Journal of Environmental Management 144 (2014) 152e159

Contents lists available at ScienceDirect

Journal of Environmental Management journal homepage: www.elsevier.com/locate/jenvman

A new bankruptcy method for conflict resolution in water resources allocation Hojjat Mianabadi a, *, Erik Mostert a, Mahdi Zarghami b, Nick van de Giesen a a b

Department of Water Resources, Faculty of Civil Engineering and Geosciences, Delft University of Technology, Stevinweg 1, 2628 CN Delft, The Netherlands Faculty of Civil Engineering, University of Tabriz, 51664 Tabriz, Iran

a r t i c l e i n f o

a b s t r a c t

Article history: Received 22 March 2013 Received in revised form 15 May 2014 Accepted 20 May 2014 Available online

Growing competition over water resources has caused political disputes among stakeholders and has brought conflict resolution in the focus of negotiation processes. In these cases, bankruptcy rules for redistributing an asset when it is not sufficient to meet all claims could be applied. In this paper, we develop a new bankruptcy rule for water resources problems that considers agents' contribution to the total resources as well as their claims, which is in accordance with the UN Watercourses Convention (1997), as important factors for reallocation. Using the Euphrates River and a hypothetical case from the literature as examples, the new rule is compared with four alternative rules. The results show that the novel solution is potentially more powerful to help solving conflicts over river sharing problems. © 2014 Elsevier Ltd. All rights reserved.

Keywords: Conflict resolution Water resources allocation Bankruptcy theory Euphrates River

1. Introduction Water resources scarcity, growing resources consumption, and non-equitable distribution of resources have caused several political disputes in the world (HomereDixon, 1994). Concerning shared water resources alone, 43 political or military acts have taken place around the world during the past 50 years. This includes 37 acute disputes that led to small-scale and extensive military acts (Wolf, 2007). Resolving disputes over water resources is a complex task. Power and politics are important, but normative arguments play a role as well. Generally, conflict resolution is only possible if all parties concerned consider the proposed solution as “fair” (Gray, 1989). Hence, parties need to legitimize or “sell” their preferred solution as fair. As Majone (1989) puts it, “even when a policy is best explained by the actions of groups seeking selfish goals, those who seek to justify the policy must appeal to the public interest and the intellectual merits of the case” in order “to bring other people around to (their) position”. Those others that need to be brought around may be the other parties in the conflict, but also influential third parties, such as funding agencies, on whose support the parties in the conflict may depend.

* Corresponding author. Tel.: þ31 15 2781029; fax: þ31 (0) 15 2785559. E-mail addresses: [email protected] (H. Mianabadi), [email protected] (E. Mostert), [email protected] (M. Zarghami), [email protected] (N. van de Giesen). http://dx.doi.org/10.1016/j.jenvman.2014.05.018 0301-4797/© 2014 Elsevier Ltd. All rights reserved.

The central issue at the heart of international water quantity conflict is that there are no internationally accepted allocation mechanisms for sharing water resources or their benefits (Wolf, 1999). With respect to the allocation of internationally shared water resources, the main normative principle is the principle of “equitable and reasonable utilization” which does not necessarily mean equal sharing of resources (Correia and Da Silva, 1999; Salman, 2007; Rahaman, 2012). Several international rules and conventions have been adopted that mention this principle, most notably the Helsinki rules on the Uses of the Waters of International Rivers from 1966 (International Law Association (ILA), 1966), the United Nations Convention on the Law of the Non-Navigational Uses of International Watercourses from 1997 (UN Watercourses Convention, 1997), and the Berlin rules on water resources from 2004, revising the earlier Helsinki rules (International Law Association (ILA), 2004). According to the Article 6 of the UN Convention, utilization of an international watercourse in an equitable and reasonable manner requires taking into account all relevant factors and circumstances, including the following (UN Watercourses Convention, 1997): (a) Geographic, hydrography, hydrological, climatic, ecological and other factors of a natural character; (b) The social and economic needs of the watercourse States concerned; (c) The population dependent on the watercourse in each watercourse State;

