Governance failures are one of the key reasons for unsustainable resources management in general, and water management in particular. Economic development often focuses on and leads to fulfilling the needs of the human population at the expense of the environment (Vörösmarty et al. 2010, Pahl-Wostl et al. 2012). Pahl-Wostl and Knieper (2014) showed that the effectiveness of formal institutions is more important than the state of economic development when explaining the failure of a governance regime. Their analyses showed that governance regimes characterized by high levels of corruption did not enhance water security, neither for humans nor the environment. Thus, understanding the reasons for and the possibilities to overcome corruption is an issue of major concern.
Ostrom (1998) defined rent-seeking as nonproductive activities that are directed toward creating opportunities for higher profits than would be obtained in an open, competitive market; e.g., the public infrastructure provider has an incentive to engage in rent-seeking by imposing high taxes on the resource users while not investing in public infrastructure. According to the rent-seeking theory, corruption has been associated with the incompetence of the state to ensure efficiency in water provision and cost recovery. It was, therefore, expected that commercialization through private sector participation (PSP) and sector reform (regulation, decentralization) would help to reduce corruption and improve the performance of water utilities (Repetto 1986).
However, Boehm (2007) suggested that the low levels of efficiency of water utilities, persistent patterns of corruption, and limited water access for the most vulnerable population show that these approaches have failed. In its turn, management practices seem to have an important role in understanding why the performance of water service delivery (WSD) remains low in spite of the sector reform and the PSP. Auriol and Blanc (2009) analyzed the problem of corruption and the capture of public water utilities in Sub-Saharan Africa. In this seminal paper, Auriol and Blanc (2008:2) point out that “water utilities run by private-public partnerships are not optimally managed either because private managers and government are incompetent or not benevolent.”
Kenya and Ghana are Sub-Saharan African countries that began to reform the water sector in the 1990s in an attempt to improve the performance of the water supply. The change in institutions and organizations of policy and regulation, provision, and consumption levels defines a specific governance model in each country. The reform affected the different WSD levels. At the policy and regulation level, both countries developed regulatory frameworks. In terms of provision, Kenyan municipal water services were transformed into public corporations, whereas Ghana embraced PSP. Both countries developed commercialization measures to increase cost recovery. At the consumption level, participation by users was introduced by adopting customer-care strategies from providers (GII 2011, TIK 2011).
Bellaubi and Visscher (2014) assessed the quality of WSD in five case studies in Kenya and Ghana and identified low levels of coverage, high levels of rationing, and low water quality in these locations. Furthermore, Bellaubi and Visccher (2016) identified a number of corruption risks in both countries by looking at the actors involved in WSD and their multiple relationships in a complex network. These relationships were analyzed using a principal-agent framework in which the agents provide a service and the principals pay a return. Corruption risks were identified by looking at the integrity, in terms of transparency, accountability, and participation (TAP) levels, of the relationships between the principals and agents involved in the different WSD levels (Bellaubi and Visscher 2010) from policy and regulation to provision and consumption.
In turn, Bellaubi (2004) suggested that clarity of rules between actors in water allocation in an irrigation system is related to different types of management (water distribution), which have an effect on the performance of the system (yields). Various types of management practices have been distinguished in the literature (Batley 2004, Huppert 2005, Molle and Berkoff 2007), namely “opportunistic” (in which the provider of a service will tend to use their power to divert benefits in their own direction), and “pragmatic” (in which the provider’s actions are based on the concept of comfort margin and minimum overload). However, these definitions remain very broad and qualitative, and we suggest a more specific categorization through the following research question: how do corruption risks and management practices affect the performance of WSD governance in Kenya and Ghana? To investigate the complex relationships between management practices, corruption, and performance of WSD, an agent-based model (ABM) built on the principal-agent theory was developed and applied to Kenya and Ghana. The conceptualization of agents and their interactions builds on game theory. The different interaction situations are conceptualized as different games that reflect social dilemmas. The results of the ABM allow observation of the total payoff of the water system (performance), identifying the most successful management strategy under specific integrity conditions. Therefore, the model can be used to set up clear remedial actions and policies to increase the quality of WSD by enhancing integrity and improving management in WSD.
Water systems may be considered social-ecological systems (SES; Anderies et al. 2004), composed of biophysical and social components with a physical and institutional infrastructure, which affects the way the system functions to cope with diverse external disturbances and internal problems over time. The low performance of SES constitutes a social dilemma when actors face choices in which the maximization of short-term self-interest yields important outcomes but their choice reduces the overall performance of the system (Ostrom 1998).
Models using game theory have been used in social sciences to simulate social dilemmas (Axelrod 1984, Lambsdorff 2007; J. Fábrega 2008, unpublished manuscript). However, game theory, which is based on rational choice theory, falls short when it comes to capturing real actors’ behaviors in various ways. Rational choice theory relies on objective probabilities for decision making, although according to Savage (1954), probabilities can also be subjective, whereas in reality, decisions are made within complex and changing environments in which objective probabilities are unobtainable (Bell 2012). People rarely have access to all the information they need to make choices. In addition, the ability to process information is usually far too limited to follow the theory’s prescriptions (Kirkebøen 2009). According to Simon’s bounded rationality concept (Simon 1955, as cited in Kirkebøen 2009), actors do not optimize but opt for satisficing choices; a behavior that results from their adaptiveness and from learning from previous decisions.
