A novel framework for water right conflict resolution considering actors’ power and inter-organizational relationships analysis

Integrated water resources management is one of the issues that need to be taken care of by a wide range of organizations and relevant policymakers. Every one of these organizations focuses on their own interests and priorities to play an important role as an actor in water resources management (Fliervoet et al. 2016). Consequently, the diversity of organizations and their interests could result in conflict of interest among stakeholders (Miles 2012). The conflicts could always occur in various parts of water resources management such as water quality management (Vanda et al. 2022), reservoirs management (Mooselu et al. 2021), surface water transfer (Ahmadi et al. 2019a, 2019b; Yuan et al. 2020; Sohrabi et al. 2022), groundwater management (Taravatrooy et al. 2019), water allocation from dam reservoirs (Mojarabi-Kermani et al. 2019), water reuse (Chhipi-Shrestha et al. 2019), irrigation water management (Xu et al. 2019), and transboundary waters between countries (Dowlatabadi et al. 2020).

Similarly, the possibility of water conflicts in Iran is potentially high, which is due mainly to the transboundary waters with neighboring countries, reservoirs, lakes, wetlands, and the diversity of rivers all over the country, as well as a large number of organizations and decision-makers involved in the surface and subsurface water resources management. Hence, it is vital to include all organizations and stakeholders, who directly or indirectly play a role, in the study of these conflicts. The main objective of this study is to investigate the water allocation from the Ilam dam as the study area. Various organizations can play significant roles in the study area, directly or indirectly. As a consequence, studying the power and relationships among these organizations, as well as the potential conflicts, will also fall within the framework of this study. While the social network analysis (SNA) method could be used to study the power and relations among different organizations, the game theory studies the conflicts among them.

SNA is one of the methods that could be used to study and analyze the relationships among actors and decision-makers (Prell et al. 2009; Lienert et al. 2013). SNA is well capable of depicting the value of relations and the power of actors in ties and nodes of the graphs, respectively, using the adjacency matrix related to the interaction of actors and the corresponding graph (Borgatti et al. 2018). The relations among actors are based on the research questions, and have been collected using a specific and standard questionnaire, which make up the adjacency matrix. Ultimately, the specific relations are analyzed based on the objectives of the study (Bodin & Prell 2011). One of the most important ties among actors is the information exchange tie in which the level of information exchange could show the intensity of relationships among the actors in the network (Bodin & Prell 2011). This exchange of information in inter-organizational relationships could occur at different levels such as official correspondence, routine meetings, cooperation memorandums, joint projects, and financial transactions among different organizations (Jafarian et al. 2016).

Another factor assessed by SNA is the actors’ power, which can be evaluated by centrality measures (Freeman 1978). Analyzing the power in the social network leads to a better understanding of the role of actors in the network and their influence on the process of decision-making (Paletto et al. 2015).

Studying the actors’ relationships and assessing their power in water resources management have been well documented in some studies in Iran. Jafarian et al. (2016 and 2017) used SNA to assess integrated water resources management in Garmsar plain, Iran. They studied the position, role, relations, and power of different organizations in the network. Likewise, Ahmadi et al. (2019a, 2019b) carried out a study to find the key actors as well as their collaborative and conflictive relations using stakeholder analysis (SA) and SNA. They studied five different categories of these relations in regard to the surface and subsurface water management in the Kan River Basin.

Based on the objectives of this study, organizations involved in the quantitative and qualitative management of Ilam dam have been introduced as the desired network. Some of these organizations directly benefit from water allocation (e.g., Urban Water and Wastewater Company [UWW] and Jihad Agricultural Organization [JAO]), and some are indirectly involved in the network. Due to the scarcity of water resources, especially in dry years, the conditions for potential conflict between the relevant organizations in terms of quantity and quality have been hypothesized. For instance, the conflict between the potable water sector (UWW), the agricultural sector (JAO), and the environmental sector (Department of Environment [DoE]) can be considered as the quantitative conflict in terms of allocated water from the Ilam dam. Similarly, the conflict between the organizations guaranteeing the quality of potable water (Health and Treatment Center [HTC]) and Water Authority Company (WAC; executive management of water allocation from the dam) is considered as the qualitative conflict. Therefore, it is necessary to analyze the relationships between the involved organizations to define the main reason of the conflict (quantitative, qualitative, or quantitative–qualitative) by considering their power.

Furthermore, the centrality measures, including in-degree and out-degree centralities, betweenness centrality, eigenvector centrality, and beta centrality, were used to assess the power of actors in the network. Studying these relationships among actors and evaluating their power before modeling and analyzing the conflict, as a novelty method, could provide the decision-makers with a better understanding and evaluation of the conflict.

