1. Introduction

Achieving cooperation in natural resource management is always a challenge when incentives exist for an individual to maximise her short-term benefits at the cost of a group. Since everybody in the group has the same rationale, the group can be trapped in a situation in which it misses out on potential gains. The Prisoner’s Dilemma and The Tragedy of the Commons (Hardin 1994) are illustrations of this problem (Bardhan 1993). Observations of natural and social systems both demonstrate that it is possible to achieve cooperation (Ostrom 1998, 2010; Nowak 2006). Therefore, the focus of attention has shifted towards the assessment of factors influencing the probability of cooperation. One such factor receiving attention is the congruence of appropriation and provision (Ostrom 1998, 2010). We thus formulate the following research question:

Does the level of cooperation regarding group water-infrastructure provision on neighbouring Namibian land reform farms depend on the character of payment rules – more specifically, the congruence of appropriation and provision?

We study our research question in the context of the Namibian land reform. For more than 18 years, land has been redistributed to previously disadvantaged groups of the Namibian society using a broad range of instruments, such as group resettlement, subsidized loans, redistribution of government land and, in a few cases, expropriation. In this paper, we focus on the Farm Unit Resettlement Scheme (FURS) which is based on the willing-seller willing-buyer principle. The Namibian state uses preferential acquisition rights to purchase suitable agricultural land whenever any owner of such land intends to dispose of it (RoN 1995). The Ministry of Lands and Resettlement divides the farms into smaller units and any Namibian citizen who has been socially, economically or educationally disadvantaged by past discriminatory laws can apply for an allotment of such units for resettlement (e.g. RoN 2002).

The research question is highly relevant in the FURS setting as there are hardly any permanent open water sources in Namibia. Farmers have to pump ground water for their livestock with diesel or wind pumps. A breakdown of water infrastructure leads to livestock losses and significant costs. If water infrastructure breaks down, farmers are forced to ask for water access at neighbouring farms. Usually fees need to be paid for such water access, and longer routes to water points contribute significant stress to the animals.

According to the lease agreements, the government is responsible for the maintenance of the infrastructure. Nevertheless, there are unclear responsibilities between ministries, and authorities are very slow to respond to infrastructure breakdowns. Therefore, it is generally more cost efficient for farmers to repair the infrastructure themselves than to bear the costs of waiting for government assistance. Farmers make no payments to the government for the maintenance.

For the self-organised infrastructure management no formal fee collection rules are specified. If FURS farmers form Water Point User Associations they are supposed to have an association bank account according to the by-laws. But in general the groups can decide themselves how to collect money and how to pay the actual maintenance expenses.

Maintaining water infrastructure is a collective challenge for FURS farmers. This fact is strongly shaped by the process of land redistribution. The splitting of larger farms, that were previously centrally managed, into smaller farm units means that beneficiaries do not have exclusive access to water infrastructure. The sharing of water infrastructure is emphasized in the lease agreement. FURS beneficiaries are forced to cooperate with their neighbouring farmers on a farm cluster. They enter the cooperation arena solely on the basis of bureaucratic decisions. They have no say as to whom they cooperate with, do not know their future cooperation partners, and, therefore, cannot rely on a history of social interaction.

Given this situation, the main water governance challenge for the farmers is the decision how much each of them contributes to infrastructure maintenance. There are two typical operational rules in the research region with regard to contributions to water infrastructure maintenance. Either farmers pay an equal fixed amount or they calculate a fee per head of livestock (Bock and Kirk 2006; Falk et al. 2009). Both payment systems have their advantages and disadvantages. The fixed payment per farmer is easy and transparent to calculate. It does not, however, reflect the unequal appropriation of water. Livestock is the main consumer of water in central Namibian farming systems and is highly unequally distributed amongst the farmers. The fee per head of livestock supports congruence of provision and appropriation which according to Ostrom (1990) increases the likelihood of successful cooperation. This is most likely also the reason why this payment system is strongly promoted by the Ministry of Agriculture. Nevertheless, the livestock based system requires a regular adaptation of the individual payments. Livestock numbers vary considerably between farmers and change permanently due to multiple dynamics within the SES. It is not easy to assess each other’s livestock numbers on relatively large and densely vegetated farms. Direct or indirect monitoring of water appropriation is costly; therefore, a payment system which achieves congruence of provision and appropriation is associated with higher transaction costs.