Another point is that an actor’s behavior is a function of the person and his/her environment, including other actors (Lewin 1943). Most importantly, actors do not consider only the utility derived from a specific interaction, but also positive or negative social impacts (social gain/cost) that result from their decisions (J. Fábrega 2008, unpublished manuscript). In game theory, the structure of the interactions between actors is restricted to being either too rigid or fully random, and none of the interaction structures properly reflect the structure of social networks.
Agent-based modeling is a modeling approach used in various disciplines and allows individual entities and their interactions to be directly represented (Gilbert 2008). This makes it an attractive approach for modeling social dilemmas (Kehagias 1994, Szilagyi 2003, Sheng et al. 2008, Szilagyi and Somogyi 2008, Power 2009), considering the role of different types of social networks (Nowak and May 1992, Hauert and Doebeli 2004, Santos and Pacheco 2005; see also http://www3.nd.edu/~netsci/TALKS/Santos_CT.pdf), and, more directly, addressing the problem of corruption (Situngkir 2003a, b, Guerrero 2009).
Although the study of corruption has been approached through laboratory (Lambsdorff and Frank 2007) and field experiments (Olken 2007), the results obtained have a high degree of abstraction and may not entirely capture the heterogeneity of an actor’s behavior and its interactions with the environment (Balacco 2011).
The ABM we describe is an exploratory learning model (Pahl-Wostl et al. 2007) that makes it possible to simulate how actors in the water system interact among themselves. The aim of the ABM is to understand the relationship of corruption risks and management practices with the performance of WSD, considering social links from a power perspective and also from the cognitive abilities of the actors. This combines adaptive (learning) and interactive (relationships with others) expectations. The ABM builds on a principal-agent representation for Kenya and Ghana WSD that results from analyzing three case studies in Kenya and two in Ghana, carried out as a part of Transparency International’s “Transparency and Integrity in Service Delivery in Africa Program” (Bellaubi and Visscher 2014). Each case study represents a specific water situation within the service area of a water provider or water utility (hence, the water system). This empirical information, both qualitative and quantitative, is used as input data for the ABM to test the conceptual model and to extract more general conclusions (Janssen and Ostrom 2006).
The principal-agent representation, based on Huppert (2005), makes it possible to represent actors (organizations or individuals) that are related to each other under specific governance mechanisms (rules such as contracts and regulations) and transactions (services and returns). The relationship is that an actor acting as an agent offers a service to an actor acting as a principal, and in return, the principal pays the agent. The agent can hide information from the principal, failing ex-ante to provide the service. In turn, the principal can refuse ex-post any return for the service provided. Finally, an external observer, i.e., an independent actor not directly involved in the principal-agent transaction, can verify and influence the transaction if sufficient information is accessible to him. Bellaubi and Visscher (2010, 2016) defined different levels of integrity for each of these transactions in terms of transparency, accountability, and participation (TAP; Table 1), in which a low level TAP identifies high corruption risks. Furthermore, the variable of social cost was introduced to estimate the grade of influence (power) of an agent over the principal or the opposite.
In turn, different management practices can be characterized by TAP levels and power balance between principals and agents (Table 2; Bellaubi and Visscher 2010, Bellaubi 2011; F. Bellaubi and F. Boehm 2016, unpublished manuscript). We differentiate between two situations: (1) those situations in which power is unequally distributed (asymmetry of power) between principals and agents and presents corruption risks. Such situations are referred to as opportunistic management. In these cases an actor who holds power over a peer may misuse it to behave opportunistically because of the low TAP levels; (2) situations in which there is a power balance between principals and agents, which present corruption risks. Such situations are referred to as pragmatic management. In these cases, principals and agents behave reactively and are motivated by their own interest because there is low TAP.
To measure the performance of WSD in each of the case studies, a water service delivery approach (WSDA) was used (Bellaubi and Visscher 2014). The WSDA analyzes the quality of the service in a specific location of the service area of a water utility and, thus, refers to its performance within that location in terms of the quality of the service obtained by the users/consumers. The performance of the WSD of a water system is considered as the result of all interactions between the principals and agents measured at the user’s end (Table 3).
The case studies in Kenya were carried out in Old Town (Mombasa), Migosi (Kissumu), and Kangemi (Nairobi). In Ghana, the case studies were carried out in Nima and Madina (Accra). The main actors involved at policy making and regulation, provision, and consumption WSD levels in each country are listed in Table 4.
The principal-agent representations in Kenya and Ghana (Figs. 1 and 2) show the principals’ and agents’ relationships and their governance mechanisms. In the case of Kenya, the governance mechanisms follow a public governance model, whereas in Ghana, the governance mechanisms relate to PSP. The legend describes the service provided by the agent and the return of the principal, the TAP, and social cost scores of the relationship with a brief explanation and the identified corruption risks and management practices based on data from GII (2011), TI Kenya (2011), Bellaubi and Visscher (2014), and Bellaubi (personal observation).
