Formation mechanism of cooperation in irrigation
Our simulation is based on the understanding of micro-level mechanism following which users form the cooperation in using irrigation, for instance, establishing a WUA. We obtain the understanding from both related studies and our field research.
Neighborhood effects
An individual’s behavior is not only influenced by the incentive of their own economic interests, for example, cost and benefit, but also influenced by other individuals in the same group. Such influences have been referred to as, among many other terms, neighborhood effects (Crane 1991). In the formation of cooperation, neighborhood effects occur in the channels of information transmission and building commonalities.
Individuals who are uncertain about the expected payoffs tend to use information from others (social comparison or imitation) instead of relying on their own information (deliberation or repetition) (Poteete et al. 2010; Janssen et al. 2015). The information transmission often takes place through communication with peers. During the communication, individuals are assumed to pool their experience regarding the various strategies they have used. In this way, all agents derive a similar map of which strategies work well. The communication may contribute to higher levels of cooperation because it enables social learning (Deadman et al. 2000; Poteete et al. 2010).
Individuals are more likely to form cooperation with those with whom they have reciprocity or have built up reputation. Equipping individuals with certain tags and symbols, several studies show that cooperation levels are enhanced when one cooperates with those carrying the same symbols (Hales 2001; Lindgren and Nordahl 1994; Riolo et al. 2001). The work on conditional cooperation (Fischbacher et al. 2001; Frey and Meier 2004) and direct reciprocity (Delton et al. 2011) explains why actors may cooperate with non-kin strangers. Many studies find that cooperation in large groups of strangers are more likely to emerge in the case that the initiator have built up a reputation (Nowak and Sigmund 1998; Lotem et al. 1999; Wedekind and Milinski 2000; Gintis et al. 2001).
Neighborhood effects are also found in our field surveys. The interview to the leaders of the WUA of the Third Dongfeng Canal show that just a few villages were involved in the association initially. When famers in other villages observed the benefit that the seed participants’ obtain, such as the declined cost of water using and the improved efficiency of irrigation, they also joined the WUA. In addition, the pioneer leaders of the WUA played a key role in the course the association forms. They mobilized their family members, friends and other fellows that have a contact with to join by demonstrating them the potential benefits and offering assistant.
Seed participants
The few initiators, who are most of time also the earliest participants (seed participants) in the cooperation, play a critical role in forming the cooperation. These seed participants are usually those who are well educated, risk-taking and with rich social relationships. They are usually members of the village committee, but not necessary the leader of the committee. Because of their reputation in the village, their participation itself has a demonstration effect to the potential participants, who can observed their benefits. In addition, they usually actively communicate the benefits of cooperation to the non-participants and motivate them to join so as to obtain the economies of scale in the cooperation (e.g. more individuals to share the coordination cost). Seed participants are usually is the leaders of WUA. They are thus well motivated to play the roles of solving the disputes related to the cooperation and acquiring the support from the government. For instance, the initiator and also the president of the WUA of the Third Dongfeng Canal in Dangyang personally made a lot of effort to mobilizing other villagers to participate and coordinating their interests Seed participants of such help reduce non-participants’ uncertainties and increase expected benefits in their decision-making, and thus increase their propensity to participate. Therefore, we believe that the personal ability and social status of seed participants and the ratio of them can affect the formation and diffusion of irrigation cooperation.
Government support
Government support is often the key that leads to households’ participation decision. The hierarchical model of “institutional mechanisms” in such processes of establish cooperative organizations in China have been intensively studied. The usually practice is that the governments (usually both central and local governments involved) package their financial subsidies and other support as projects targeting different policy aims, and the villages conducting the aimed practice apply the projects (She and Chen 2011; Zhou 2005, 2012; Qu et al. 2009; Qu 2012; Chen 2013). Developing the irrigation systems is one of the governments’ projects. Through this project, the governments contract out their financial subsidies to villages or farmer organizations such as WUAs to develop their irrigation systems. The villages and WUAs usually need to compete for the subsidies. Here the leaders could play an important role in acquiring. The subsidies can help the participants lower the entry threshold and reduce related costs. During our surveys, we found all the successfully running WUAs received financial support from the government, and those with “abler” leaders tend to receive more subsidies.
Figure 1 presents the framework of how the cooperation in using irrigation, usually as a WUA, can be formed in a village.
Overall, a farmer household decides to participate the cooperation when the household first perceives it is feasible to cooperate and then its propensity to cooperate is high enough. The feasibility to cooperate that a household perceives is determined on the costs that it needs to bear in order to join the cooperation and its willingness to pay the costs. The costs of cooperation are essential the interest that participates need to give up for the collective aim (e.g. the sustainable use of the irrigation resource) and cost of coordinating all participants. They depend on the number of participants, because the more the participants, the higher the coordination cost, and there are more participants to share the cost. Meanwhile, government support can reduce the cooperation costs by providing the financial subsidy, entitling the legal status of the WUA as non-profit organizations and offering the management and income rights of irrigation facilities to the WUA. A household’s willingness to pay the cost is essentially determined by its dependence on the irrigation resource, represented by its distance to the resource, and its scale of production that relies on the resource. A household closer to the irrigation resource generally arranges its farming in a way more reliant on irrigation and thus has stronger intention to maintain the sustainability of the irrigation. The scale of production affects a household’s willingness because a small scale usually indicates that a household’s income is mainly from non-farming activities (e.g. working in the cities). In general, it becomes feasible for a household to cooperate once the result of cost-benefit analysis favors cooperation; that is, the cost of cooperation is not higher than its willingness to pay.