Modeling and analysis of conflicts always require a useful and effective tool to clarify the future of conflicts for decision-makers and stakeholders, which is the main objective of conflict analysis. Game theory is one of the most effective tools to study conflicts, which can provide an appropriate analysis of the future of conflicts using factors such as players, their strategies, priorities, and payoffs (Madani 2010). Overall, game theory models are divided into two categories: non-cooperative and cooperative games. In a non-cooperative game, every individual player tries independently to gain the maximum payoff based on their own goals, while in the cooperative game, the players agree on joint coalition, and the decisions are made jointly by all members. At the end of the game, the payoffs achieved will also be divided equally among all members of the coalition (Madani 2010). Therefore, it is necessary to determine the type of relationships among actors in the game, whether it is cooperative or non-cooperative, so that a proper method of analysis to be selected based on that. In order to study the behavior of actors in the conflict, it would be vital to first analyze the structure of inter-organizational relationships in water resources management comprehensively.

The inter-organizational relationships in water resources management in Iran have not been defined based on integrated water resources management and sustainable development. In this type of relations, each organization tries to achieve its own priorities and benefits in the short run using quick-return strategies. Thus, the management pattern relies mostly on the inter-organizational knowledge and lacks the necessary conditions to balance between policies, plans, and priorities of those involved to utilize the resources in a sustainable manner (Jafarian et al. 2016). Hence, the risk of conflicts among different organizations would be high due to the current management situation. These conflicts are usually considered as non-cooperative as based on their policies, and the possibility of cooperation among them is very low. In such a condition, the decision-makers in each organization will only try to gain the maximum payoff from the game. As far as these conflicts are concerned, it is advised that the non-cooperative solutions in game theory be used to resolve the conflicts among different organizations.

In order to use the non-cooperative solutions in game theory, the non-cooperative stability concepts are defined which are used in the Graph Model for Conflict Resolution (GMCR). These stability concepts consist of Nash Stability (Nash 1951), General Meta-Rationality (GMR) (Howard 1971), Sequential stability (SEQ) (Fraser & Hipel 1979), and Symmetric Meta-Rationality (SMR) (Howard 1971).

The application of the GMCR model in water resources management is such prominent that efforts are made to resolve the conflicts based on the status quo using a probable solution (probable equilibrium) (Yu et al. 2015). In the GMCRII model (Hipel et al. 1997), the conflict analyzer would have done the analysis using the status quo indirectly, while after the development of this model, known as GMCR+ by Kinsara et al. (2015), it is capable of giving the analysis output as conflict graphs as well as analyzing the conflict using post analysis. This would enable the analyzers to directly access the probable equilibrium and the outcome of the conflict considering the status quo. Moreover, unlike GMCRII, which is only capable of modeling the conflict for a maximum of five actors and 100 status of conflict, this model is capable of modeling the conflict for an infinite number of actors and status of conflict (depending on the system processor) (Kinsara et al. 2015). Thus, for conflicts with numerous actors and possible states, using GMCR+ would become the preferable option.

In general, there is a research gap in determining the key players and their power in the GMCR. Previous studies such as Yu et al. (2015) defined players and their power based on the background of the conflict using the GMCR framework. However, in real-world conflict, especially among some organizations with different goals, the definition of players and evaluation of their power can be considered as a controversial issue because these organizations pursue a quick-return strategy, and their priorities and goals may change over time. These conflicts require a specific approach to define the reason for the conflict, the players, and their power before analyzing the conflict. SNA, which is capable of dealing with such issues, would be an effective approach.

This study aims to investigate the conflict in both basic and power-asymmetric conflict analysis models using GMCR+ by considering the intensity and nature of actors’ relationships as a novel approach. This would help the decision-makers to comprehend both the role of power and the relations among the actors in the outcome of the conflict in a more tangible way.

In this study, the Ilam dam is considered as the study area to investigate water quantity and quality allocation. Golgol, Chaviz, and Ama are three sub-basins of the Ilam dam watershed depicted in Figure 1. The main goals of building this dam are (1) potable water allocation to supply Ilam city water demand; (2) agricultural water allocation to satisfy water demand of downstream farms; (3) flood management of the Konjamcham river located in the intersection of Golgol, Chaviz, and Ama rivers; (4) the improvement of region's ecosystem condition (Mahab Ghods Consulting Engineering Company 2011). Moreover, the definition of the problem is depicted in Figure 2.

The organizations directly related to the main goals of constructing the Ilam dam are presented in Figure 2. However, other organizations can also participate in the process of the dam management whose identification and their inter-organizational relationships play a pivotal role in conflict resolution.

The concept of power is one of the most complicated concepts in inter-organizational relationships due to its wide range of relationships and dimensions. Hence, studying the relationships among different organizations can be an effective approach to better understanding inter-organizational power in this respect (Ramos et al. 2019). Based on the SNA, there are some measures to evaluate centrality indicator in the network structure in which the definitions and relevant formulas are elaborated below:

• 1.
  Degree centrality: degree centrality refers to the number of direct relationships (ties) connecting an actor (node) to other actors in a network (Freeman 1978). An actor with a high degree of centrality can access great resources in the network. In addition, degree centrality is known as in-degree and out-degree centralities in an undirected graph calculated by formulas (1) and (2) (Freeman 1978):

  

  (1)

  

  (2)

  where ID_j and OD_i are the in-degree and out-degree centralities related to the jth node and ith node, respectively. N is the number of nodes and A_ij is the element of the adjacency matrix (ith row and jth column) (Ahmadi et al. 2019a, 2019b).