It has to be emphasised that this paper is not intended to summarize the historical and political background of the Namibian land reform. We provide more background information in Appendix 1 and refer otherwise to more comprehensive assessments such as Werner (1993), Kaukungua et al. (2004), Werner (2004), LAC (2005), Werner and Kruger (2007), RoN (2010), Werner and Odendaal (2010). This paper focuses on one particular challenge of FURS beneficiaries namely the management of shared water infrastructure on small scale clusters of land reform farm units.

In our sample a cluster consists of up to six units and has a size between 750 ha and 4.600 ha. The farmers lease the land from the government. They receive farm income mainly from meat production and enjoy a lifestyle which is much romanticised in Namibia (Falk et al. 2009). We study specifically the choice of a payment system to achieve water management cooperation.

In a first step towards answering our research question, we conducted an explorative assessment of our case based on the Social-Ecological-System (SES) Framework of Ostrom (2009) (see Appendix 1). The framework based assessment helped us deepen our general understanding of the complexity of the system. In the application of this approach, we benefited from ten years of interdisciplinary collaboration within the Biodiversity Monitoring Transect Analysis in Southern Africa (BIOTA) Project. The joint work of social and natural scientists contributed greatly to offering a more holistic answer to the research question. It was, however, not the objective of this research to describe the full complexity of the interactions of human and natural systems of FURS farms as one might expect in some schools of system research (see e.g. Foran et al. 2014). Our behavioural study follows the approach of taking into account diverse system features when interpreting causal relationships between asset heterogeneity, rule definition and group cooperation. As such, the explorative assessment forms the basis for theoretical considerations on the collective infrastructure provision challenge of FURS farmers.

In a next step, we introduce a rangeland ecosystem model, which was linked to the land users’ decisions on water infrastructure management. In this way a role-play design emerged based on a computer-simulation model. The role-play design allows us to capture resource dynamics in studying collective action. Janssen (2010) emphasises the need to increase the relevance of behavioural experimental approaches by strongly taking into account system dynamics. As such, we believe to supplement more standardised and often static experimental research. However, adding complexity to the game also has some disadvantages. It becomes, as in real-life, more difficult for the players to understand all relations between different system variables. As a consequence, it is impossible to control for all interactions. The game, therefore, only produces relevant knowledge if it offers a sufficiently close representation of the real-life decision situation.

2. The research site

Research was conducted in the Omaheke region in east central Namibia (Figure 1). The vegetation is dominated by an Acacia-Terminalia tree-and-shrub savannah of the Central Kalahari (Mendelsohn et al. 2002). FURS land reform beneficiaries in our sample, farm with livestock, mainly cattle, and operate in a commercial farming setting. The farm unit clusters are clearly marked and fenced. FURS farmers are allotted individually fenced shares of the cluster. The size of studied individual farm units ranges between 50 and 2000 ha which is far below the average of commercial farm sizes in Omaheke (Olbrich 2012).

Table 1 summarizes the basic descriptive statistics of our sample. The majority of respondents (82%) use the farm units for more than 4 years. This means they have already had considerable time to develop infrastructure maintenance rules.

3. Theoretical considerations on water provision in the FURS setting

In the following section we present a summary of some theoretical considerations related to the challenge of water provision cooperation in Central Namibia. Our model aims at drawing theoretical hypotheses regarding farmers’ contributions and free ride incentives in the management of water infrastructure. A more detailed description on our theory and the connected assumptions is given in Appendix 2.