In Kenya, the regulator, Water Services Regulatory Board (WASREB), acts as an agent and the government Ministry of Water and Irrigation (MWI) acts as a principal. The relationship is characterized by low TAP (regulatory opportunism risk) and the unequal distribution of power between the principals and agents resulting in an opportunistic management in which politicians have the opportunity to abuse some regulatory powers for their own purposes. A similar situation happens in Ghana with the regulator, Public Utilities Regulatory Commission (PURC) acting as an agent and the government Ministry of Housing, Works and Water (MHWW) as a principal.
In Kenya, municipalities act as agents and water companies, Water and Sanitation Program (WSPs), act as principals. The low TAP (political opportunism risk) and the fact that municipalities exert their power to influence the decisions of the companies for their own benefit indicate an opportunistic management.
In Ghana, the water operator, Aqua Vitens Rand Ltd. (AVRL), is the agent and the water agency, Ghana Water Company Ltd. (GWLC), is the principal. The low TAP between agent and principal points to a state capture risk in which AVRL may take advantage of GWLC, shaping the design rules of the service management contract in its favor. However, the fact that there is a balance of power between both actors makes it difficult for AVRL to profit from its situation resulting in a pragmatic management.
In Kenya and Ghana, the relationship between water companies (agents) and users (principals) is characterized by low TAP and balance of power between the agent and the principal resulting in pragmatic management. Moral hazard and free-riding were identified as corruption risks, meaning the possibility of encountering two different situations: users may free-ride the service, or water companies may take advantage of the service provided by the utilities.
Regarding the WSD, performance of the water systems in Kenya and Ghana was calculated as the average of the differently scored indicators per case study. In Kenya, the total performance in the various case study locations ranged from 20% to 26.6%. In Ghana, the total performance ranged from 13.3% to 20% (Table 5).
The ABM is described according to the overview, design concepts, and details protocol (ODD) in Bellaubi et al. (2014) and was implemented in Netlogo version 4.1.3 (Wilensky 1999). The ABM builds on a principal-agent representation in Kenya and Ghana (Figs. 1 and 2), in which actors playing as agents or principals relate to each other in terms of services and returns, respectively. The transaction sets up a game in which cooperation means following the rule of law, whereas defecting is equivalent to breaking the rule of law. Actors can play in multiple games simultaneously and can be a principal in one game and an agent in another game at the same time. The empirical observation of the actors in the case studies suggests that decisions to cooperate or defect consider both the utility maximization derived from a specific interaction, and the positive or negative social impacts (social gains/costs) as a result of their decisions (J. Fábrega 2008, unpublished manuscript). According to Janssen (2008), experimental research has shown that people value not only material payoff but also nonmaterial consequences, such as an improvement or deterioration in social relationships.
The performance of WSD refers to the payoff obtained by an actor as the result of a service or a return for this service. The TAP and social cost/gain values of the relationships determine the payoff table from which the actors get their payoff according to their decisions to cooperate or defect. The total performance of WSD is measured as the sum of the different payoffs obtained by all the actors involved as the result of the transactions among all of them.
The model time step is one month and it runs for 12 months, simulating the cycle of water service provision through one whole year. The games are played in each time step sequentially with the agent acting first and the principal second. The sequence gives to the agent a “first-to-choose” power over the principal. This situation is counterbalanced by the principal being aware of the agent’s decision. This sequence reproduces the principal-agent representation in which the agent offers services and the principal gives a return. The agent reiterates his previous decision if this has been good enough when comparing his payoff with the other actors linked to him (neighbors). If this is not the case, he tries to improve by taking into account expectations of the principal’s behavior to maximize his utility. The principal is affected by, and knows about, the previous decision of the agent, and the principal is, thus, easily able to maximize based on the previous decision of the agent. Afterwards, the agent adapts his expectations of the principal’s behavior. The various agents’ and principals’ choices per round constitute the strategy of the game. These strategies may vary over time and they can be cooperation-cooperation (Cc), defection-defection (Dd), cooperation-defection (Cd), or defection-cooperation (Dc).
The ABM is calibrated against the performance of the WSD of the water system found in the case studies. Finally, the ABM’s resulting strategies for each game and the associated payoffs (representing WSD performance) are compared with different management practices defined by the principal-agent representation of the case studies.
Each game is defined by a payoff table in which R is the reward for mutual cooperation, T is the temptation to defect, S is the “sucker’s payoff,” and P is the payoff for mutual defection. The values in the payoff table are derived from the transparency, accountability, participation (TAP) and social cost/gain scores of the transactions between a principal and an agent.
R is the service offered by the agent or the return that the principal pays to the agent to obtain the service when both cooperate. The optimal service/return can be arbitrarily valued as 1, i.e., R = 1. It is assumed that if both act according to the law, this has no effect on social relationships.
T is the temptation of the agent to provide only a suboptimal service while receiving an optimal return, or the temptation of the principal to receive an optimal service but to provide only a suboptimal return. T can hence arguably be higher than R. This depends, however, on the accountability of the transaction, which reflects punishment through the control mechanisms in place. To reflect on these considerations, the following settings were made: T = 1.5 - accountability, where accountability ϵ [1, 0] and, therefore, T ϵ [1.5, 0.5].