H. Mianabadi et al. / Journal of Environmental Management 144 (2014) 152e159

(d) The effects of the use or uses of the watercourses in one watercourse State on other watercourse States; (e) Existing and potential uses of the watercourse; (f) Conservation, protection, development and economy of use of the water resources of the watercourse and the costs of measures taken to that effect; (g) The availability of alternatives, of comparable value, to a particular planned or existing use. The Berlin rules add to these factors the sustainability of proposed or existing uses and minimization of environmental harm and states explicitly and unequivocally that there may be more relevant factors. Equity is generally seen as key to international water resources allocation (Wolf, 1999; Zaag et al., 2002). Yet, despite several studies, there is not yet an universal consensus on the meaning of “equitable and reasonable utilization”. Salman (2007) notes that the management of transboundary river basins remains the most significant issue that is not yet regulated by a global convention or treaty.1 This problem has acted as a formidable obstacle on the road to peaceful negotiations in transboundary basins (e.g. the conflict among Egypt, Ethiopia and Sudan and other riparian states on the Nile Basin (Just and Netanyahu, 1998; Ansink, 2009), the conflict among Tajikistan, Afghanistan, Kyrgyzstan, Uzbekistan, Turkmenistan on the Amu Darya Basin (Rahaman, 2012), the dispute between USA and Mexico over three shared rivers (Drieschova et al., 2008), and the conflict among Turkey, Syria and Iraq in the case of Euphrates-Tigris Basins (Korkutan, 2001; Zawahri, 2006)). Aanalytical methods may be useful for determining the meaning of “equitable” and “reasonable” in specific cases. Zaag et al. (2002), for instance, developed some analytical methods to reallocate all (blue and green) water resources based on equal division only, catchment area only, or basin population only, and applied these to the Orange, Nile, and Incomati rivers (Zaag et al., 2002). Yet, analytical methods should ideally consider all the relevant factors and circumstances mentioned in Article 6 of the UN Watercourses Convention. While there is certainly no guarantee, the more attributes of the “equitable” and “reasonable” allocation they consider, the bigger the chance that they will be acceptable to policy makers and other stakeholders and will contribute to conflict resolution in practice. One of the analytical methods that could be used for conflict management in resource allocation problems is bankruptcy theory. The aim of this method is to distribute an asset (E) among a group of creditors, when this amount is insufficient to satisfy all their claims (C) (Herrero and Villar, 2001). Over the years, several bankruptcy rules have been developed. Some of these rules are based on the associated cooperative bankruptcy game (Grundel et al., 2011). The most used bankruptcy rules are the proportional rule (PRO), constrained equal losses (CEL), and constrained equal awards (CEA), which are based on equal proportions of the claims, equal losses (difference between claim and award) and equal awards, respectively. These three rules which have strong theoretical and empirical support (Ansink and Marchiori, 2010), have been used in many €chter and Riedl, 2006; Herrero et al., practical studies such as (Ga 2009; Xia and Cui, 2009; Sheikhmohammady et al., 2010) and (Ansink and Weikard, 2012). The proportional rule (PRO) is probably the best known and most widely used solution method among

1 The Helsinki rules and the Berlin rules have been developed by a professional organization e the International Law Association e and are not conventions signed by states. The UN Convention is a convention, but it has not yet entered into force because too few states have ratified the convention.

153

bankruptcy rules (Herrero and Villar, 2001). An overview of bankruptcy rules have been documented by Thomson (2003) and Bosmans and Lauwers (2011). In recent years, several researchers have sought to examine the applicability of bankruptcy theory to different natural resources allocation problems, such as groundwater resources management (Madani and Dinar, 2013), multipurpose resources allocation (MPRA) problems (Grundel et al.,2011) and fisheries (Inarra and Skonhoft, 2008). Zarezadeh et al. (2013) proposed bankruptcy optimization models to allocate water based on four bankruptcy rules with respect to time sensitivity of water deliveries during the planning horizon. Ansink and Weikard (2012) extended a class of sequential sharing rules (SSRs) and used them in water resources management (Ansink and Marchiori, 2010). Madani and Zarezadeh (2012) studied the utility of bankruptcy rules in resolving water resources conflicts using a range of bankruptcy rules in a hypothetical groundwater bankruptcy problem. In addition, a comprehensive review of the connection between the bankruptcy theory and river sharing problems has been given by Beard (2011). Sheikhmohammady et al. (2010) applied several well-known bankruptcy procedures to allocation of Caspian seabed resources, oil and gas, across the five Caspian states. Furthermore, Zarezadeh et al. (2012) used PRO, CEA, CEL, and Adjusted Proportional (AP) rules to suggest fair allocation plans in different climate and development scenarios for an internal Iranian river shared by eight provinces. Such studies reveal that the bankruptcy theory can be applied to natural resources allocation including water resources problems in river basin systems. Most of the previously mentioned rules such as the PRO rule do not take into account the contribution that the agents have made to E. The aim of the present study is to give an analytical method that does consider this contribution. The other factors mentioned in art. 6 of the UN Watercourses convention such as social and economic needs and dependent population, can be taken into account when assessing the claims of the different parties. In this paper, these claims are assessed using scientific studies. To apply the proposed bankruptcy rule, it is essential that all relevant factors (cf. art. 6 UN Watercourses Convention) are considered in determining the demands of each riparian country and that the political and military power of each state does not lead to exaggerated claims. This paper is arranged as follows. The new proposed rule will be explained in the next section. In Section 3, the proposed rule will be applied to the Euphrates River and to the hypothetical case study proposed by Ansink and Weikard (2012). In the same section, we also compare the results of the proposed rule with four alternative solutions of bankruptcy to an illustrative river allocation problem. Finally, Section 4 summarizes the conclusions of paper. 2. Methodology There are two reasons for using bankruptcy rules to address rivers reallocation problems (Ansink and Weikard, 2012). First, as in real bankruptcy problems, claims exceed the available resources. Secondly, bankruptcy rules are relatively simple and can be used easily by agents and policy makers in rivers sharing problems. An ordinary bankruptcy problem differs from a bankruptcy problem in river systems problems. First, in an ordinary bankruptcy problem, there are three variables modeling the problem: (1) a finite set of agents N ¼ {1,2,…n}, (2) the asset E which should be divided among the agents, and (3) the claims of agents (ci). In rivers sharing problems, there is another variable which shapes the problem: (4) the contribution of agents to E (ai). In case of transboundary river basins ai is the amount of flow originating in basin state i. In other words, in a simple bankruptcy problem claimants are characterized only by their claims ci, but in a river allocation