• In-degree and out-degree centralities indicate the power and influence of an actor in a network, so these centralities are considered as fundamental measures to evaluate the power level in a network.

• 2.
  Betweenness centrality: betweenness centrality is the number of shortest paths between all actors (nodes) passing through the actor itself (formula 3). Furthermore, normalized betweenness centrality is used to compare the amount of betweenness centrality in a specific node with all nodes in the network calculated by formula (4) (Freeman 1978).

  

  (3)

  

  (4)

  where P_ij(m) is the number of geodesic distances between nodes i and j which contain node m. P_ij is the total number of paths connected node i to node j (Ahmadi et al. 2019a, 2019b). An actor, considering a high level of betweenness centrality, has the power to organize the interests of society and pass information to the entire network (Prell et al. 2009).
• 3.
  Eigenvector centrality: in this kind of centrality, communication with the actors who have a high level of relationships can play a pivotal role (Borgatti & Everett 1997). In other words, two factors lead to the increase of the amount of eigenvector centrality, namely the total number of adjacent actors (nods) and the importance (eigenvector centrality score) of adjacent actors (Bihari & Pandia 2015). Thus, this centrality is connected to the power and influence of actors which is calculated by formula (5) (Bonacich 1987):

  

  (5)

  where N₀ is the number of vertex sets associated with the node (Ahmadi et al. 2019a, 2019b).
• 4.

  Beta centrality: Bonacich (1987) explains that, in certain circumstances, the mentioned centrality measures cannot find powerful actors; therefore, he defined a new concept of centrality known as beta (Bonacich) centrality. In the special networks, the situation of the powerful actors may not be in the center of the network, while these actors have semi-peripheral situations, so beta centrality can be used to evaluate the power of the actors (Cook et al. 1983). Several scholars have studied the relationship between actors’ power assessment and centrality measures (Table 1).

The concept of power can play a pivotal role in game theory, which can be considered the greatest ability of a player (actor) against other players. It can change the actions and goals of players participating in the game (Finne et al. 2015). Based on the classification of game theory, the GMCR belongs to non-quantitative approaches (Hipel & Fang 2005). Similarly, the main goal of this study is inter-organizational conflict resolution according to non-cooperative approaches. Hence, we can benefit from the GMCR to model and analyze the conflict and predict the outcome of the conflict based on the equilibrium states. In addition, the latest version of GMCR (GMCR+) (Kinsara et al. 2015) can display the total number of feasible states along with unilateral improvements, which are helpful to find the possible equilibrium based on the status quo of the conflict. The concept of power is required to be considered in this model, which is due to the effective role of players’ power in the outcome of the conflict. Yu et al. (2015) investigated the impacts of players’ power in the conflict, which is the first study about the application of power in the GMCR. Overall, the assessment of players’ power, in some cases, is considered as a controversial issue that cannot be inferred from the background of the conflict. In these cases, before modeling and analyzing the conflict, we can evaluate players’ power and relationships using an appropriate method to have a clear perception of the real-world conflict.

As can be noticed, the concept of power and actors’ power assessment has extensive utilization in SNA and game theory that can be considered as a bridge between these methods and setting the main goal of our study. In this study, we evaluated the actors’ power based on SNA centrality measures and then investigated the influence of the most powerful actors (players) on the water right conflict. Players’ power can affect some parts of modeling as well as analyzing the conflict, such as choosing influential players, defining players’ strategies, removing infeasible states, setting the relevant priorities, and achieving possible equilibrium states, which have been depicted in Figure 3.

Based on Figure 3, the first step of SNA in this study is defining the inter-organizational network (Section 2.1), followed by defining the network boundary based on the objective of the study. The snowball sampling is used to complete the list of organizations involved in the issue (Section 2.5). Finally, the data is collected based on the structured interviews with the experts working in the relevant organizations (Section 2.6).

Moreover, besides the centrality measures calculated by UCINET software, the intensity and the nature of relationships (cooperation/conflict) can play a crucial role in conflict analysis. Based on Figure 3, after visualizing the nature of relationships with NETDRAW software, the main issue of the conflict among the most powerful organizations (players) can be determined, which is the first step of the GMCR process. In addition, the intensity of relationships, specifically the relationships with the most powerful player, directly affects the prioritization of organizations and the outcome of the conflict (equilibria).

