Authors:
Arun Agrawal*, Daniel G. Brown*, Gautam Rao*, Rick Riolo†, Derek Robinson*, Michael Bommarito†
*School of Natural Resources and Environment, University of Michigan, 440 Church Street, Ann Arbor, MI 48109-1041; and
†Center for the Study of Complex Systems, University of Michigan, 321A West Hall, 1085 S. University Ave., Ann Arbor, MI 48109-1107
Edited by:
Much of the research on common property has focused on how different kinds of institutions shape the incentives of users who rely on a common-pool resource system for their daily needs. Writings on the commons have greatly advanced knowledge about how institutions can be designed to improve sustainable resource governance. A significant puzzle that has occupied this scholarship is the nature of the differences between formally designed and introduced institutions vs. self-organized informal network norms, and how such differences affect resource governance outcomes. This paper analyzes the different effects of formal institutions and informal norms in an agent-based model of fvillagers who choose levels of forest consumption based on the information they derive from social interactions with their neighbors (an informal network with two-way flows of information) and an externally imposed institution that announces prescribed limits on forest product extraction. The paper investigates how changes in the relative dependence of users on information from formal institutions versus informal networks affect user behavior, harvesting levels, and forest-related outcomes. agent-based modeling | common pool resource | fuelwood extraction | institutional governance | norms | social networks
ToDo
Institutions of different kinds play a particularly important role in influencing local resource use and outcomes for renewable resources such as forests, pastures, irrigation and drinking water and coastal fisheries (Baland and Platteau 1996, Dietz et al. 2003, Ostrom 1990). The literature on common-pool resources – one of the more successful research programs in the social and ecological sciences -- has focused on understanding how institutions can be designed to improve sustainable resource governance, the relationship of resource users to each other, and institutional processes themselves (Berkes 1989, Chhatre and Agrawal 2008, Wade 1989). This literature rarely examines interactions between two major types of institutions: formal governance arrangements that often have a material manifestation in the form of written rules, organizational form, and hierarchical relationships among employees, versus less formal social networks that link different resource users through relations of information exchange and social interactions. The importance of such social networks has been broadly recognized in the work on development and natural resource governance (Lal 1999, North 1990, Putnam 1993, Pretty 2003), particularly through writings that examine the role of social capital as social ties and networks. The influence of social capital and institutions on resource outcomes has been studied separately; sometimes formal institutions have been viewed as a form of social capital. Yet, it is clear that social capital (in the form of networks) and formal organizations are different types of institutions, typically coexisting in a given context, and we need to understand the how they influence each other as well as resource outcomes jointly (cf. Leach et al. 1999, Lewins 2007).
In a given resource governance context, the signals and sanctions provided by formal institutions interact with existing social networks and norms, in combination with a range of socioeconomic, demographic, and biophysical factors, yield diverse resource outcomes (Dietz et al. 2003,
Agrawal et al. 2008). Institutional interactions, as influenced by variations in signaling, enforcement mechanisms, network structures, and user preferences provoke an important question for theories and practices of natural resource governance: How are user behaviors and resource outcomes affected by governance rules imposed by formal resource governance institutions and network norms as generated through informal social interactions?
This paper focuses on the relationships between institutions and social networks related to resource use and management. It does so by modeling the actions of individual agents who make resource-use choices. In our model, their choices depend on the information they receive from institutions and social networks, the weight they place on self-interested consumption versus adherence to institutional rules for promoting sustainability, and norms that contribute to improvements in collectively owned common-pool resources.
Household agents both ascertain and create community norms by interacting with other agents in their social network (Bettenhausen and
Murnighan 1985, Ullmann-Margalit 1977). In the context of community use of common-pool resources -- e.g., consumption of firewood from collectively used forests -- norms can be seen as informally recognized expected consumption behavior. The level of such consumption can be influenced by individuals attempting to match the behaviors of others with whom they interact, i.e., network norms in part shape individual behavior. A large literature examines the different underlying bases of such structuring: individuals’ desires to avoid informal network sanctions, seeking of conforming behavior by network members, positive preferences for contributing to group well-being, acquisition of adaptive behaviors, and the like (Axelrod 1986, Henrich and Boyd 1998, Bowles 2008, Schultz etal 2007).
Figure 1 indicates that the flow of information occurs through different pathways for institutions versus social networks. Formal institutions monitor the state of the resource and results of prior aggregate behavior for the entire community, and make decisions related to levels of resource extraction based on those outcomes. These decisions are made more infrequently than the resource-use decisions of the agents influenced by institutional decisions. These differences in time-scale have been shown to produce lags in the system that create large-scale inefficiencies <citation> and increase the risk of individuals’ collectively exhausting common pool resources (Hardin 1968). In contrast to aggregate level assessments by formal institutions, information flow through informal social networks is generally more localized, utilizing higher frequency individual interactions that consist of observations of behaviors and actions carried out by socially and spatially nearby constituents <citations>.
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The relationships shown in Figure 1 suggest that as institutions shape outcomes by structuring formal rules, the prescriptions those rules dictate may come into conflict with informal community norms that affect behavior. Faced with the choice of adhering to either rules or to norms, individuals choose among various combinations of the two by selecting a combination that yields high individual “utility,” given their desires for higher incomes or consumption, leisure, lower risks of sanctions imposed by formal institutions or informal social networks, as well as their desire to contribute to sustainable performance of the community’s shared resources. Thus effective formal institutions achieve desirable outcomes by recognizing the existing preferences and social networks in a community, and then using available policy mechanisms (e.g., prescriptive rules) to shape incentives for a sufficient number of individuals and households, such that desired aggregate behavior—sustainable resource use--- is achieved and norms are shifted towards behaviors that also contribute to those outcomes.
This paper describes an agent-based model (ABM) designed to explore how different individual preferences, social networks and the community norms that result alter the effectiveness of rules implemented by formal institutions as a means to promote sustainable use of a forest resource near a small village. The ABM represents villagers’ choices of forest-resource consumption, made on the basis of information derived from (a)
rules enforced by a formal institution to limit fuel-wood extraction and (b) norms of resource use that emerge through social interactions among networks of neighbors. Because forests in rural areas are one of the most frequent types of common pool resource and provide livelihood benefits to hundreds of millions of rural residents, we use the hypothetical example of a communally used forest to motivate the model. However, the choice of forests is not critical to our results.
Fig. 1. Conceptual model of the flow of information between institutions, individual agents, and social networks.
Model Description Our model is composed of three components: two types of agents that represent the key actors (households and formal institutions) and the resource being utilized (the forest). We model agent behaviors and resource changes over time using discrete monthly time steps. Our focus is on the decisions households make: in particular, at each step, households must decide how much resource to extract. The resource being extracted is fuel-wood, which is obtained from local forests and constitutes the primary energy used for cooking in India (ABE 1985,
Misra et al. 1988, Bhatt and Sachan 2004). Our ABM represents a hypothetical place, but uses several parameter values derived from data and literature on Himachal Pradesh in India (see supplemental text).
Household Agent Decisions. Household agent decision making is represented using an approach framed as bounded rationality (Simon
<citation>). The household agent 1 decides how much wood to extract from the forest at each time step. A household’s preferences over how much to extract, x, are represented by this utility function
U(x) = C(x)