Given it is feasible for a household to cooperate, it is more likely to cooperate when its propensity is higher. A household’s propensity to cooperate is determined by its own and sometimes also the initiator’s personal characteristics, the neighborhood influence it receives, and its dependence on the irrigation resource. A farmer with higher preference of risk-taking (i.e. entrepreneurship), education and incomes is generally more likely to accept a new way of using the irrigation. Nontrivially, those have high degree of social relationship and high entrepreneurship in a village usually act as the role of “initiator” in the process of forming cooperation. They have stronger mobilization ability and can reduce the cost of enforcing a new rule through their charisma and social capital. Neighborhood effects come through several channels. First, the potential participants use the information of cooperation benefits from earlier participants to update their cooperation decision. If only a few agents are expected to get their payoff of cooperation (cooperate at a low level), most of the agents will not cooperate. But if the expected level of cooperation is relatively high, then more and more agents will cooperate (i.e. conditional cooperation and direct reciprocity). Second, households could face the pressure coming from two aspects: (1) Group identity. If many households have joint in the WUA, the non-participants might feel being isolated or raise the concern of being considered asocial. Such lack of group identity will make one to cooperate if he observes or expects his neighbors cooperate; (2) Collective decision. If a high proportion, e.g., as two-thirds, of the village have already cooperated, the collective decision could become a regulation that all villagers must obey. Meanwhile, the strong ego-involvement as a form of social norms will also nudge the cooperation among the individuals. Third, the initiator or earlier participant usually first choose to mobilize those people who are similar to them and trust them, i.e. agents carrying the trustworthy symbols.
Based on the above presented behavioral mechanism, we developed an agent-based model to simulate the formation of cooperation in the use of irrigation system in a village. Below we describe our model employing the ODD protocol. Using this model, we will test the following hypotheses:
Hypothesis 1
The velocity that households joint the cooperation is positively associated with the proportion of seed participants.
Hypothesis 2
Both the velocity that households joint the cooperation and the coverage of the cooperation are positively associated with the governmental subsidies.
The ODD protocol model description
Purpose
The purpose of the model is to understand how cooperation in managing an irrigation resource is formed among autonomous individuals, e.g., farmers in the same villages. The initial way of managing irrigation individually is not sustainable. To avoid “tragedy of the commons” (Hardin 1968), a small portion of individuals, e.g., those who have high concern about the sustainability, propose to manage the irrigation resource cooperatively. That is, for instance, all users limit the amount they use to a certain level. Equivalently, every individual needs to give up a certain amount of its well-being. In the model, this is represented by that an individual needs to pay a fee to join the cooperation.
Entities, state variables and scales
The model comprises four types of entities: social system, irrigation resource, user (also owners) of the irrigation resource and government.
Social system is the environment where agents’ (i.e., the users of the irrigation resource) collective actions of using an irrigation resource take place. Specifically, it is a village with farmer households collectively owning an irrigation resource. To represent the social relationships between farmers, the village is simulated as a social network, wherein nodes represent households and ties represent relationship ties between households. In this model, the social network is set either a random network or a scale-free network. Random network is generated according to Erdős–Rényi (ER) model; that is, each tie has a fixed probability of being present (Prob-ER), independently of the other ties. Scale-free network is generated according to Barabási–Albert (BA) model and using a preferential attachment mechanism. In the generation of scale-free network, the initial number of nodes is SF-initial and the probability of rewiring ties is SF-rewire.
Irrigation resource is a sum of the water and related irrigation infrastructure that households collectively own in a village. At the initial time, the irrigation resource is used in a way that all households take maximum amount of water they want. Realizing this is not sustainable, some households start to set a restriction on the amount they can take so that the use of the irrigation resource is sustainable for the village. That is, they adopt a new practice of cooperation in using the irrigation resource.
Users of the irrigation resource in a village are all the farmer households in this village. The households are connected with each other through social networks. Each household has three attributes: scale of production, entrepreneurship, dependence on the irrigation resource. Scale of production determines the amount of water that a household demands—the larger the scale, the higher the demand. It, along with the dependence on the irrigation resource, also determines the amount of the fee that a household is willing to pay in order to join the cooperation of using the irrigation resource sustainably. We assume that the distribution of scale of production among the households in a village follows normal distribution in the model. The coefficients of the normal distribution are calibrated according the features of amount of land that a household manages in the empirical data. Entrepreneurship is a synthesis of an individual’s personal characteristics such as risk preference, education, leadership ability that reflect the innovativeness of a household. We assume that the distribution of entrepreneurship among the households follows normal distribution in the model. The coefficients of the normal distribution are calibrated according the features of the schooling years of a household’s head in the empirical data. A household’s dependence of irrigation resource is represented as the distance to the irrigation source in the social system (the artificial world in the model). The closer a household is located to the resource, the higher its dependence on the resource.