Consider a group of N farmers collectively using the same water infrastructure whose maintenance costs need to be covered to be functional. Each farmer i has to contribute an amount C_i,i∈{1, …, N} into the water fund WF_t to cover the maintenance costs K. At the end of each period, after subtracting the maintenance costs K, the amount remaining in the water fund WFt-1 is transferred to the next period which represents the connection between two rounds. At the beginning of each period, the water fund WF_t has in total

In real life, the maintenance costs of water pumps vary from year to year and are unknown to the farmers. We assume that these costs are continuous uniformly distributed along the interval [0, V], with V being the value of a new water infrastructure. In order to be operational every period, the amount in the water fund must cover the maintenance costs, otherwise the infrastructure breaks down. Therefore, the functioning probability of the water infrastructure depends on the probability that the amount in the water fund is higher than the maintenance costs:

In case the infrastructure breaks down each farmer usually takes her cattle to the neighbouring farm where she has to pay fees per head of cattle, which we label here OC (opportunity costs). This alternative water source has a direct influence on the farmers’ incentive to participate in the maintenance of their own water infrastructure. From an opportunity costs perspective, each farmer would choose to use the water source which is less costly for her. From these considerations comes the following:

Proposition 1a: A group will contribute to the maintenance of their water infrastructure, if the group opportunity costs OC_N are higher than the group’s total contributions C_N.

Proposition 1b: An individual will contribute to the maintenance of their water infrastructure, if her opportunity costs OC_i are higher than her contributions C_i.

Considering her individual opportunity costs OC_i, the contribution of other farmers and the uncertain maintenance costs, each farmer i chooses the contribution C_i that minimizes her expected costs EC(C_i). On the basis of the model (see Appendix 2), we can draw conclusions about the theoretical reaction of one farmer to the payments of other farmers. In equilibrium the strategic reaction of farmer i to the contribution of the other farmers in her cluster is to reduce her contribution. On the strength of this conclusion we establish our next proposition:

Proposition 2: Farmer i’s contribution is negatively correlated with the contribution of other farmers in her group.

When a short-sighted strategic farmer i computes her optimal decision, neglecting future interaction and not holding other-regarding preferences, she takes the contribution of other farmers as given. Any additional payment of farmer i increases the survival rate of the water infrastructure which is beneficial to all farmers in the cluster. If farmer j raises her contribution, farmer i will strategically reduce her contribution to the group water fund. This behaviour conflicts with the inequity aversion concept of Fehr and Schmidt (1999) and conditional cooperation of Fischbacher and Gächter (2010).

Another important aspect for the decision making is the fact that a farmer’s opportunity costs are determined by her number of livestock. Independent of fairness norms, she is willing to increase payments if her opportunity costs increase. She strives to avoid higher opportunity costs if the infrastructure breaks down; thus, she has an incentive to contribute. From this we derive the following:

Proposition 3: The larger the number of livestock of a farmer, the greater her contribution into the water fund.

The congruence of appropriation (livestock number) and provision (individual contribution) can be observed in this result (Ostrom 2010). A farmer with a large number of livestock will pay more than a farmer with a small number of livestock. However, as already mentioned, farmers can either pay an equal fixed amount or they can choose to calculate a fee per head of livestock. If herd endowment is relatively homogenous across farmers, then the individual payments will be similar under both payment rules. The amounts differ, however, in groups with heterogeneous livestock endowments. From this we establish the following:

Proposition 4: The payment system with equal contribution per farmer i is stable in groups with homogeneous endowments. It is less stable in groups with heterogeneous endowments.

Propositions 2 and 3 predict that poorer farmers, in terms of livestock, will expect wealthier farmers to contribute more to the water fund. An equal payment would deviate from the optimal reaction, thus, from the equilibrium, when livestock numbers are unequal. From propositions two, three and four it follows that heterogeneous groups, in terms of livestock endowment, are, in equilibrium, more likely to choose the rule payment per head of livestock.

The explorative SES assessment made us aware that water provision cooperation by Namibian land reform beneficiaries has to be achieved in systems of high dynamic complexity. Amongst others, these are marked by permanent and often delayed changes, multiple feedbacks at different speeds, nonlinear relationships of variables, and often irreversible developments (Sterman 2001, 2006; Barreteau et al. 2001). The systems are reflexive, acting on decision makers who, through their actions, affect various components of the system (Bousquet et al. 2002). More specifically, we learned from the explorative SES assessment that complex system interactions create strong dynamics of total and relative livestock numbers. In summary, we expect that a payment system which is linked to livestock numbers and achieves stronger congruence of provision and appropriation is more stable in maintaining group cooperation.