154

H. Mianabadi et al. / Journal of Environmental Management 144 (2014) 152e159

problem they are characterized by their contribution ai as well as their claims ci. Secondly, the geographical position of agents can be important in river sharing problems. In ordinary bankruptcy problem this is not the case. Consider a set N of n  2 agents who are claimants and whose claims are ci  0; C ¼ (c1,…,cn) and their contributions are ai  0; a ¼ (a1,…,an). A bankruptcy problem in river systems is defined as F(N, E, ci, ai); i ¼ 1,2,…,n. The aim of bankruptcy method is to determine the allocation of each agent, denoted by F(N, E, ci, ai) ¼ xi which xi  0; x ¼ (x1,…,xn). For a resource allocation problem, we have: n X

E¼

ai

(1)

Fig. 1. The river sharing problem.

i¼1

C¼

n X

ci

(2)

i¼1 n X

ai ¼

i¼1

n X

xi

(3)

i¼1

0  xi  c i

(4)

Eqs. (1) and (2) remark that the contribution of the agents and their claims make up E and C, respectively. The third equation assumes that all assets (E) are fully allocated but not over-allocated. In that case, the sum of the allocations equal E. In the case of water resources this assumes that allocations are made in terms of net water use e abstractions minus any return flows e and not in terms of abstractions only. Eq. (4) states that the allocation an agent receives cannot be negative and never exceeds its claim. The proportion of agent i's claim which is allocated to him (pi) is defined as follow:

pi ¼

xi ci

(5)

useful for river sharing problems in which agents are linearly ordered (see Fig. 1). For such a problem, consider an ordered set N of n  2 agents located along a transboundary river with agent 1 the most upstream and n the most downstream. Agent i is upstream of j whenever i < j. Denote by Ui ¼ {j2N:j < i} the set of agents upstream of i, and denote by Di ¼ {j2N:j > i} the set of agents downstream of i. Moreover, the agents' contribution ai  0; a ¼ (a1,…,an) is the proportion of total inflow of river which originates in the territory of each agent (Ansink and Weikard, 2012). In addition to the given definitions, some new definitions and equations are defined. Definition 1. The total available water on the territory of agent i is denoted by Ei. It is the sum of river inflow on the territory of i and any unallocated upstream water (Ansink and Weikard, 2012).

Ei ¼ ai þ

Definition 2. The excess downstream claims of agent i (CD) is defined as the sum of claims net of assets of all agents downstream of i (Ansink and Weikard, 2012):

CDi ¼

E ¼ rci where r ¼ C

xCEA ¼ minðl; ci Þ where i

X

minðl; ci Þ ¼ E

(7)

i2N

CEA assigns each agent an equal share (l) of E, except that no creditor receives more than his or her claim. The Constrained equal losses (CEL) rule is defined as follows:

xCEL ¼ maxð0; ci  lÞ where i

X

maxð0; ci  lÞ ¼ E

(8)

i2N

CEL allocates each claimant a share of the asset such that their losses in comparison with their claims (l) are equal, constrained to no claimant receiving a negative allocation. As mentioned before, the problem of applying these bankruptcy rules in water resources allocation is that they do not consider the contribution (ai) that the agents make to the resource (E). The sequential sharing rules (SSRs) were developed by Ansink (2009). Although SSRs considers the contribution of agents, this rule is only

X  cj  aj

(10)

j2Di

(6)

in which C and E are the total amount of claims and assets, respectively. PRO allocates each agent the same proportion r of its claims. The constrained equal award (CEA) rule is defined as follows:

(9)

j2Ui

The proportional rule (PRO) is defined as follows:

xPRO i

X  a j  xj

The SSR based on PRO calculates the allocation of each agent using follow equations2:

li ¼

Ei ci þ cDi

(11)

and

xi ¼ li :ci

(12)