S is the sucker’s payoff that results in being cheated when offering an optimal service or an optimal return but receiving only a suboptimal service or suboptimal return. S increases with the level of participation of the transaction and decreases with the social cost involved of not reciprocating. Participation thus includes the observation of the transaction through third parties (e.g., NGOs, the general public, regulators) and the resulting incentive to act according to the law, even if cheated by one’s peers. This incentive is modeled as the benefit received by the cheated, if he/she decides to cooperate. In turn, the social costs reflect the social consequences for an individual of his/her personal decision and becomes relevant in cases in which the agent or the principal has strong social ties with the peer, e.g., a bribe that is offered and the rejection of which causes a disturbance in the receiver’s social relationships in terms of social costs. The rationale is that actors may suffer from the so-called “bureaucrat’s dilemma:” “sometimes [bureaucrats] need to bend rules to remain a participant on [sic] network of reciprocity (even at his own risk and without immediate retribution)” (J. Fábrega 2008:28 unpublished manuscript). Actors are, thus, members of networks and their decisions are influenced by their role as a member of the network. The social cost quantifies the power of the agent over the principal or the opposite in terms of the level of ties between the agent and principal; when the ties between peer actors are high then the social costs are also high, assuming that asymmetries of power between peer actors increases the social costs (the actors are bounded to positively reciprocate because of the social ties). It is assumed that direct social ties weigh more than participation. The following was set: S = (participation / C) - social cost, where participation ϵ [0,1], social costs ϵ [0, 0.5], and consequently, S ϵ [-0.5, 0.5]. C is a variable allowing the calibration of the model. Social costs are equivalent to social gain: when social costs are low, then (participation / C) - social costs > social gains, therefore S > P.
P is the suboptimal service or return of the principal and the agent, respectively, when both defect and can be considered almost nil. It is considered that when both the agent and principal break the rule of law, there is a corrupt deal (Lambsdorff 2007) involving social gain as a result of the social ties of reciprocity between the agent and the principal. Social gains are considered to be equivalent to the social costs introduced above, such that P ϵ [0, 0.5].
According to the principals’ and actors’ choices to cooperate or defect, the payoff values obtained are R, T, S, or P for the agent and r, t, p, or s for the principal (Table 6).
The processes executed for each round of the games between agents and principals are: (1) the agent’s decision, (2) the principal’s decision, (3) getting a payoff, and (4) updating expectation. A sequence diagram is given in Figure 4.
(1) In the agent’s decision, the agent reiterates his previous decision if, on average, he/she has been better off than his/her neighbors (other actors linked to him/her). The assumption is that the agent does not have the full information about the consequences of acting differently and, therefore, evaluates his previous decision as “good enough” as long as he is at least as well off as his peers in the network. If this is not the case, he tries to improve his position through taking a deliberate decision based on the maximization of the expected utility (EU) considering the expectation about the principal’s behavior (EPC), as follows:
EUagent (C) = EPC * R + (1 - EPC) * S
EUagent (D) = EPC * T + (1 - EPC) * P
EUagent (C) > EUagent (D), then agent Cooperate
EUagent (C) ≤ EUagent (D), then agent Defect
(2) In the principal’s decision, the principal maximizes his payoff (EU) based on the knowledge of the agent’s prior decision to cooperate or defect.
if at t, agent_decision = cooperate
then EUprincipal (c) = r and EUprincipal (d) = s
if at t, agent_decision = defect
then, EUprincipal (c) = t and EUprincipal (d) = p
EUprincipal (c) > EUprincipal (d), then principal cooperate
EUprincipal (c) ≤ EUprincipal (d), then principal defect
(3) While obtaining a payoff, payoff values are assigned to the agent and the principal according to the values of the payoff table, taking into consideration both decisions.
(4) Finally in updating expectation, the agent’s expectation of the principal’s behavior is updated based on the principal’s decision. The agent’s expectation that the principal will cooperate (EPC) or defect (1 - EPC) is influenced by the learning capacity of the agents that weights off the current experience with the expectations that have been built up in previous games.
If the principal decides to cooperate, then the expectation that the principal will act in a similar way in future games is increased.
if at t, principal_decision = cooperate
then, EPC (t + 1) = EPC (t) + (1 - EPC (t)) * Lc
with Lc being the learning rate assigned to each agent, where 0 < Lc < 1.
If the principal decides to defect, then the expectation that the principal will cooperate in future time steps decreases.
if at t, principal_decision = defect
then, EPC (t + 1) = (1 - Lc) * EPC (t)
The initial value of EPC is equal to the transparency of the principal-agent transaction.
To calibrate the model, it is necessary to determine the variables affecting the outcomes (strategies and payoffs) in the ABM. This is done through the simulation of an agent and a principal playing a single game (single principal-agent model).
The analysis focuses on understanding the importance of the various variables in the ABM so that the actors can reach the equilibrium (“stable” strategy on time), considering a strategy as set up by the agent’s and principal’s decisions. The resulting strategy depends on the values of accountability, participation, and social costs that define R, T, S, and P, the agents’ and principals’ initial decisions and the agent’s expectations of the principal’s behavior. The latter is a function of the learning capacity of the agent and the transparency of the relationship between the principal and the agent. The multiplicity of all the possible games played by the principals and agents can be abstracted into three social dilemmas known from game theory (http://www3.nd.edu/~netsci/TALKS/Santos_CT.pdf): the snow drift (SD) game (R > T > S > P), the prisoner’s dilemma (PD; T > R > P > S), and the stag hunt (SH) game (R > T > P > S).