Acknowledging the complexity of social ecological systems initiated the debate on how to decide which variables should be included in particular studies. Catalogues of third tier SES framework variables collected from various studies quickly contain hundreds of variables. There is a common understanding that only such variables should be taken into account which are relevant for a particular study. The explorative SES assessment helped us to identify relevant control variables. Especially for the quantitative analysis another selection criteria has been important. We included only such variables in our analyses which show a considerable variance across our sample. With our study design we cannot make any statements about the importance of features of the SES which are identical across our sample. Such variables can still have a strong impact on cooperation patterns. Good examples are historical or political factors. We provide in the introduction and in Appendix 1 some context information on such variables.

4. Role-plays as approach to observe cooperation behaviour in complex and dynamic decision making situations

In order to answer our research question and test our theoretical propositions, we decided to use role-plays. Role-plays can be used to achieve multiple objectives. They help us to acquire knowledge, validate models, support farmers’ decision making and negotiation processes, and develop institutional capacity (Barreteau et al. 2001; Bousquet et al. 2002).

Our role-play is based on two models. On the one hand, we followed the logic of the theoretical model described above. On the other hand, we used an ecological-economic-simulation model in order to capture the ecological interactions and dynamics of the system (Lohmann et al. 2014). The combination of both models simulates the complexity and dynamics of important parts of the social-ecological system in the context of water provision on Namibian FURS farms. The resulting role-plays created a virtual world in which farmers could experiment, rehearse decision making, and play in a compressed time and space (see also Barreteau et al. 2001; Sterman 2001, 2006). The model provided them with immediate feedback and allowed them to adjust decisions. Experimenting with the simulation model induces much lower costs and risks for the players than a real-life trial and error process of institutional change (Barreteau et al. 2001; Sterman 2006).

Compared to standard experiments, this approach has a number of obvious disadvantages. The internal validity is low as it is difficult to control many parameters. As a consequence the results are difficult to compare (Bousquet et al. 2002). The role plays are not suitable for testing general theoretical hypothesis. Generating accepted scientific evidence requires controlled experiments which discriminate between hypotheses and produce replicable results (Sterman 2006). Nevertheless, the more complex the phenomenon, the more difficult it is to draw conclusions from standard experiments on real life decision situations.

The advantage of the simulation-model based role-plays is a higher external validity and a more realistic reproduction of real-life decision situations (Barreteau et al. 2001). The objective of the role-play games is to assess a representation of reality rather than to study a theoretical pre-given one (Bousquet et al. 2002).

As a starting point for developing our role-play, we used an existing vegetation model (Tietjen et al. 2010) and parameterised it for environmental conditions in the Omaheke region of Namibia. The model simulates the dynamics of natural resources depending on environmental conditions (climate, hydrology, ecological interactions) and land use impacts. For details see Lohmann et al. (2012, 2014), Appendix 3, and Supplementary Appendix. Resource dynamics derived from this model were dynamically linked to a social-economic model based on our theoretical model (Appendix 3). Specifically relevant for the given question here is the fact that the livestock numbers in the model responded to the vegetation state, the health of the animals as well as off-take decisions. The vegetation state, again, depends on external factors such as random rainfall, but also on the stocking rate. From a land users perspective this framework represents the highly unpredictable and complex dynamics of the real-life social-ecological system.

The combined ecological-economic rangeland model was then converted into a computer based role-play of basic farming decisions and, in particular, the voluntary contribution to the group’s water provision. We designed a user interface that allows for the communication between a facilitator and the model. The interface presents an output of all state variables and allows for a subsequent input of the farmers’ decisions.

We communicated the initial ecological and economic model states using photographs and simple lists in the respondent’s mother tongue. Based on this illustratively communicated information, farmers made decisions regarding their stocking rates as well as their individual contribution to the maintenance of water infrastructure (i.e. the amount of money to be paid to a water fund) (see the interface and illustrations in the Supplementary Appendix).

The role-play starts with an individual and group account balance of zero. Each player is given a herd and farm size representing the respective real-life values from the farms as given in 2008. Animals and vegetation are in a good and above average state and the water infrastructure is functioning at the beginning of the game.