Selecting the actors (organizations) and defining the network boundary are the first step to modeling the inter-organizational network. As mentioned, we considered the inter-organizational relationships in the allocation of Ilam dam water right as the inter-organizational network. At the second step, snowball sampling (Goodman 1961) was used to choose the actors (organizations) who play a role in the context of this study. In this sampling approach, by designing a questionnaire and asking the actors in the primary circle of the network boundary, we sought the organizations that directly or indirectly influence the network. Finally, the list of organizations related to the research topic was obtained (Table 2).

Based on the goals of Ilam dam construction, after the dam became operational in 2001, routine meetings were held in the WAC to manage water quantity and quality allocation among the stakeholders (agricultural, urban, and environmental sectors). In these meetings, some experts from the associated organizations such as Provincial Government (GOV), DoE, HTC, JAO, Natural Resources and Watershed management office (NRM), and UWW also participated. Some organizations in Table 2 play a direct role in the problem, and the others can play a supportive role by supplying enough budget from the central government, such as the Member of Islamic Consultative Assembly (ICA). In addition, when the conflict is escalated, the Justice (JUS) can benefit from its power to participate in the conflict and protect the public's right. Also, the other organizations who are in the network boundary are determined by snowball sampling.

Data collection is the main part of the network modeling. In this section of the study, we used some structured interviews with the experts working in the mentioned organizations (Table 2). These interviews include two major parts. In this regard, we designed a questionnaire and asked them for the identification of inter-organizational relationships based on their organizational documents. This identification was determined by the Likert scale (Likert 1932) to score the level of relationships based on Table 3 (Jafarian et al. 2016; Ahmadi et al. 2020).

Moreover, in the second part of the interview, collaborative and conflictive relationships were examined by another questionnaire. These types of relations were sorted into four groups according to the quantitative and qualitative water allocation of the Ilam dam. These groups included 1 – collaborative relationships, 2 – conflictive relationships (type 1) related to quantitative water allocation (such as Ilam dam water right management), 3 – conflictive relationships (type 2) related to qualitative water allocation (such as Ilam dam water quality management), and 4 – conflictive relationships (type 3) (both quantitative and qualitative water allocation). These groups are determined by their codes (1–4) in the relevant matrix represented in the Supplementary Material.

Having collected the data, UCINET software (Borgatti et al. 2002) was used to evaluate actors’ power according to the adjacency matrix (Supplementary Material). In this matrix, the Likert scale (0–5) should be transferred to a binary scale (0–1). In order to dichotomize the adjacency matrix, we used the code ‘1’ for the relations greater than 3 and the code ‘0’ for the other relations. Finally, the binary adjacency matrix was processed by UCINET to find centrality measures presented in Figure 4. UCINET applies formulas (1–5) to calculate in-degree and out-degree, betweenness, and eigenvector centralities. Also, this software can calculate beta centrality by exact and iterative methods. The exact method is slow for large networks but should be the preferred method due to the possibility of divergence for the iterative method in some cases. Therefore, the exact method was used in this study.

As can be seen in Figure 4(a), in-degree and out-degree centralities are normalized. Additionally, GOV and WAC have the highest rank in this figure. Apart from these powerful organizations, UWW and JAO are considered as powerful organizations, while the DoE has average power. Likewise, Figure 4(b)–4(d) represent betweenness, eigenvector, and beta centrality, respectively, that are indicated the actors’ power, and similarly, GOV, WAC, UWW, JAO, and DoE can be considered as the most powerful organizations among all.

At the next stage, we investigated the collaborative and conflictive relationships between the mentioned powerful organizations and the rest using NETDRAW software (Borgatti et al. 2002). All characteristics of relations, including the intensity and nature (cooperation/conflict), were drawn by NETDRAW based on the adjacency matrices (Figures 5 and 6).

In Figures 5 and 6, the size of the ties and nodes indicates the intensity of the relationships and in-degree centrality, respectively. Similarly, the red, green, and blue lines show conflictive relationships (type one, two, and three, respectively). As can be seen in Figures 5 and 6, and Supplementary Material, JAO, for instance, has the relationships with GOV and WAC at the fourth level in terms of the intensity, indicating that they participate in some projects based on inter-organizational bureaucracy, while there is a conflict between them for quantitative water allocation, especially in dry years.

Generally, most conflictive relationships are related to the quantitative water allocation (six relationships) that emphasizes the importance of this issue among the actors. This type of conflictive relationship (type 1), which is completely obvious among actors with a high level of power, can be scrutinized by the explicit definition, modeling, and analyzing the conflict, considering the actors’ power and relationships.

The increase in water demand causes quantitative water allocation conflict (water right conflict) among organizations with a high level of power, including GOV, WAC, JAO, UWW, and DoE. In this conflict, three stakeholders, including UWW, JAO, and DoE, have the right to maintain their water demands by the specific water resource (Ilam dam), but the analysis of the network's relationships determines to what extent this right can be achieved. Besides, GOV has the political power from the central government to participate in the conflict when it is escalated. Also, WAC has the operational power from the Ministry of Energy to satisfy stakeholders’ water demands (Zanjanian et al. 2018). In this study, analyzing the network graph (Figure 6) and annual water allocation graph (Figure 7) can provide a relatively clear definition of the water right conflict.