The single principal-agent model shows that a game (social dilemma) can develop several strategies through the year depending on the initial decisions of the agent and the principal. When the agent’s initial decision is such that he is at least as well off as the principal (neighbor), and the principal maximizes his payoff with his initial decision, equilibrium is attained in the first round. In some cases, the principal does not maximize his payoff with his initial decision and then equilibrium is attained in the second round. When the payoff for the agent is smaller than the payoff for the principal (neighbor), the agent’s expectations of the principal’s decision plays a role in defining the subsequent decisions and the equilibrium of the game. The agent’s expectations of the principal’s decision take into account the agent’s learning and the previous expectation of the principal’s decision. The higher the agent’s learning, the more the initial decision of the principal is taken into account. Whereas the lower the agent’s learning, the transparency between the agent and the principal influences the agent’s expectations of the principal’s decision (Fig. 4).
Figures 5, 6, and 7 show the evolution of strategies for each social-dilemma, when an agent’s initial decision payoff is smaller than the principal’s initial decision payoff and for different values of the agent’s learning.
Figure 8 displays different payoff tables for a single principal-agent model, in which each payoff table represents a social dilemma. Each payoff table shows the possible equilibriums according to game theory (marked with *), the ABM resulting equilibrium strategies (marked in bold) and the path (in arrows) in how ABM resulting strategies are reached when the agent’s and principal’s initial decisions differ from these resulting strategies.
Subsequently, the dynamics of strategies over time only become important if the initial setting is not the resulting equilibrium of the specific game. In fact, agents’ and principals’ initial decisions have a delaying role in reaching equilibrium within the year represented by 12 runs, as stated by game theory for the different social dilemmas. As a result, the overall performance over the year in question differs from the one predicted by game theory for the different social dilemmas.
The calibration of the model is done comparing the WSD’s performance given by the ABM with the WSD performance measured from the case studies. The WSD’s performance given by the ABM is the sum of the payoffs of all the actors’ relationships. In the case studies, the WSD performance of the water system results from all the actors’ interactions involved at the different WSD levels: policy and regulation, provision, and consumption and this is measured at the user’s end (Table 5). Because the WSD’s performance of the case studies is not measured in absolute but in relative terms to benchmarking, a percentage of the performance is given. This percentage is then applied to the resulting payoffs of the ABM and, thus, both performance and payoffs can be compared.
The input variables for the calibration of the ABM in Kenya and Ghana are:
The NetLogo BehaviourSpace tool produces the total payoff outputs for all the C values. Figures 9 and 10 list the C variables in relation to the total payoff values with the more similar values, in comparison to the relative WSD performance, as measured in the case studies in Kenya and Ghana (Table 5). The WSD performance average in Kenya was taken at 23.3%, which equals to a total payoff of 61 for the ABM when all the actors’ initial decisions are defection and 67.0 when all the actors’ decisions are cooperation. In Ghana, the average WSD performance was set at 16.6%, which equals a payoff of 56.9 and 61.9 when all the actors’ initial decisions are defection or cooperation, respectively.
The resulting C values of the calibration in Kenya (1.6) and in Ghana (1.8) show that in both cases, social ties weigh more than participation. In addition, the results show that when the actors’ initial decisions are cooperation, the payoff is higher than when they choose defection.
We examine the resulting strategies from the different games played between agents and principals in the Kenyan and Ghanaian ABM in relation to the observed corruption risks and management practices at the different WSD levels from the respective country principal-agent representation. Resulting strategies in each game are compared with the equilibriums of social dilemmas derived from game theory (Table 7). The following points are observed.
Dd strategies resulting from the ABM may explain corruption risks, opportunistic management, and low performance. Dd strategies emerge in two cases: first, when the temptation for the agent to defect is high (T ≥ R), the principal will defect if the social gain is high (P > S), resulting in a Dd strategy as in the prisoner’s dilemma, i.e., the principal cannot refuse a corrupt “contract” offered by the agent because strong social ties of positive reciprocity exist. The higher the social gain, the higher is the payoff of the agent and the principal. Second, Dd strategies are also reproduced when the temptation of the agent to defect is low (R > T) and the social gain is high (P > S). In this case, Dd strategies occur as in the stag hunt dilemma. However, this second situation is not found in the model.
Corruption risks and pragmatic management are characterized by Cd/Dc strategies. Cd/Dc strategies appear when the agent and the principal play a snow drift dilemma. Empirical findings from the case studies at consumption level suggest a successive shift in Cd/Dc strategies in the ABM to reproduce moral hazard and free-riding situations. However, the sequential structure of the model with the agent “moving” first does not allow this situation to be reflected. When the agent’s temptation to defect is high (T > R), the principal will cooperate if the social cost is low and participation is high (S > P), resulting in Dc strategies as in the snow drift dilemma, i.e., the principal can afford to refuse the agent’s decision. In other words, the principal will cooperate if the payoff through participation is high and the social cost is low. The symmetric situation (Cd strategies) arises if the agent initially chooses to cooperate and, consequently, the principal defects. The equilibrium reflects negative reciprocity in both cases.