The vegetation state is changing every round of the game and is communicated using exemplary photographs taken from different vegetation states in the research region. The same approach, of showing pictures, is used for illustrating the body score condition of the livestock. Printout outputs in the player’s mother tongue are generated for every time step to present the following player-specific information:

• rainfall in the previous role-play period¹
• the player’s individual number of livestock at the beginning of the role-play period
• age structure of the player’s livestock herd at the beginning of the role-play period
• the player’s number of livestock losses in the previous role-play period
• the player’s account balance at the beginning of the role-play period
• the player’s total farm expenses to be covered in the role-play period²
• the account balance of the group’s water fund at the beginning of the role-play period.

In each round the players can make two independent decisions: 1) they can buy or sell livestock and 2) they can choose an amount to pay from their individual account into their group’s water fund. Both decisions are made simultaneously.

The role-play is set up in such a way that all players have the opportunity to continuously communicate face to face as this is the most efficient form of communication for developing institutions (Balliet 2010) and is a realistic representation of the real-life situation.³ We did not restrict the time the players could communicate. Furthermore, the players had the opportunity to find out the decisions of the other players. This strategy was chosen because fellow farmers can in reality talk to each other and we did not intend to provide another evidence for the fact that communication supports cooperation.

After all players have made their decisions, new ecological and economic states (e.g. condition of livestock and account balance) are calculated by our simulation model. These new states are again the basis for decisions in the next round of the game. Figure 2 illustrates the role-play process.

The modelled water-infrastructure costs vary from year to year, reflecting randomly appearing maintenance costs. In the role-play, each group shares water infrastructure, which consists of one diesel and one wind driven pump. The costs are modelled on the basis of expert interviews with an annual average cost of N$ 2350 (σ=785) for the diesel driven pump and N$ 750 (σ=250) for the wind driven pump. Players were not informed at the beginning of the game how we calculated the maintenance costs. We told them, however, that there is a setup of two pumps and that costs are based on expert estimates of real-life costs. They were further told that the costs randomly vary from period to period in the game. Previous experiences of the players and specific differences between the farms may affect the decisions on the amount to be paid into the water fund especially in the first periods of the game. We hope to capture this noise in our data analysis by controlling for the highest maintenance costs in the previous rounds of the game. In addition, we control for farming experience and training received. Further, we separately analyse the second half of the role-plays when we assume they have learned approximately how high the maintenance costs are in our game. Throughout the game, farmers were not informed about the periods’ water costs before making their contribution; therefore, they have to make decisions under uncertainty.

In the case that the money available in the fund is insufficient to cover the maintenance costs, the infrastructure breaks down. In this case the players had to pay a fee of N$ 50 per head of cattle. The amount represents the opportunity costs in our theoretical model. It is based on interviews with farmers even though, in reality, there is a lot of variation. The opportunity costs were announced at the beginning of the game; therefore, players could calculate them for each round throughout the game.

We conducted the role-play sessions between January and April of 2009. The research team cooperated with the Emerging Commercial Farmers’ Support Programme (ECFSP), which provided lists of all land reform farms in the Omaheke Region. By the time of the research there were 196 Farm Unit Resettlement Schemes (FURS), and 45 of them (23%), sharing 14 farm clusters, were included in the study.⁴ The selection of participants was not random, but predetermined by the accessibility of beneficiaries. It happened only once that a respondent declined to participate in the study. In most of the cases, if farms could not be included in the study, it was impossible to establish contact with the farmers. This means that we probably have a bias towards full-time farmers even though the team arranged interviews with part-time farmers outside of their farms in order to reduce this problem. It should be mentioned that the research area is relatively large (84.981 km²) and that the team drove up to 300 km every day, on dirt roads, to visit the farms. The small sample as well as the sample selection process has to be taken into account when interpreting our results.

In an attempt to simulate the real-life cooperation situation, the role-plays where played among groups of farmers who in fact share a water point. This also means that for each game the group size varied from between two and six players. The role-plays took between one and three hours. Participants did not receive any game related payments.

For the data analyses, we used the standard deviation of payments to identify groups agreeing to a rule. If the group’s standard deviation of water payments was zero in a specific period of the role-play, we concluded that the group was following the rule of equal payment per person. If, in a specific period, the group’s standard deviation of water payments when divided by livestock numbers was zero, we concluded that the group was following the rule of payment per head of livestock. The role-play data was analysed using regression models. We used a hierarchical mixed-effects regression model in STATA 12. This allowed us to control for variables on different scales. As such, we considered individual layer and group-context layer information.