First of all, as can be seen in Figure 6, the DoE builds conflictive relationships with JAO, UWW, WAC, and GOV on the increase of environmental water right. Similarly, increasing agricultural and potable water demand creates conflictive relationships between JAO, UWW, and other powerful organizations. However, UWW develops high cooperative relationships (Figures 5 and 6) with GOV and WAC. In other words, communication with highly powerful organizations (GOV and WAC) is an important point that can affect the conflict's outcome.

Moreover, analyzing the water allocation data in each sector can effectively give a proper perception of the conflict outcome. As shown in Figure 7, reservoir volume and reservoir inflow can be considered as two fundamental factors to satisfy the water demand of each sector. Also, this graph can be divided into two parts based on the climate situation. In the first part, including the wet years (2005, 2006, 2009, 2010, and 2013), the reservoir situation was satisfactory in terms of total volume and charge. On the other hand, in the dry years (2007, 2008, 2011, and 2014), the Ilam dam had an undesirable situation, leading to decreased environmental and agricultural water allocation. Considering the wet and dry years, the comparison of water allocated to different sectors can lead to the modeling and analysis of the real-world conflicts.

After that, the conflict was modeled and analyzed into two main sections, namely basic and power-asymmetric conflict analysis approaches.

The first step of conflict modeling is to identify the key players. In some cases, with increasing organizations and their relationships, the assessment of key players becomes a controversial issue. Thus, in this conflict, we benefit from SNA as a valuable approach to reduce conflict modeling complexities. Based on the results of centrality measures (Figure 4), GOV, WAC, UWW, JAO, and DoE are the key actors who play a crucial role in the conflict. With an assumption of ‘n’ strategies for all the players, the total number of conflict states equals 2^n. So, increasing the players and their strategies complicates the conflict. In order to simplify the conflict model, it is assumed that GOV and WAC build a coalition for three reasons. Firstly, WAC is responsible for allocating water right for each sector, and GOV is responsible for resolving the escalated conflict. Hence, these organizations can create the coalition as the operational and political power authorized by the central government. Secondly, according to our survey results, GOV and WAC have held the weekly meeting on Ilam dam water allocation. Additionally, based on the inter-organizational network analysis (Figure 5), these organizations have close communication about this conflict, leading to close priorities and goals. Finally, this assumption eliminates the complexities involved in the modeling of the conflict and leads to the tangible equilibrium states that make the conflict analysis simple. Accordingly, the key organizations (players) and their strategies with the status quo of the conflict are presented in Table 4.

The table indicates that JAO and UWW have taken water more than their water right or have kept/reduced existing water right. Also, the DoE can approve/reject environmental impact assessment as the legal strategy to put pressure on other organizations to obey their existing water right. When the conflict is escalated, the DoE can choose the strategy of suing other organizations for receiving the negligible environmental water right (Zanjanian et al. 2018). GOV and WAC can gain power in the basic conflict to convince other organizations to cooperate through weekly meetings. In the basic approach, the coalition, as the actor with the highest level of power, participates in the conflict indirectly, which can select one strategy to encourage other actors to reach the desired equilibrium. According to the status quo of the conflict, JAO and UWW pursue the strategy of taking water more than their water right to reach their goals quickly, and the DoE chooses the S5 (putting pressure on other organizations) because the strategy of suing other organizations makes the conflict escalated (Zanjanian et al. 2018).

As seen in Table 4, the total scenarios of this game are seven. Therefore, all the possible states of the game will be 128 (27). However, one of the important stages of conflict modeling is removing the infeasible status. In other words, removing the states that are not likely to occur, or the occurrence is illogical, would reduce the feasible states in the conflict. The conditions that might occur in this game due to the existing rules and lead to the removal of some states are as follows: (1) JAO and UWW can not approve or reject their scenarios simultaneously. (2) If either JAO or UWW selects the receipt of more water right option, the DoE will choose the legal pressure to receive its water right as well; but if these organizations prefer their secondary scenario, the DoE can not sue them because none of the organizations has violated the rules, and choosing the confrontation scenario by the DoE will be illogical. (3) Also, based on the inter-organizational hierarchy, the DoE first sticks to the legal leverage, and in case the conflict is escalated and they are deprived of their water right, a lawsuit will be filed. (4) As the coalition between GOV and WAC includes only one strategy, which is not logical to ignore it, these organizations will benefit from this strategy in all feasible states of the conflicts (Y). Therefore, regarding the rules mentioned, the states occurring contrary to these rules will be eliminated from the conflict. By removing these states, the total feasible states in the conflict will be seven, as presented in Table 5.

Regarding Tables 4 and 5, state 2 is considered as the status quo in the basic conflict analysis model.