In terms of performance and according to Bellaubi and Boehm (2016, unpublished manuscript), wins and losses of the actors involved in a water system play a role in the WSD performance. Therefore, resulting payoffs mimicking wins and losses of principals and agents through different games for different WSD levels can be related to the ABM strategies and further with the identified management practices derived from the case studies. Through a comparative analysis that establishes a possible relationship between two variables (x, y) in different given situations (A, B), it is possible to observe how different payoffs relate to certain management practices in Kenya and Ghana. The results of the ABM depicted in Table 7 show that payoffs associated with the prisoner’s dilemma are, in both countries, lower than payoffs resulting from the snow drift dilemma.
The ABM presented is a deterministic explanatory learning model that aims to explain how corruption risks and management practices affect WSD’s performances in Kenya and Ghana, considering the role of learning and social networks.
The ABM draws on the principal-agent theory. In the model, coupled actors play different simultaneous games to reflect the various social dilemmas involved in WSD in Kenya and Ghana. This distinguishes the model from similar ones of competition for natural resources in which several actors play the same game (Janssen 2008; see also http://www3.nd.edu/~netsci/TALKS/Santos_CT.pdf). Despite the maximization behavior of the agents, their bounded nature is taken into consideration by the ABM. There are two elements that go beyond a simple (repeated) utility maximizing game: (1) the social costs of not reciprocating, which changes the payoff structure of the (simple) game; and (2) learning about the success of different strategies whereby strategies are considered good if the payoff is at least as high as the neighbor’s average.
The relation between management practices and corruption risks established by the ABM may explain the performance that emerges from social-dilemma strategies. In other words, the strategies in the ABM may explain the principal-agent behavior (cooperation or defection) under specific corruption risks and management practice situations and the resulting performance. Furthermore, the ABM allows these management practices and the associated corruption risks to be related to the characteristics of the transaction between the agent and the principal, namely transparency, accountability, participation and social costs, the agent’s learning, and initial decision values.
In broader terms, the ABM relates the integrity of rules among water actors that constitute the governance aspect of their relationships with the behavioral norms grounded in asymmetries of power, which shape the water political arena (hydro-politics). Management practices can be seen as the interface of policies and politics, with the resulting WSD performance being a characteristic of the governability (Kooiman et al. 2008) of the water system.
In terms of results, the ABM model shows that regulatory and political opportunism corruption risks may occur under opportunistic management. The ABM strategies associated with opportunistic management are in line with the prisoner’s dilemma equilibrium, which point to strong social ties between principals and agents. That is the case of regulatory bodies and government in Kenya and Ghana and between water companies and municipalities in Kenya, as shown by the principal-agent representation based on empirical findings of the case studies.
Under pragmatic management, moral hazard, free-riding, and state capture may occur. In this case, ABM resulting strategies match with equilibriums of the snow drift game, involving low social cost and gain between the principals and the agents. This situation appears between the water companies/water operator and the users in Kenya and Ghana, and between the water operator and the water agency in Ghana.
The results also show that the payoffs resulting from the prisoner’s dilemma are lower than those from the snow drift dilemma. This suggests that opportunistic management and corruption risk involving strong social ties between relevant actors of the water system have a higher negative impact on the WSD performance.
These results can be put into perspective regarding the work done by Ostrom (1998), stating that when reciprocity rules are in place creating a linkage between players and collective action, players tend to collaborate receiving more benefits than if they all do not cooperate. According to our research and in line with , J. Fábrega (2008, unpublished manuscript), reciprocity can have an adverse effect when specific players want to keep a dominant role as members of a network because of their social links, as shown when opportunist management occurs.
Certainly, our research shows that certain types of management practices associated with corruption risks play a role by negatively affecting the performance of WSD in Kenya and Ghana. It has also shown that case studies and social modeling can be combined to help visualize the situation of water systems, thus providing opportunities to improve performance and enhance integrity. Nevertheless, one of the limitations of the ABM is the simplification of the actors involved in the different WSD levels. This does not allow the social network role and the learning in actors’ behaviors to be fully evaluated. In other words, what happens in one game does not necessarily influence what happens in another game. The simulations show that this learning has little influence on the results. It was observed in several cases that equilibrium is reached after a number of interactions are played between principals and agents. The question remains as to whether a higher number of actors with an increasing number of neighbor relationships would have an impact on how equilibrium strategies are developed.
We thank Georg Holtz, Geeske Scholz, Jorg Krywkow, and Gema Carmona.
Anderies, J. M., M. A. Janssen, and E. Ostrom. 2004. A framework to analyze the robustness of social-ecological systems from an institutional perspective. Ecology and Society 9(1):18. [online] URL: http://www.ecologyandsociety.org/vol9/iss1/art18
Auriol, E., and A. Blanc. 2009. Capture and corruption in public utilities: the cases of water and electricity in Sub-Saharan Africa. Utilities Policy 17:203-216. http://dx.doi.org/10.1016/j.jup.2008.07.005
Axelrod, R. 1984. The evolution of cooperation. Basic Books, New York, New York, USA.