It is clear that CD can be calculated for all agents. Besides, based on definition 1, the sum of river inflow on the territory of agent 1 that is the most upstream agent (E1), is equal to the inflow of river which originates in the territory of this agent (a1) then E1 ¼ a1. Hence, l1 and x1 are derived using Equations 11 and 12. Specifying the amount of x1, E2 is calculated using Equation (9). Then, l2 and x2 are determined using Equations 11 and 12. The problems can be solved recursively in the linear order of agents along the river from upstream to downstream. Based on definition of sequential sharing rule by Ansink and Weikard (2012), a sequential sharing rule for

2 A complete description of this rule is found in (Ansink, 2009; Ansink and Weikard, 2012).

H. Mianabadi et al. / Journal of Environmental Management 144 (2014) 152e159

155

Fig. 2. Tigris-Euphrates basin (UNEP/DEWA/GRID-Geneva, 2000).

river sharing problem q is a sharing rule F which allocates to each creditor the allocation provided by repeatedly applying a bankruptcy rule (G) to its corresponding sequence of reduced river sharing problems(q1,q2,…,qn), so that Fi(q) ¼ Gi(qi), ci2N. Using sequential sharing rules, the allocated water to each creditor is equal to allocation calculated by the recursive solution of its corresponding sequence of reduced problems (Ansink and Weikard, 2012). Ansink and Weikard (2012) remark the difference between SSR based on PRO and PRO methods is that SSR based on PRO generates a solution with different values for li, whereas PRO would result a constant value for li. In spite of this fact that SSR based on PRO considers the agents’ contributions for reallocation of assets, this rule has two fundamental problems in water resources allocation (Ansink, 2009; Ansink and Weikard, 2012). First, this method is only useful if claimants are ordered linearly, such as river sharing problems. It is not appropriate if states do not have an upstream and downstream position such as in the case of reallocation of lake of water or reserves of a shared sea. Secondly, as Ansink and Weikard (2012) prove, this method favors downstream agents, who always receive larger proportions of their claims in contrast with upstream ones. This is because the allocation of upstream states considers the claims of downstream states, but the allocation

of downstream states does not consider the claims of upstream states (Ansink and Weikard, 2012). Because of these shortcomings, we propose a new division rule. The proposed rule is based on the principle that the total deficit, the difference between C and E, should be divided inversely proportional to the agents' contribution to E and their claims: the larger their contribution, the smaller the difference between their claim and the allocation they get. To do this, we define two factors: rate of contribution and rate of claim. The rate of contribution is the proP portion of the agent's contribution to supply the total asset (ai/ ai) and the rate of claim is the proportion of the agent's claim to the P total amount of claims (ci/ ci). It is reasonable that agents who contribute more to the assets and claim less are allocated a relatively larger proportion of their claim. According to this logical attitude, we develop a new bankruptcy solution method. The total deficit (D) is denoted as follow:

D¼CE

(13)

The method proposes to divide the total deficit (D) proportionally to the proportion of the claims and contribution of agents and then subtract the deficit or loss for each agent (di) from their claim. In other words, the total deficit should be divided inversely

(134%e172%)

12000e14000 5400e12600 25000e28100 31800 42400e54700

(38%e44%) (17%e40%) (79%e88%)

H. Mianabadi et al. / Journal of Environmental Management 144 (2014) 152e159

Beaumont (1998)

156

proportional to the agents' contribution to E and their claims. Thus, di is calculated as follow:



Pcni

di ¼

c i¼1 i

þ 1  Pani



a i¼1 i

n

*D

where :

di  ci

(14)

in which ci and ai are the claim and asset of agent i. n is the number of agents and D is the total deficit. The allocation of each agent (xi) is then calculated using the following equation:

(112%) (155%)

(164%)

14500 5500 15500 31680 35500 21500 13400 16000 31000 50900 (149%)

21600 11995 17000 32720 50595 (52%) (32%) (65%)

18420 11300 23000 35580 52720 (100%) km (100%)

km (41%) km (23%) km (36%)

(89%) (11%) (0%)

31580 4000 0 e 35580 1230 710 1060 e 3000

Ministry of F.A of Turkey, (1996); Ibrahim and Sonmez (2002)

Water demand and claim

Contribution of flow Ministry of F.A of Turkey, (1996); Ibrahim and Sonmez (2002); Lupu (2002); Kucukmehmetoglu (2009) Composition of length Kliot (1994)

(15)