5. Results of the role plays

Using simple correlation analysis reveals that 38% of our players increase their payments if the other group members also increase their payments.⁵ Thirteen per cent of the sample adjusted their payments to their share of the group’s livestock herd. The payments of another 6% of the players correlated with both the payments of the other players and their livestock share. This is possible if there is a relatively stable relation of livestock numbers amongst the group members. The payments of 42% of the players correlated neither with the other group members’ payments nor with their share of the livestock herd. We do not observe consequent free riding as all players contributed to the maintenance of the water infrastructure.

In 86% of the decisions the individual payments are lower than the costs for using the neighbours’ water source. In 92% of the decisions, the total opportunity costs of all group members are higher than their total contributions into the water fund. The sum of payments for the whole game is always higher than the total group opportunity costs. On the individual level there are still, however, 5 individuals (11%) wherein their total game payments exceed their opportunity costs. As such, Proposition 1a and 1b are confirmed, albeit with a few surprising exceptions.

Analysing the role-plays’ contributions using regression models (Table 2) allows us to reject Proposition 2. In none of the models we observe a negative relation between farmer i’s contribution and the contributions of other group members. The Mixed-effects model, covering all game rounds, indicates that players increase their payments if the other group members increase theirs. This could be interpreted as inequity aversion (Fehr and Schmidt 1999) or conditional cooperation (Fischbacher and Gächter 2010).

Our results confirm Proposition 3. The players adjusted their payments to represent their livestock numbers. This indicates that farmers act on implicit norms of congruence of provision and appropriation. The players largely failed, however, to formalise these norms. The rule of payment per head of livestock, which guarantees the highest congruence of provision and appropriation, was unpopular amongst our players. Only one group switched, in the course of the game, from equal payment per person to payment per head of livestock. Another group agreed, at the beginning of the game, to the rule of payment per head of livestock, but in round two one player defected and the cooperation could not be re-established. Five groups agreed to the rule of equal payment per person. Overall, six out of 14 groups agreed to follow a clear payment rule consistently throughout the game. Five groups cooperated from the first round, and one group started to cooperate after round four.

In reference to Proposition 4, we cannot confirm that adopting the rule of payment per head of livestock was positively correlated with the variance in livestock endowment within groups. Table 3 indicates that groups with less variance in livestock endowments were more likely to come to an agreement on a payment rule. In contrast, groups with a greater variance in initial livestock endowments often failed to provide sufficient funds in order to avoid an infrastructure breakdown. Nevertheless, players who were confronted with situations of unequal livestock possession were more likely to adopt an implicit norm of congruence of provision and appropriation. In contrast, the implicit norm of adjusting payments to other group members’ payments was more frequently observed in groups that closely resembled a homogeneous livestock endowment (Table 3).

Our regression models (Table 2) provide evidence that groups agreeing on a payment per head of livestock made higher payments than groups agreeing on no rule. In a similar way groups adopting the equal payment per person also paid more. The models confirm that in the face of higher variance of livestock endowments within groups, adopting the rule to pay per livestock does not increase payments (see interaction term, Table 2). The models for the overall game even indicate a negative relationship.

Correlation analysis indicates that players who consciously agreed to the payment system per person made larger water contributions than players who informally adjusted their payments to the payments of other players (Pearson r=0.566, p=0.014, N=18). Also players who consciously agreed on a payment system per head of livestock tend to make higher payments compared to players informally adjusting their payments to the distribution of livestock within the group (Pearson r=0.551, p=0.099, N=10). Nevertheless, the people formally following a rule and the ones informally following a norm had similar overall water expenses per livestock unit (individual payments plus breakdown fees) (P-values for two-tailed t-test are 0.36 and 0.18 for payment per person and payment per head of livestock respectively). It is interesting to note that farmers with smaller livestock numbers have been more reluctant to explicitly commit to any rule (Pearson r=–0.3911, p=0.008, n=45). Mainly owners of larger herds formalised the rule of equal payment per farmer while owners of smaller herds rather adjusted their payments informally to the other players’ payments (Pearson r=0.4691, p=0.050, n=18). One should keep in mind that in groups with heterogeneous livestock ownership the farmers with large herds are favoured by the equal payment per farmer.