Balacco, H. R. 2011. Sobre algunas posibles limitaciones del análisis econométrico. Facultad de Ciencias Económicas, Universidad Nacional de Cuyo, Mendoza, Argentina. [online] URL: http://bdigital.uncu.edu.ar/objetos_digitales/4058/balaccoeconometria.pdf
Batley, R. 2004. The politics of service delivery reform. Development and Change 35(1):31-56. http://dx.doi.org/10.1111/j.1467-7660.2004.00341.x
Bell, W. P. 2012. Progressing from game theory to agent based modelling to simulate social emergence. Sociology Lens 17 September. [online] URL: http://www.sociologylens.net/topics/collective-behaviour-and-social-movements/progressing-from-game-theory-to-agent-based-modelling-to-simulate-social-emergence/10746
Bellaubi, F. 2004. Water efficiency and equity in an irrigation system: the case study of Walawe River Basin, Sri Lanka. Thesis. Institut Agronomique Méditerranéen, Montpellier, France.
Bellaubi, F. 2011. Enhancing integrity to improve service delivery in water service supply provision. Water governance: meeting the challenges of global change. ESF Conference in Partnership with LFUI. Universitätszentrum Obergurgl, Austria, 5-10 June 2011. European Science Foundation, Strasbourg, France.
Bellaubi, F., and J. T. Visscher. 2010. Enhancing integrity to improve service delivery in water service supply provision. Pages 1-19 in J. Butterworth, editor. Pumps, pipes and promises: costs, finances and accountability for sustainable WASH services. IRC Symposium 16-18 November 2010, IRC, The Hague, Netherlands. [online] URL: http://www.ircwash.org/resources/enhancing-integrity-improve-service-delivery-water-supply-service-provision-paper
Bellaubi, F., and J. T. Visscher. 2014. Water service delivery in Kenya and Ghana: an area-based assessment of water utility performance. Water International 39(7). http://dx.doi.org/10.1080/02508060.2015.985976
Bellaubi, F., and J. T. Visscher. 2016. Integrity and corruption risks in water service delivery in Kenya and Ghana. International Journal of Water Governance 4:1-22.
Bellaubi, F., G. Holtz, and C. Pahl-Wostl. 2014. An agent-based model to identify management practices, integrity and performance in Kenya’s and Ghana’s water service delivery. CoMSES Computational Model Library. [online] URL: http://www.openabm.org/model/4144/version/4
Boehm, F. 2007. Regulatory capture revisited - lessons from economics of corruption. Working Paper No. 22. Internet Center for Corruption Research, Passau, Germany. [online] URL: http://www.icgg.org/downloads/Boehm%20-%20Regulatory%20Capture%20Revisited.pdf
Ghana Integrity Initiative (GII). 2011. Ghana’s national water supply integrity study. Mapping transparency, accountability and participation in service delivery: an analysis of the water supply sector in Ghana. Ghana Integrity Initiative, Accra, Ghana.
Gilbert, N. 2008. Agent-based models. Sage, Thousand Oaks, California, USA. http://dx.doi.org/10.4135/9781412983259
Guerrero, O. 2009. Bribery dynamics: an agent-based approach with evolutionary learning. Working paper. George Mason University, Fairfax, Virginia, USA. [online] URL: http://andromeda.rutgers.edu/~jmbarr/EEA2009/guerrero.pdf
Hauert, C., and M. Doebeli. 2004. Spatial structure often inhibits the evolution of cooperation in the snowdrift game. Nature 428:643-646. http://dx.doi.org/10.1038/nature02360
Huppert, W. 2005. Water management in the ‘moral hazard trap,’ the example of irrigation. World water week 2005 Seminar on Corruption in the water sector: how to fight it? Swedish Water House, Stockholm, Sweden. [online] URL: http://agriwaterpedia.info/images/e/e7/Huppert,_W._(2006)_Water_Management_in_the_Moral_Hazard_Trap.pdf
Janssen, M. A. 2008. Evolution of cooperation in a one-shot prisoner’s dilemma based on recognition of trustworthy and untrustworthy agents. Journal of Economic Behavior and Organization 65:458-471. http://dx.doi.org/10.1016/j.jebo.2006.02.004
Janssen, M. A., and E. Ostrom. 2006. Empirically based, agent-based models. Ecology and Society 11(2):37. [online] URL: http://www.ecologyandsociety.org/vol11/iss2/art37/ http://dx.doi.org/10.5751/es-01861-110237
Kehagias, A. 1994. Probabilistic learning Automata and the prisoner’s dilemma. Journal of Liberal Arts 1:41-55.
Kirkebøen, G. 2009. Decision behavior - improving expert judgment. Pages 169-194 in I. T. W. Williams, K. Samset, and K. J. Sunnevåg, editors. Making essential choices with scant information. Front-end decision making in major projects. Palgrave-Macmillan, New York, New York, USA.