According to Equations (14) and (15), it is obvious that each agent having a higher rate of contribution and lower rate of claim would be allocated relatively more, and vice versa. The merit of this method compared with the CEL rule is that the losses and deficits are divided equally among claimants in CEL rule, whereas the proposed method divides the losses and deficits with respect to the rates of contribution and claim of agents. Moreover, the main advantage compared with SSR based on PRO is that the upstream or downstream position of agents has no effect on the agent's allocation. 3. Application In this section the proposed bankruptcy rule will be applied to the Euphrates River as well as to the hypothetical case proposed by Ansink and Weikard (2012). The Euphrates River (Fig. 2) originates in the Anatolian Highlands of Turkey and flows through Syria and Iraq to join the sea at the head of the Persian Gulf. Turkey contributes 89 percent of the water flow of the Euphrates River making Syria and Iraq heavily dependent on external supplies of water (Lupu, 2002; Kucukmehmetoglu, 2009). Relations regarding the rivers were generally peaceful and cooperative in nature until the 1960's when Turkey, Syria, and Iraq began developing the Tigris and Euphrates Rivers, including water storage, irrigation, and hydropower dams for their industrial and agricultural development, as well as for addressing their Kurdish ethno-political concerns. In particular, the construction of the major development project known as the Southeastern Anatolia Project or Guneydogu Anadolu Projesi (GAP) of Turkey and, to a lesser extent the Euphrates Valley Project of Syria, for irrigation, has served to increase tensions (Korkutan, 2001; Zentner, 2011). The equitable and reasonable use of these rivers plays a significant role in political disputes among the riparian states leading to great tensions among them. For example, in 1975, Syria and Iraq came very close to a full-scale war when Syria blocked the water flow in the Euphrates River (Schulz, 1995). The main hydrological difference between the Euphrates and the Tigris River is that the Tigris receives water from a series of major tributaries in the mid-portion of its course. The mainstream of the Tigris has a flow of 23,210 MCM annually at Mosul in northern Iraq, while the tributaries contribute a further 29,455 MCM each year that the largest tributary is the Greater Zab, which produces almost half the flow of all the tributaries (Beaumont, 1998). In contrast, all of the major tributaries of the Euphrates are in the extreme upper part of the basin. This has significant tributaries for the control of these two rivers. It means that a single

Turkey Syria Iraq Available water Total

Table 2 The rate of contribution and claim of states on the Euphrates River (MCM/y).

Riparian

Table 1 Contribution and water demand (MCM/y) of riparian states on the Euphrates River with respect to different research.

Kolars (1994)

(66%) (37%) (52%)

(69%) (43%) (52%)

Altinbilek (1997) Kliot (1994)

(46%) (17%) (49%)

xi ¼ ci  di ; 0  xi

Riparian

Contribution rate

Claim rate

Turkey Syria Iraq Total

31580 (89%) 4000 (11%) 0 (0%) 35580

14000 (26%) 12600 (23%) 28100 (51%) 54700

H. Mianabadi et al. / Journal of Environmental Management 144 (2014) 152e159

157

Table 3 Reallocation of riparian states on the Euphrates River (MCM/y). Riparian

Turkey Syria Iraq

PRO

CEA

CEL

SSR based on PRO

The proposed approach

xi

di

pi

xi

di

pi

xi

di

pi

xi

di

pi

xi

di

pi

9106 8196 18278

4894 4404 9822

65% 65% 65%

11860 11860 11860

2140 740 16240

85% 94% 42%

7626 6227 21727

6373 6373 6373

54% 49% 77%

8720 8315 18544

5280 4285 9556

62% 66% 66%

11652 5475 18453

2348 7125 9647

83% 43% 66%

Table 4 A hypothetical example of a trans-boundary river shared among four riparians (adopted from Ansink and Weikard (2012)). Riparian

Contribution

Claim

1 2 3 4 Total

80 (61%) 30 (23%) 10 (8%) 10 (8%) 130

50 (29%) 10 (6%) 20 (12%) 90 (53%) 170

As a second application, Table 4 summarises the proposed solution to the river sharing problem to the hypothetical case proposed by Ansink and Weikard (2012). As can be seen in this table, the total water resources are almost 25% less than the total claims. Using Equations (6)e(15), we reallocate the resources of this river using five mentioned bankruptcy rules and results are shown and are compared in Table 5. 4. Discussion

dam in the upper part of the Euphrates is capable of controlling a very large proportion of the flow of the river that the Ataturk Dam in Turkey achieves this level of control (Beaumont, 1998). Whereas the Tigris receives water from the Greater Zab, the Lesser Zab, the Adhaim and the Diyala and it means that overall water management in this basin is more complex and requires the construction of a series of major dams on the individual tributaries to provide a comparable control of the flow (Beaumont, 1998). Turkey, Syria and Iraq realized early after the announcement of the GAP development plans that coordination and cooperation were necessary to manage the Tigris-Euphrates waters effectively (Zentner, 2011). However, there was much conflict over allocation rights and data accuracy, with estimates of irrigable land and soil water requirements in each riparian country allegedly being skewed by the national experts that produced them (Kibaroglu and Ünver, 2000), which are shown in Table 1. Several scholars have surveyed the irrigable lands and water demand as well as the hydro-policy of each riparian country for both the Euphrates and Tigris rivers such as (Beaumont, 1978, 1998; Kliot, 1994; Kolars, 1994; TMFA and Ministry of Foreign Affairs Dept. of Regional and Transboundary Waters, 1996; Altinbilek, 1997; Ibrahim and Sonmez, 2002; Lupu, 2002; Kucukmehmetoglu and Guldmann, 2004; Kucukmehmetoglu, 2009). Most of this research concluded that there is not sufficient water in these rivers to satisfy the demands of the three riparian countries. As shown in Table 1, the total claims (C), which is the total determined demands of states, are estimated to be up to 72% more than the total resources E in the Euphrates river basin. We reallocate the resources of this river using five bankruptcy rules: PRO, CEA, CEL, SSR based on PRO and the proposed method. For this purpose, we use the upper determination of Beaumont (1998) as the states' demands, which are shown in Table 2 because this study is newer than other studies. Using Equations (6)e(15), the allocation of each state is calculated using different rules and results are shown and compared in Table 3.