In the basic conflict analysis model, the most powerful player (the coalition of GOV and WAC) will neither use the direct force nor the relationship to influence actors’ priorities. Therefore, both JAO and UWW will prefer to receive more water right, and the rival organization will also choose the option of not using more water right, the DoE will not file a lawsuit either (state 4 for JAO and state 3 for UWW). On the other hand, when the rival organization receives more water right, and these organizations choose the less water right option, it will also be considered as the lowest priority (state 3 for JAO and state 4 for UWW). The highest priority for the DoE will also be the state in which neither JAO nor UWW receives more water right (state 1). Accordingly, the lowest priority for the DoE will be the state in which both JAO and UWW receive more water right, and the DoE will not sue (state 2). Finally, similar to the DoE, the highest priority for the coalition of GOV and WAC will also be state 1, as in this state the conflict will come to an end and there will be no legal claim either. However, in case these organizations violate the rules and the DoE also sue (escalated conflict), they will consider it as their lowest priority (state 5). Table 6 presents the actors’ priorities in the basic conflict analysis model.

Based on the analysis carried out, states 1 and 5 were the equilibrium points in the basic conflict analysis model (Table 7). It is now possible to reach the probable equilibrium by analyzing the conflict graph (taking into account the conflict Status quo). Figure 8 shows the unilateral improvements in the basic conflict analysis model.

As seen in Figure 8, the conflict begins from state 2, and after getting escalated, the DoE will sue and it reaches state 5 (probable state). As can be noticed, the coalition strategy has no influence on this state of conflict, and the organizations are highly inclined to violate the rules (receive more water right). Thus, in the next stage, the modeling will be carried out considering both the power of actors and their relations, and the results will also be analyzed accordingly.

In this state, the actors and their scenarios are similar to the basic conflict analysis model (Table 4) with the difference that for the coalition of GOV and WAC, there will be two ‘punish’ scenarios (S8 and S9) for JAO and UWW, respectively, which have more water right. In fact, as previously mentioned, because this coalition has direct power, they can use it in their scenario. This type of scenario is known as negative power in which the violators are punished; on the other hand, the actors with more powers could also use other scenarios with positive power in which the actors who can potentially violate the rules are rewarded (by providing them with the facilities and budget to satisfy their needs and make progress). However, the mentioned coalition does not have the opportunity to use this type of scenario in this conflict as the facilities and budget of these organizations are provided by the Ministry of Agriculture-Jihad and the Ministry of Energy. Thus, this coalition has no role in allocating budget to the violating organizations. Consequently, the coalition can either choose S8, as a negative power scenario, to punish JAO unilaterally or S9 to punish UWW.

As for the removing infeasible states, apart from the rules stated in the basic approach, new rules (with the addition of ‘punish’ scenarios for the coalition) are also added: (1) the coalition could only choose one of the options of ‘Reward’ or ‘Punish’, but can select both ‘Punish’ options (for JAO and UWW) simultaneously, and cannot reject all its options either (N). (2) The DoE should first choose the suing option (S6), and then the coalition can use the ‘punish’ scenario (S8 and S9). (3) If JAO and UWW do not choose ‘the more water right’ scenarios (S1 and S3), the coalition cannot use the ‘Punish’ option. So, similar to the section of key players and strategies, power also plays an important role in this section and can result in the removal of some states of the conflict.

By removing the infeasible states, the total feasible states of the conflict will be 12 (Table 8). Considering the power and relations among the actors, the status quo of the conflict is, in fact, the same as the probable equilibrium in the basic conflict analysis model; therefore, based on Figure 8, the status quo of the conflict is state 5.

In prioritizing scenarios, JAO and UWW prefer to receive more water right, just like the basic approach, and the rival organization also chooses its second scenario. As a result, the states in which the organizations choose ‘the more water right’ scenario and the coalition choose the ‘reward’ scenario will be the highest priority. Another priority for these organizations will be the states in which they receive more water right and lead to the legal claim of DoE, while the coalition of GOV and UWW chooses the ‘reward’ scenario. This is because the power of DoE in this conflict is weak, and this will be the reason that the violating organizations consider DoE's legal action to the coalition (the actor with more power) as an unsuccessful act. One of the significant differences between power-asymmetric and basic conflict analysis models is that the ‘punish’ states option for these organizations (by the coalition) will be of low importance. Also, the priority of DoE is the state in which the organizations have not violated the rules, or in case of any violation, the coalition will use their power to punish them. Nevertheless, as this organization has the same level of relationships with the violating organizations (Figure 5); thus, this organization does not prioritize any violating organization over another and chooses equal priorities for both organizations (Table 9, blue cells).

On the other hand, the coalition prefers that JAO and UWW do not violate the water right. However, according to Figure 5, as the relationships between the coalition and UWW are much stronger, the preference is that UWW can receive more water right, but JAO does not use this option. So, if JAO chooses this option, they will face punishment. Furthermore, the lowest priority of this organization will also be the states in which they punish UWW for more receipt of water right (S10 and S11). Therefore, based on the discussions, the actors’ priorities, considering the actors’ power, will be as depicted in Table 9.