Kooiman, J., M. Bavinck, R. Chuenpagdee, R. Mahon, and R. Pullin. 2008. Interactive governance and governability: an introduction. Journal of Transdisciplinary Environmental Studies 7:1-11. [online] URL: http://dare.uva.nl/document/2/59200
Lambsdorff, J. G. 2007. The institutional economics of corruption and reform: theory, policy and evidence. Cambridge University Press, Cambridge, UK. http://dx.doi.org/10.1017/cbo9780511492617
Lambsdorff, J., and B. Frank. 2007. Corrupt reciprocity: an experiment. Passauer Diskussionspapiere, Volkswirtschaftliche Reihe, No. V-51-07. Universität Passau, Passau, Germany. [online] URL: https://www.researchgate.net/publication/252698676_Corrupt_reciprocity_An_experiment
Lewin, K. 1943. Defining the ‘field at a given time.’ Psychological Review 50:292-310. http://dx.doi.org/10.1037/h0062738
Molle, F., and J. Berkoff. 2007. Water pricing in irrigation: mapping the debate in the light of the experience. Pages 21-93 in F. Molle and J. Berkoff, editors. Irrigation water pricing: the gap between theory and practice. Centre for Agriculture and Bioscience International, Wallingford, UK. http://dx.doi.org/10.1079/9781845932923.0021
Nowak, M. A., and R. May. 1992. Evolutionary games and spatial chaos. Nature 359:826-829. http://dx.doi.org/10.1038/359826a0
Olken, B. A. 2007. Monitoring corruption: evidence from a field experiment in Indonesia. Journal of Political Economy 115(2):200-249. http://dx.doi.org/10.1086/517935
Ostrom, E. 1998. A behavioral approach to the rational choice theory of collective action: presidential address, American Political Science Association, 1997. American Political Science Review 92(1):1-22. http://dx.doi.org/10.2307/2585925
Pahl-Wostl, C., and C. Knieper. 2014. The capacity of water governance to deal with the climate change adaptation challenge: using fuzzy set qualitative comparative analysis to distinguish between polycentric, fragmented and centralized regimes. Global Environmental Change 29:139-154. http://dx.doi.org/10.1016/j.gloenvcha.2014.09.003
Pahl-Wostl, C., L. Lebel, C. Knieper, and E. Nikitina. 2012. From simplistic panaceas to mastering complexity: towards adaptive governance in river basins. Environmental Science and Policy 23:24-34. http://dx.doi.org/10.1016/j.envsci.2012.07.014
Pahl-Wostl, C., J. Sendzimir, P. Jeffrey, J. Aerts, G. Berkamp, and K. Cross. 2007. Managing change toward adaptive water management through social learning. Ecology and Society 12(2):30. [online] URL: http://www.ecologyandsociety.org/vol12/iss2/art30/ http://dx.doi.org/10.5751/es-02147-120230
Power, C. 2009. A spatial agent-based model of N-person prisoner’s dilemma. Cooperation in a socio-geographic community. Journal of Artificial Societies and Social Simulation 12(1):8. [online] URL: http://jasss.soc.surrey.ac.uk/12/1/8.html
Repetto, R. C. 1986. Skimming the water: rent-seeking and the performance of public irrigation systems. Research Report No. 4. World Resources Institute, Washington, D.C., USA.
Santos, F. C., and J. M. Pacheco. 2005. A new route to the evolution of cooperation. European Society for Evolutionary Biology 19:726-733. http://dx.doi.org/10.1111/j.1420-9101.2005.01063.x
Savage, L. J. 1954. The foundations of statistics. Wiley, New York, New York, USA.
Sheng, Z.-H., Y.-Z. Hou, X.-L. Wang, and J.-G. Du. 2008. The evolution of cooperation with memory, learning, and dynamic preferential selection in spatial prisoner’s dilemma game. 2007 International symposium on nonlinear dynamics. Journal of Physics: Conference Series 96:1-6. http://dx.doi.org/10.1088/1742-6596/96/1/012107
Situngkir, H. 2003a. Moneyscape: a generic agent-based model of corruption. Working Paper WPC2003. Bandung Fe Institute, Bandung, Indonesia. [online] URL: https://core.ac.uk/download/pdf/9314969.pdf
Situngkir, H. 2003b. The dynamics of corruption. Journal of Social Complexity 1(3):3-17.
Szilagyi, M. N. 2003. Simulation of multi-agent prisoner’s dilemma. Systems Analysis and Modeling Simulation 43(6):829-846. http://dx.doi.org/10.1080/0232929021000055488
Szilagyi, M. N., and I. Somogyi. 2008. Agent-based simulation of N-person games with crossing payoff functions. Complex Systems 17:427-439. [online] URL: http://www.complex-systems.com/pdf/17-4-7.pdf
Transparency International Kenya (TIK). 2011. National water integrity study (NWIS). Keep the TAP flowing. Transparency International Kenya, Kisumu, Kenya. [online] URL: https://www.tikenya.org/index.php/integrity-studies?download=203:national-water-integrity-study
Vörösmarty, C. J., P. B. McIntyre, M. O. Gessner, D. Dudgeon, A. Prusevich, P. Green, S. Glidden, S. E. Bunn, C. A. Sullivan, C. R. Liermann, and P. M. Davies. 2010. Global threats to human water security and river biodiversity. Nature 467:555-561. http://dx.doi.org/10.1038/nature09440
Wilensky, U. 1999. NetLogo. Center for Connected Learning and Computed-Based Modelling, Northwestern University, Evaston, Illinois. [online] URL: http://ccl.northwestern.edu/netlogo