Comparison of the results shown in Tables 3 and 5 reveal that the CEA rule favors the agents with smaller claims, who get a relatively higher portion of their claims. In contrast, the CEL rule favors agents with larger claims. PRO is located between CEA and CEL (cf. (Herrero and Villar, 2001; Ansink and Marchiori, 2010)). Although the SSR based on PRO, as we noted in the previous section, considers the agents' contributions for reallocation of assets, this rule favors downstream agents, who always obtain higher satisfaction of their claims than upstream ones. In comparison with these rules, the proposed method distributes the assets with respect to the rate of the contribution and claim of agents and irrespective of geographical location. Based on this approach, a larger proportion of the total deficit is allocated to each agent who has a higher claim and lower contribution. According to the evaluation of Beaumont (1998), the total deficit of the Euphrates River is almost 19120 (MCM/y). As shown in Table 3, the contribution and claim rate of Turkey on the Euphrates River are 89% and 26%, respectively. These rates for Syria are 11% and 23% whereas, they are 0% and 51% for Iraq. It may be considered equitable and reasonable that Turkey endures the smaller deficit with respect to its demand since it contributes most and it claims almost the least. Conversely, Iraq, which has no contribution to the Euphrates River and claims more than half of its flow, suffers a greater proportion of the deficit. The results are similar for the hypothetical example. Applying the proposed method, the highest satisfaction and the least deficit is assigned to agent 1 who has the most contribution and less claim in contrast with others. In contrast, agent 4 who has the least contribution and the highest claim (8% and 53%, respectively) loses the most deficit from implementation of the proposed method. Accordingly, the results of the PRO, CEA and CEL rules may not be considered equitable and reasonable by many states because they do not consider the contribution of states to supply total flow. This decreases the possibility to achieve an agreement. Although the SSR based on PRO considers this factor, it prefers the downstream agents in contrast with upstream ones. The proposed

Table 5 Allocations to riparian states in the hypothetical example. Riparian

1 2 3 4

PRO

CEA

CEL

SSR based on PRO

The proposed approach

xi

di

pi

xi

di

pi

xi

di

pi

xi

di

pi

xi

di

pi

39 7 15 69

12 2 5 21

76% 76% 76% 76%

50 10 20 50

0 0 0 40

100% 100% 100% 56%

40 0 10 80

10 10 10 10

80% 0% 50% 89%

33 8 16 73

17 2 4 17

67% 77% 79% 81%

43 2 10 75

7 8 10 15

86% 17% 48% 84%

158

H. Mianabadi et al. / Journal of Environmental Management 144 (2014) 152e159

such as PRO, CEA, CEL, and SSR based on PRO is that the assets are allocated considering agents' contribution to the total resources as well as their claims, which is in accordance with the UN Watercourses Convention (1997). The Euphrates river and a hypothetical case were used as to illustrate the application of the proposed method to water resources allocation problems. We compared our approach with four alternative solutions for two river system allocation problems. The results reveal that this method results in different allocations. Moreover, it has a great potential to help solving conflict and dispute in negotiations over river resources allocation problems.

References

Fig. 3. Redistribution of extra contribution of agent 3 between agents.