Having analyzed this conflict (stability analysis), the conflict equilibrium is in the states of 1 and 8 (Table 10). According to the conflict graph, in the state where the power of actors are considered (Figure 9), this conflict starts from state 5, which is the equilibrium for the basic conflict analysis model and reaches equilibrium in state 8 (considering the unilateral improvement by the coalition of GOV and WAC). In state 8, the JAO and UWW will choose the more water right option, but due to the close relationship between GOV and WAC, the punishment will be biased and will only be imposed on JAO; the situation will also be such that water right allocation from the Ilam dam for this organization will be reduced by executive authorities (WAC). This reduction in the water right has been especially more tangible during the dry years when the amount of rainfall has noticeably reduced, and the organizations faced a tragedy due to the lack of resources. As can be seen in Figure 7, the annual inflow to the reservoir, and consequently the reservoir volume, of the Ilam dam has decreased and reached almost its lowest amount in 2007 and 2008 (21 MCM in 2007 and 17 MCM in 2008 in terms of reservoir volume), which in turn resulted in the reduction of water rights for agriculture in these years, from 50 MCM in 2006 to 14 MCM in 2007. As a result of this reduction and lack of resources, the water allocation from the reservoir to the agriculture sector has been completely cut in 2008 and 2009. In the coming years of 2010, 2011, 2013, and 2014, the reservoir volume has relatively recovered, and allocation of water to the agriculture sector has been resumed to a small amount (<10 MCM). However, during these 10 years (2005–2015), the required water for domestic use has been allocated to UWW with a relatively increasing trend (annually about 15 MCM).

It is clear that the priorities of the GOV and WAC coalition, with regard to their power as well as their collaborative and conflictive relationships with other organizations, play a direct role in reaching this equilibrium. In other words, the future of the conflict somehow depends on the relations and policies of coalition with other organizations.

Based on Figure 4, which shows the power distribution among actors based on different centrality measures, the DoE, with less relative power than other organizations (JAO, UWW, GOV, and WAC), was included in the modeling of the conflict. Moreover, JAO and UWW have got equal relative power, but due to the strong relations of UWW with the most powerful organizations in the network (GOV and WAC), the conflict reached the probable equilibrium state in favor of this organization, with the rival organization (JAO) being punished. Consequently, the result of power and the intensity of the relations among organizations could directly influence the future of the conflict. However, it is necessary to analyze the states of conflict that prioritize actors with little power (DoE).

In this conflict, the priorities of DoE are states 1, 9, 11, and 12. State 1 is the desired equilibrium (Pareto point) in this conflict, which was discussed in Zanjanian et al. (2018). Also, a third party (an arbitrator) who has the authority to remove some special states of the game should intervene in the conflict to reach this state. The other three states of the conflict (9, 11, and 12) are the ones in which any violating organization will be punished by the more powerful actor (the coalition of GOV and WAC). In order to study these states, the ‘Post Analysis’ section in ‘GMCR + ’ could be referred to. In this section, the status quo (state 5) is first determined, followed by the target state (state 12). Based on the results achieved from this section, the coalition should prefer state 12 over states 10, 5, and 8, so that state 12 is considered as the powerful equilibrium state (NASH, SEQ, GMR, and SMR) in this conflict. In the next stage, the conflict could reach a stable state by punishing the actors of the game, i.e., in state 9 (by punishing JAO), in state 11 (by punishing UWW), or in state 1 (by punishing both actors). Therefore, it is evident that the future of this conflict is fully affected by the action of the actor with more power. In case the actor with less power could make its relations with the coalition stronger, it is likely that state 12 would be preferred over states 10, 5, and 8, which are the priority for JAO or UWW (or both). Consequently, the role of inter-organizational relations in the outcome of the conflict is of high importance.

In this study, the role of SNA is quite prominent as a means of studying organizational relations. Organizational relations play a crucial role in the outcome of the conflict. The organizations that have a leading role in the conflict were determined using SNA, which is quite different from methods used in the previous studies to determine the actors in the conflict. In other words, in previous studies, the decision on the presence or absence of that actor in the conflict was made based on the conflict background and the role of each actor. Nevertheless, in this study, considering the complexities involved in inter-organizational conflicts as well as the difficulty of precisely deciding which organizations to participate in the conflict, the SNA was used to overcome these complexities. For instance, considering the results achieved from the SNA in this study (Figure 4), the organizational power of a Member of ICA is low, while this actor has the potentiality to question the Ministers of Energy (the UWW and WAC are the subsets of this ministry) and Agriculture-Jihad, regarding the conflict, and directly influence the outcome. On the contrary, this actor has no special relationships with other organizations in the study area with respect to this study; as a result, this actor is not included in the modeling of the conflict, whereas this actor is fully authorized to get involved. On the other hand, it is likely that this actor will get involved in the conflict in another study area with the same subject due to the local concerns for that specific area. Thus, the SNA tool can decide on the presence or absence of actors in complex games.