Having learned about the payment behaviour still leaves the question open whether the rule formation had an impact on the ecological and economic outcomes of the farmers in the games. We count together the individual payments into the water fund and the individual fees paid in cases of infrastructure breakdowns. These two amounts together are the farmers’ total water expenses. We can see that the total water expenses per livestock unit are likely to be lower for the farmers who agreed on a rule compared to the ones not having agreed (means of 952 N$/LSU and 2397 N$/LSU respectively; P-value for two-tailed t-test is 0.08). There are no significant differences between the two payment systems. We further see that in situations with more homogeneous livestock possessions players tended to make higher contributions to the group fund (Pearson r=–0. 580, p=0.000, n=45) and had lower overall water expenses per livestock unit (individual payments plus breakdown fees) (Pearson r=–0.4 36, p=0.003, n=45).

We cannot observe any impact of the rule formation on the total game income or changes in the value of the herd. The design of the underlying system model gives the stocking decisions a much stronger weight on these outcome variables than the water payments. This is actually also true for the state of the pasture. We observe, however, that the players agreeing to a rule degraded their pasture much more than the ones not agreeing (P-value for two-tailed t-test is 0.03; no differences between payment rules). Nevertheless, it would be bold to assume causality in this regard. Correlation analysis indicates that farmers with larger livestock numbers more likely agreed to a payment rule. Independent from the water payments these farmers are more likely to put stronger pressure on the pastures.

Looking at the individual control variables provides some interesting results. Female players made lower contributions than their male counterparts. Beneficiaries with more real-life human and financial capital as well as better farming productivity made relatively higher contributions in the game.

Our Mixed-Effects regressions give some encouraging results indicating a high external validity of our game. Firstly, farmers who made bigger real life investments into water infrastructure also made higher contributions in the game. Secondly, players farming on units where the water infrastructure is in fact better maintained also contributed higher amounts in the role-play (Table 2). We asked our respondents how many pumps they have on their farm and how many pumps are indeed working with the result that the larger the share of working pumps the higher the payments.

6. Discussion and conclusion

We observe in our game relatively high levels of cooperation and no consequent free riding. These results are likely to be effected by the accessibility of social information on individual payment levels. Our main motivation to make payments transparent was to increase the external validity. There is a low degree of privacy in the researched communities. According to Carpenter and Seki (2011) and Henrich et al. (2010) participant behaviour in experimental settings is based on their real-life experiences. The participants in our role-plays share in real life the same water infrastructure and the joint management of this infrastructure is a typical challenge for them. Furthermore, they can easily observe each other’s actions.

Revealing the individual payments very likely makes players adjust their payments to what they believe is approved by fellow players. Not to free-ride might be motivated by avoiding shame. Our design does, however, not allow us to draw conclusions about the effect of the anticipated approval or disapproval on the players’ decisions.

The rule of payment per head of livestock has only been consciously agreed upon by one group in our role-play, while five groups adopted the rule of equal payment per person. This tendency can possibly be explained by the transaction costs of monitoring livestock numbers which is necessary to determine the individual payments. In each round of the game the payment has to be adopted to reflect the changing livestock numbers, while the amount is fixed under the rule of equal payment per person. In theory, a system of equal payment per person achieves a relatively high congruence of provision and appropriation if the variance of livestock endowment in a group is low. Since the payments under both rules match in groups with a relatively equal distribution of endowments, these groups are more likely to cooperate. We can clearly observe that groups with a lower variance in livestock endowment are more likely to reach a payment agreement. However, they generally choose the rule of equal payment per person.

It is not seen that groups with a greater variance of livestock endowment are more likely to adopt the rule of payment per head of livestock. Does this empirical result allow us to reject Proposition 4? We do observe implicit norms of congruence of provision and appropriation. Independent of whether groups came to an agreement on a payment system, players owning more livestock tend to make higher contributions. Furthermore, players confronted with situations of unequal livestock distribution were more likely to informally adjust their payments to reflect their number of livestock. This result suggests the possibility that our players avoided the formalisation of a rule achieving high congruence of provision and appropriation due to the higher transaction costs associated with it. Despite this fact, a share of the players demonstrated a fairness norm suggesting an autonomous and informal adaptation of provision efforts to appropriation level. Nevertheless, more research is needed in order to reach a convincing conclusion on Proposition 4.