method divides the total deficit with respect to the rates of contribution and claim of states; hence, it allocates the least deficit to Turkey and riparian 1, which have the most contribution and almost the least claim, and assigns the highest rate of deficit to Iraq and riparian 4. To illustrate how changes in the contribution of agents affect the allocation, the contribution of agent 3 in the hypothetical case (Table 4) has been increased from 10 to 20. This results in some changes in the allocation for all agents as shown in Fig. 3. As can be seen in this figure, CEA rule results in no extra allocation to agent 3 and the proposed approach in the largest increase It should be stressed at this point that we do not claim that the proposed method on its own can solve conflicts among riparian countries. Conflicts among countries are often rooted in politics, economics, culture, history, etc. But using the results of this study may facilitate negotiation between riparian countries to reach consensus over allocation mechanism. Furthermore, there is not yet consensus on the meaning of equitable and reasonable utilization. Hence, we do not claim that the suggested approach is a comprehensive method which is able to consider all relevant criteria and aspects of the equitable and reasonable reallocation of the shared river resources. These efforts can be seen as first steps towards these goals. Nevertheless, this method, in contrast with the most often used rules, is able to take into account more attributes for reasonable reallocation of the shared water resources. It is crucial to mention that all relevant factors and conditions including social, population, natural and ecological characters, economic and sustainable development criteria should be taken into account when assessing the claim of each riparian country. To do this, it needs generally accepted or acceptable criteria, joint research if possible, or independent third party assessment of all contributions and claims in the same way. Although considerable theoretical advances have been achieved within this new method for allocating shared water resources, some issues remain open. Clearly, bankruptcy methods are not limited to the applied rules. Another path for future research is to examine the application of other bankruptcy methods. Besides, it is suggested using satellite data to support the determination or assessment claims and contributions of riparians, especially when they do not want to share all the data. 5. Conclusion In this paper, the common and different attributes as well as application of bankruptcy theory in the water resources allocation problems are surveyed. Moreover, we developed a new bankruptcy method to allocate water in shared river systems. The significant feature of the new proposed method compared to bankruptcy rules

Altinbilek, H.D., 1997. Water and land resources development in Southeastern Turkey. Int. J. Water Resour. Dev. 13, 311e332. Ansink, E., 2009. Game-theoretic Models of Water Allocation in Transboundary River Basins. PhD dissertation. Wageningen University, Wageningen, The Netherlands. Ansink, E., Marchiori, C., 2010. Reallocating Water: An Application of Sequential Sharing Rules to Cyprus. Fondazione Eni Enrico Mattei Working Papers. Ansink, E., Weikard, H.-P., 2012. Sequential sharing rules for river sharing problems. Soc. Choice Welf. 38, 187e210. Beard, R., 2011. The River Sharing Problem: a review of the Technical Literature for Policy Economists. MPRA Paper 34382. Beaumont, P., 1978. The Euphrates Riverdan international problem of water resources development. Environ. Conserv. 5, 35e43. Beaumont, P., 1998. Restructuring of water usage in the Tigris-Euphrates basin: the impact of modern water management policies. In: Albert, J., Bernhardsson, M., Kenna, R. (Eds.), Transformations of Middle Eastern Natural Environments: Legacies and Lessons. Yale School of Forestry and Environmental Studies, New Haven, CT, pp. 168e186. Bulletin Series, No. 103. Bosmans, K., Lauwers, L., 2011. Lorenz comparisons of nine rules for the adjudication of conflicting claims. Int. J. Game Theory 40, 791e807. Correia, F.N., Da Silva, J.E., 1999. International framework for the management of transboundary water resources. Water Int. 24, 86e94. Drieschova, A., Giordano, M., Fischhendler, I., 2008. Governance mechanisms to address flow variability in water treaties. Glob. Environ. Change 18, 285e295. €chter, S., Riedl, A., 2006. Dividing justly in bargaining problems with claims. Soc. Ga Choice Welf. 27, 571e594. Gray, B., 1989. Collaborating: Finding Common Ground for Multiparty Problems, first ed. San Francisco. Jossey-Bass, San Francisco. Grundel, S., Borm, P., Hamers, H., 2011. A Compromise Stable Extension of Bankruptcy Games: Multipurpose Resource Allocation. Center Discussion Paper No. 2011-029. Herrero, C., Villar, A., 2001. The three musketeers: four classical solutions to bankruptcy problems. Math. Soc. Sci. 42, 307e328. Herrero, C., Moreno-Ternero, J.D., Ponti, G., 2009. On the adjudication of conflicting claims: an experimental study. Soc. Choice Welf. 34, 145e179. Homer-Dixon, T.F., 1994. Environmental scarcities and violent conflict: evidence from cases. Int. Secur. 19, 5e40. Ibrahim, G., Sonmez, B., 2002. Water issues among the riparian states of Euphrates and Tigris transboundary rivers. In: Castelein, S. (Ed.), From Conflict to Cooperation in International Water Resources Management: Challenges and Opportunities. UNESCO., Delft, The Netherlands, pp. 278e286. Inarra, E., Skonhoft, A., 2008. Restoring a fish stock: a dynamic bankruptcy problem. Land Econ. 84, 327e339. International Law Association (ILA), 1966. Helsinki rules on the uses of the waters of international rivers. In: Report of the Fifty-Second Conference of the International Law Association. International Law Association, London, pp. 447e533. International Law Association (ILA), 2004. The Berlin rules on water resources. In: Report of the Seventy-First Conference of the International Law Association. International Law Association, London, pp. 334e421. Just, R.E., Netanyahu, S., 1998. International water resource conflicts: experience and potential. In: Just, R.E., Netanyahu, S. (Eds.), Conflict and Cooperation on Transboundary Water Resources. Kluwer Academic Publishers, Boston, p. 460. Kibaroglu, A., Ünver, I.H.O., 2000. An institutional framework for facilitating cooperation in the Euphrates-Tigris river Basin. Int. Negot. 5, 311e330. Kliot, N., 1994. Water Resources and Conflict in the Middle East. Progress in Human Geography. Routledge, London. Kolars, J., 1994. Problems of international river management: case of Euphrates and Tigris. In: Biswas, A.K. (Ed.), International Waters of the Middle East -frome Euphrates -Tigris to Nile. Oxford University Press, pp. 44e94. Korkutan, S., 2001. The Sources of Conflict in the Euphrates-Tigris Basin and Its Strategic Consequences in the Middle East. Storming Media, California, USA. Kucukmehmetoglu, M., 2009. A game theoretic approach to assess the impacts of major investments on transboundary water resources: the case of the Euphrates and Tigris. Water Resour. Manag. 23, 3069e3099. Kucukmehmetoglu, M., Guldmann, J.-M., 2004. International water resources allocation and conflicts: the case of the Euphrates and Tigris. Environ. Plann. A 36, 783e801.