A fewer farmers are also the members of local government. They are generally those with both high entrepreneurship and high high degree (number of ties with other households) in the social network. These farmers can help obtain support from the government. The participation of these farmers can lead to the increase of the subsidies that government provides.
Government in the model is the entity that can provide subsidies to the households that participate the cooperation and directly reduce the cost of coordinating the cooperation (i.e., coordination cost).
Process overview and scheduling
In the initial period, a small portion of households in the village are set to participate in the cooperation. These households are called seed participants. The value of the portion is denoted by seed_ration. The seed participants are either those who with highest dependence on the irrigation resource (i.e., closest to the resource), highest degree, or highest entrepreneurship.
In the iteration periods, each non-participating household first checks if the fee it needs to pay in order to join the cooperation, i.e., cooperation fee (denoted by coop_fee) is within the limit that it is willing to pay (denoted by pay_willingness). Cooperation fee is equal to the difference between coordination cost and government subsidy divided by the number of users that have participated in the cooperation, given by
$$coop\_fee = \frac{coor\_cost \cdot (1 - subsidy\_ratio) }{num\_part}$$
The coordination cost is represented as an exponential function of the number of participants, given by
$$coor\_cost = num\_part^{\gamma }$$
where γ is the coefficient of coordination cost (an exogenous variable). A household’s willingness to pay for cooperation is determined by its scale of production and dependence on the irrigation resource, given by
$$pay\_willingness = \beta \cdot \frac{scale}{dist}$$
where β is the coefficient of cooperation expenditure (an exogenous variable), scale is the scale of family assets, following the normal distribution randomly in the whole group.
Then, each non-participant who is willing to pay more than the cooperation fee will participate with the probability of its cooperation propensity (prob_coop). Cooperation propensity is determined by a household’s distance to the irrigation resource (dist), personal characteristics represented by entrepreneurship (entr), and importantly, the number of neighbors who have already participated, given by
$$prop\_part = \alpha \cdot entr \cdot \frac{part\_neib + 1}{dist}$$
where α is the exogenously given coefficient of cooperation propensity.
Figure 2 presents the behavioral flow of non-participants at each irritation period.
At the end of each iteration, the number of participant’s updates. Accordingly, coordination cost and cooperation fee are updated.
Design concepts
Emergence
Emergent effects that could be observed as outcomes of the model are households’ collective action of using their irrigation resource cooperatively. Opposite to using the irrigation resource individually, the collective action is an approach of sustainable use of the resource. The collective action is the outcome of households’ participation in the cooperative use of the irrigation resource. The collective action might not be achieved because too few households participate the cooperation.
Adaptation
In each iteration, each non-participating household updates their decision to participate the cooperation or not based on cooperation fee it needs to pay and the number of neighbors that have already participated.
Learning
There is no learning mechanism implemented in the model.
Objectives
Households and government do not have explicit objectives in the model. Households have an implicit objective of maximizing their benefits of using the irrigation resource. This is implemented through deciding whether to participate the cooperation or not.
Prediction
Households in the model do not predict.
Sensing
Households are aware of which households have participated in the cooperation in their village.
Interaction
Households updates their propensity to participate the cooperation according to the number of their neighbors that have already participated.
Stochasticity
Households are distributed in the villages and their locations (x and y coordination in the artificial world) are set following normal distribution. Their distances to the irrigation resource and thus dependence on the resource are also random. In addition, households’ other characteristics, scale of production and entrepreneurship, are assigned following the normal distribution.
Collectives
All households in the model belong to a village and on the social network of the villages. No other kinds of collective emerge in the simulation.
Observation
The model provides an observation of the diffusion of cooperation in using common resource. A curve displaying how the number of participating households change over time can be produced. In the case that the cooperation fails to diffuse, no participating household will be observed.
Initialization
The environment of the model is initialized by creating a network that consists of households and ties between the households, the characteristics of the households, and an irrigation resource in the network. The network is either a random network or a scale-free network. The characteristics of the households are scale of production, distance to the irrigation resource, and entrepreneurship. The initial state of the model world is set by the following variables.
The parameters in the simulation model are calibrated using the survey data as well as referring to existing studies. The principle is to set the mean according to the empirical data and give some flexibility (Table 1).
Input
This model does not use input from external sources.
Sub-models
This model does not include sub-models.
The model is implemented in NetLogo and is publicly available at https://www.openabm.org/model/4975/version/1. We run each parameter combination 100 times. There are 38,400 combinations in total, and the model runs each of these combinations 100 times. Finally, 3,840,000 sets of simulation results were generated.