With the vast increase of relations among organizations and institutions associated with water resources management, it is important to study these relations to fully understand the status of these organizations to analyze the possible conflicts among them. Accordingly, the concept of power could play a significant role in the conflict. Thus, it is vital to study the level of power among different actors using a proper method. As suggested in some literature, the SNA method can be used as a proper tool to analyze the relations and status of power among different actors. Moreover, this method has the advantage of classifying and plotting the relations among different actors in different states, such as collaborative and conflictive relations among them.

In this study, the organizations involved in the water quantity and quality allocation have opted as the network boundary, so that the efficiency of this method can be evaluated with the important issue of water allocation. Water allocation is a challenging issue in Iran due to the administrative bureaucracy, which, in turn, could engage different organizations in the conflict. This means that the outcome of the conflict will depend on the evaluation of relations among the engaged organizations. In addition, studying the relations among the involved actors will make it easier to define the conflict more precisely. In fact, in this problem, the conflict could be quantity, quality allocation, or quantity–quality, which can only be properly defined by analyzing the relations among actors and is also considered one of this study's novelties. Having analyzed the collaborative and conflictive relations in the network, the conflict on the water quantity allocation among the actors of the network was defined.

Furthermore, the concept of power was evaluated using centrality measures including in-degree and out-degree centralities, betweenness centrality, eigenvector centrality, and beta centrality. As a result, the most powerful organizations in the network were the GOV, WAC, JAO, UWW, and the DoE. It is noteworthy that it might be the first time the analysis of actors’ power, with the application of computational methods, was directly used in the modeling of a known conflict in such a study.

Having determined the key actors, the GMCR model (GMCR+ version) was used to solve the conflict. Like the SNA method, GMCR+ also enables us to analyze the existing states using the conflict graph. To study the concept of actors’ power, this conflict was modeled in two approaches, namely basic and power-asymmetric. In addition, to reduce the conflict states and simplify the modeling as well as the analysis, the WAC and GOV, as the political and executive powers, were considered as one coalition. Moreover, the number of scenarios in the basic and power-asymmetric conflict analysis models was 7 and 9, respectively, which is due to the power exercised by the coalition. In other words, while the power of actors is considered in the conflict, the coalition can use its right to directly punish the violators (JAO or UWW), which is called the negative power scenario. Having removed the infeasible states of the conflict, using the rules and mechanisms among players, the number of feasible states in the basic and power-asymmetric conflict analysis models was 7 and 12, respectively. In the final stage of conflict modeling, the actors’ priorities to the existing states of conflict were applied. In this stage and in the basic model, JAO and UWW prefer to receive more water right (states 3 and 4, respectively), while the DoE and the coalition prefer to choose state 1, in which no organization violates the rules, and the conflict will end. On the other hand, in the power-asymmetric model, the violating organizations prefer to receive more water right, just like the basic model, on condition that they would not be punished. One of the differences of this model with the previous one is that the states resulting in the punishment of violating organizations by the coalition will be of low priority. So, the role of the intensity of relations among organizations in the power-asymmetric approach is also of high significance in determining the priorities, which is considered as one of the novelties of this study. Based on the graph depicting the intensity of the relations among actors, the level of relations between DoE and JAO/UWW is equal, making the preferences of this actor the same as the basic conflict model. On the other hand, the coalition has strong relations with UWW, and as a result, their priorities will tend towards this actor with the preference of receiving more water right without being punished.

Finally, having modeled the conflict, it would be possible to compare the probable equilibria in two conflict models with respect to the status quo of the conflict. In the basic approach, the probable equilibria will be states 1 and 5, and regarding the status quo (state 2), the conflict will reach equilibrium in state 5. This indicates that JAO and UWW have violated, and as the coalition is not considering the direct punishment for the violators in this state, the conflict will reach equilibrium in the escalated form. On the other hand, in the power-asymmetric model, the probable equilibria will be states 1 and 8, and regarding the status quo (state 5), the conflict will reach equilibrium in state 8. In state 8, JAO and UWW are willing to receive more water right, while the coalition, as an actor with higher power, is biased towards JAO and more inclined towards UWW, which will result in the one-sided punishment of JAO by WAC as well as reducing its water right. This equilibrium indicates the role of power and relations among actors in the outcome of the conflict as well as being matched with the 10-year water allocation graph from the Ilam dam.

To conclude, as mentioned in the conflict analysis, considering the role of power and relations among actors, the outcome of the conflict and the probable equilibrium will not be inclined towards satisfying the ecosystem and environmental water right needs, which could be considered as the desired equilibrium, and this can help the decision-makers to have a better understanding of the conflict outcomes in the real world.

The authors received no specific funding for this work.

On behalf of all the authors, the corresponding author stated that there is no conflict of interest.

All relevant data are included in the paper or its Supplementary Information.