H. Mianabadi et al. / Journal of Environmental Management 144 (2014) 152e159 Lupu, Y., 2002. International law and the waters of the Euphrates and Tigris. Georget. Int. Environ. Law Rev. 14, 349e366. Madani, K., Dinar, A., 2013. Exogenous regulatory institutions for sustainable common pool resource management: application to groundwater. Water Resour. Econ. 2e3, 57e76. Madani, K., Zarezadeh, M., 2012. Bankruptcy methods for resolving water resources conflicts. In: Loucks, D.P. (Ed.), World Environmental and Water Resources Congress 2012. American Society of Civil Engineers, Reston, VA, pp. 2247e2252. Majone, G., 1989. Evidence, Argument, and Persuasion in the Policy Process, first ed. Yale University Press. Rahaman, M.M., 2012. Principles of transboundary water resources management and water-related agreements in Central Asia: an analysis. Int. J. Water Resour. Dev. 28, 475e491. Salman, S.M., 2007. The helsinki rules, the UN watercourses convention and the Berlin rules: perspectives on international water law. Int. J. Water Resour. Dev. 23, 625e640. Schulz, M., 1995. Turkey, Syria, and Iraq: a hydropolitical security complex e the case of Euphrates and Tigris. In: Ohlsson, L. (Ed.), Hydropolitics: Conflicts Over Water as a Development Constraint. Zed Books, London, UK, pp. 91e122. Sheikhmohammady, M., Kilgour, D.M., Hipel, K.W., 2010. Modeling the Caspian sea negotiations. Group Decis. Negot. 19, 149e168. Thomson, W., 2003. Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey. Math. Soc. Sci. 45, 249e297. TMFA, Ministry of Foreign Affairs Dept. of Regional and Transboundary Waters, 1996. Water Issues Between Turkey, Syria and Iraq. Turkish Ministry of Foreign Affairs, Dept. of Regional and Transboundary Waters, Ankara, Turkey.

159

UN Watercourses Convention, 1997. Convention on the Law of the Non-navigational Uses of International Watercourses. United Nations. Adopted on May 21, 1997. United Nations. UNEP/DEWA/GRID-Geneva, 2000. Tigris and Euphrates Dams Map [WWW Document]. UNEP's global group of environmental information centres. URL. http:// www.grid.unep.ch/products/4_Maps/tigris_damb.gif. Wolf, A.T., 1999. Criteria for equitable allocations: the heart of international water conflict. Nat. Resour. Forum 23, 3e30. Wolf, A.T., 2007. Shared waters: conflict and cooperation. Annu. Rev. Environ. Resour. 32, 241e269. Xia, X., Cui, J., 2009. Study of water resource allocation mechanism. In: The Eighth International Symposium on Operations Research and Its Applications (ISORA'09). Zhangjiajie, China, pp. 212e219. Zaag, P., Van der Seyam, I., Savenije, H., 2002. Towards measurable criteria for the equitable sharing of international water resources. Water Policy 4, 19e32. Zarezadeh, M., Madani, K., Morid, S., 2012. Resolving transboundary water conflicts: lessons learned from the Qezelozan-Sefidrood river bankruptcy problem. In: World Environmental and Water Resources Congress 2012. American Society of Civil Engineers, Reston, VA, pp. 2406e2412. Zarezadeh, M., Madani, K., Morid, S., 2013. Resolving conflicts over trans-boundary rivers using bankruptcy methods. Hydrol. Earth Syst. Sci. Discuss. 10, 13855e13887. Zawahri, N.A., 2006. Stabilising Iraq's water supply: what the Euphrates and Tigris rivers can learn from the Indus. Third World Q. 27, 1041e1058. Zentner, M.A., 2011. Assessing the Design of International Water Supply and Hydropower Arrangements for Managing Certain Climate Change Scenarios. PhD dissertation. Oregon State University, Corvallis, Oregon, USA.