Our role-plays simulated a real life cooperation situation using a social-ecological model. The virtual environment was sufficiently similar to reality, but simple enough to be played (Gurung et al. 2006). In this way, we increase the potential for players to learn about the real-life behaviour of one another through the role-play. Using the terminology of Roe and Just (2009), we increase our ecological validity to the extent that the context of the research is similar to the context of interest. As a consequence, the possibility to replicate our results is limited. Nevertheless, playing with subjects who actually experience similar decisions as represented in the game allows us to make specific statements about their behaviour. We see it as an indicator for the success of our approach that individuals who made higher payments in the role-plays also manage to keep their real-life infrastructure in better condition.

The simulation-model based role-plays produced not only knowledge but provided support to stakeholders in their decision making (Barreteau et al. 2001; Barreteau 2003; Gurung et al. 2006; Guyot and Honiden 2006; Becu et al. 2008). There was uniform response from the participants that they perceived the exercise as training rather than research activity. Gurung et al. (2006) emphasizes that one key objective of participatory modelling is to facilitate dialogue, shared learning, and collective decision making through interdisciplinary research; thus, strengthening the adaptive management capacity of local communities. Modelling in combination with role-plays is a way to experiment with rules and strategies and, in this way, explore probable ecological and economic consequences. It limits the costs of trial and error methods and shifts the approach from costly learning by doing towards learning by simulating (Barreteau et al. 2001). Our approach simultaneously deepens the understanding of cooperation processes and encourages discussion and institution building. In this sense, we supported Namibian land reform beneficiaries in a current and relevant challenge. It would have been difficult to measure any impact of our research given the small sample and methodological limitations. Nevertheless, we believe that our work demonstrates the potential of the research approach to contribute to achieving more productive, sustainable and resilient agricultural development. Future research should also focus on measuring such impact.

The authors acknowledge that this study can only provide a snap shot picture. The role-play approach was intended to assess decisions that are taken over a long period of time within a few hours which is a clear advantage of this method. Of course this could also be a limitation as real life decision processes are much more complex than the ones which can be modelled in a role-play.

Which policy implications can be drawn from our research? First of all, the research confirms the ongoing challenge of institution building faced by land reform beneficiaries. This is not a short-term issue anymore as some of the beneficiaries were resettled more than 20 years ago. Government and non-government extension services currently have a strong focus on developing farmers’ technical skills. Institutional capacity development in pre- and post-resettlement support needs more attention. This is a challenging process as there are no standard rules which fit all cases. Currently the Ministry of Agriculture, Water and Forestry mainly promotes the payment system per head of livestock. Our research indicates, however, that this rule is not necessarily the most preferred one.

The process of rule negotiation has to be open to the preferences of different groups and their specific circumstances. Given the difficulties to externally enforce by-laws of FURS groups it is important that the groups strongly support a rule on a moral and social basis (see also Falk et al. 2012). But maybe the loose social relations are also a chance. Schnegg and Linke (2015) show that social networks can actually hamper the effectiveness of water management institutions. The specific context also raises the question whether institutions indeed have to be always formalised. Why should groups formalize what they are doing anyway? There is always the risk that formalisation crowds out clearly observable informal norms (see e.g. Cardenas et al. 2000; Vollan 2008; Bowles and Polanía-Reyes 2012). At the same time, why are farmers not prepared to formalize what they are doing anyway? In our games the people agreeing to a rule had overall lower expenses for water per livestock unit compared to the ones who followed informal norms only. It seems, however, that in particular smaller farmers fell less comfortable with committing to formal rules. Are they more worried that the rules turn against them? Is it more difficult for them to assert their interests in negotiations on the formalisation of rules? Our study cannot answer these questions but it can create awareness for the fact that in the process of institutional capacity development special attention should be paid to owners of smaller herds.

Another important policy implication of our research is the need to pay special attention to less homogenous groups in terms of livestock endowments. The Ministry of Lands and Resettlement could consider taking the heterogeneity of livestock ownership into account when allocating land units.