism that jointly facilitate the implementation of s:

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Games: How to define a gametheoretic basis for s that both reflects their operational cost dynamics and allows the integration of normative rules?

Coordination: How to uniformly represent the regulatory dimension of s using incentive rules and normative policies?

Coordinated Games: How to develop a framework that integrates normative coordination methods into games to enable the fair and stable implementation of desirable s—with respect to an established policy?
Dealing with s’ complex industrial context Yazdanpanah et al. (2016), an ideal implementation platform would be tunable to specific industrial settings, scalable for implementing various topologies, and would not require industries to sacrifice financially nor restrict their freedom in the market. Below, we present the overview of an approach for developing an implementation framework with properties close to the ideal one.
2. Overview of The Approach
As discussed in Albino et al. (2016); Yazdanpanah and Yazan (2017), the total obtainable cost reduction (as an economic benefit) and its allocation among involved firms are key drivers behind the stability of s. For any set of agents involved in an , this value—i.e., the obtainable cost reduction—characterizes the value of the set and hence can be seen as a basis for formulating s as cooperative games. On the other hand, in realistic s, the symbiotic practice takes place in presence of economic, social, and environmental policies and under regulations that aim to enforce the policies by nudging the behavior of agents towards desired ones. This is, while policies generally indicate whether an is “good (bad, or neutral)", the regulations are a set of norms that—in case of agents’ compliance—result in an acceptable spectrum of collective behaviors. We follow this normative perspective and aim to use normative coordination to guarantee the implementability of desirable s—modeled as games—in a stable and fair manner. In the following subsections, we indicate how games can be modeled and coordinated using regulatory incentive rules and normative socioeconomic policies.
2.1. ISNs as Cooperative Games
In the gametheoretic representation of s, the value of any set of agents is defined Yazdanpanah and Yazan (2017) using the difference between the total cost that firms have to pay in case the does not occur, i.e. costs to discharge wastes and to purchase traditional primary inputs (denoted by ), and the total cost that firms have to pay collectively in case the is realized, i.e. costs for recycling and treatment, for transporting resources among firms, and transaction costs (denoted by ). Formally, the among agents in a nonempty finite set of agents is a normalized superadditive cooperative game where for , is equal to if , and otherwise.
Benefit sharing is crucial in the process of implementation, mainly because of stability and fairness concerns. Roughly speaking, firms are rational agents that defect unbeneficial collaborations (instability) and mostly tend to reject relations in which benefits are not shared according to contributions (unfairness). Focusing on the Core and Shapley allocations Osborne and Rubinstein (1994); MasColell et al. (1995)—as standard methods that characterize stability and fairness—these solution concepts appear to be applicable in a specific class of s but are not generally scalable for value allocation in the implementation phase of s. In particular, relying on the balancedness of twoperson games, denoted by , we can show that any is implementable in a fair and stable manner. However, in larger games—as balancedness does not hold necessarily—the core of the game may be empty which in turn avoids an implementation that is reasonable for all the involved firms. So, even if a symbiosis could result in collective benefits, it may not last due to instable or unfair implementations. A natural response which is inline with realistic practices is to employ monetary incentives as a means of normative coordination—to guarantee the implementability of “desired” s. To allow a smooth integration with normative rules, we transform games into basic MCNets^{1}^{1}1A basic MCNet represents a game in as a set of rules , where , , , , and is the set of rule indices. For a group , a rule is applicable if and . Then will be equal to where denote the set of rule indices that are applicable to . This rulebased representation allows natural integration with rulebased coordination methods and results in relatively low complexity for computing allocation methods such as the Shapley value Lesca et al. (2017); Ieong and Shoham (2005). through the following steps: let be an arbitrary game, be the set of all groups with two or more members where denotes its cardinality. We start with an empty set of MCNet rules. Then for all groups , for to , we add a rule to the MCNet.
2.2. Normative Coordination of ISNs
Following Shoham and Tennenholtz (1995); Grossi et al. (2013), we see that norms can be employed as game transformations to bring about more desirable outcomes in games. For this account, given the economic, environmental, and social dimensions and with respect to potential socioeconomic consequences, s can be partitioned in three classes by a normative socioeconomic policy function , where is a finite set of firms. Moreover, , , and are labels—assigned by a thirdparty authority—indicating whether an is promoted, permitted, or prohibited, respectively.
The rationale behind introducing policies is mainly to make sure that the set of promoted s are implementable in a fair and stable manner while prohibited ones are instable. To ensure this, in real practices, the regulatory agent introduces monetary incentives, i.e., ascribes subsidies to promoted and taxes to prohibited collaborations. We follow this practice and employ a set of rules to ensure/avoid the implementability of desired/undesired s by allocating incentives^{2}^{2}2See Meir et al. (2011); Zick et al. (2013) for similar approaches on incentivizing cooperative games.. Such a set of incentive rules can be represented by an MCNet in which is the set of rule indices. Then, the incentive value for , is defined as where denotes the set of rule indices that are applicable to . It is provable that for any game there exists a set of incentive rules to guarantee its implementability.
2.3. Coordinated ISN Games
Having policies and regulations, we integrate them into games and introduce the concept of Coordinated s (s). Formally, let be an and be a set of regulatory incentive rules, both as MCNets among agents in . Moreover, for each group , let and denote the value of in and the incentive value of in , respectively. We say the Coordinated Game () among agents in is a cooperative game where for each group , we have that .
It can be observed that employing such incentive rules is effective for enforcing socioeconomic policies. In particular, we have that for any promoted game, under a policy , there exist an implementable game. Analogously, similar properties hold while avoiding prohibited s or allowing permitted ones. The presented approach for incentivizing s is advisable when the policymaker is aiming to ensure the implementability of a promoted in an adhoc way. In other words, an that ensures the implementability of a promoted may ruin the implementability of another promoted . To avoid this, the set of collaborations that a policy marks as promoted should be mutually exclusive. Accordingly, we have the desired result that the mutual exclusivity condition is sufficient for ensuring the implementability of all the s among promoted groups in a fair and stable manner.
3. Concluding Remarks
The details of the components for developing the implementation framework—rooted in cooperative games and coordinated with normative rules—consist of algorithms for generating incentive rules and policy properties to ensure the implementability of promoted s. We plan to explore the possibility of having multiple policies and tools for policy option analysis Mehryar et al. (2017) in s. Then, possible regulation conflicts can be resolved using prioritized rule sets (inspired by formal argumentation theory Modgil and Prakken (2013); Kaci and van der Torre (2008)). We also aim to focus on administration of s by modeling them as normative multiagent organizations Boissier and Van Riemsdijk (2013); Yazdanpanah et al. (2016) and relying on normaware frameworks Dastani et al. (2016); Aldewereld et al. (2007) that enable monitoring organizational behaviors.
The project leading to this work has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 680843.
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