C * L(x)

L * A(x)

A (1) where C(x) is utility from consumption of the extracted fuel-wood, L(x) is the utility from “leisure” (i.e., from time not spent gathering fuel-wood) and A(x) is utility from adhering to institutional rules or community norms regarding fuel-wood extraction (which affect the sustainability of the common forest shared by the community). The  ’s (each in [0, 1] and summing to 1) represent the household’s relative preferences for the three components, and thus can vary across households. Details on the form of C, L, A, and the parameter values we used are given in the supplemental text. In short: utility from consuming firewood, C(x), increases with x, but with diminishing returns as x approaches a value that depends on household size 2 . L(x) varies inversely with x, since more time gathering amount x means less time for other things; L(x) also depends on the state of the forest – less wood in the forest means more time required to collect fuel-wood (see supplementary material). A(x) is a weighted function of two factors that represent the relative importance the agent places on adhering to institutional rules or community norms:
A(x) = r * R(x) + (1-r)* N(x), 0 <= r <= 1 (2)
R(x) js 0 at or above the level of consumption prescribed for that household by the formal institution’s rules (designed to maintain a sustainable forest), and R(x) increases to the extent the household’s extraction level x is less than that level. N(x) is maximal (1) when the household’s extraction level x matches the level of extraction suggested by community norms, as indicated by the average extraction level of the household’s neighbors (spatial or social—see below) during the previous time step; N(x) decreases as x deviates from that norm The weighting factor r, which can vary across households, determines the degree to which a particular household places more importance on adhering to institutional rules
(larger r) or on community norms (smaller r).
To determine how much to extract in a given time step, a household agent selects 10 candidate levels of extraction and chooses the level x* that maximizes the household’s utility, calculated as described above. The candidate levels are drawn from a normal distribution centered on the
1 We assume the household acts as a single entity.
2 The utility a household derives from consumption is a decreasing returns function of the amount extracted and on the size of the household, which determines the level required for subsistence, as described in the supplemental materials. Note that markets for fuel-wood are essentially non-existent in the locations we studied (Heltberg et al. 2002).
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extraction level the household chose the prior time step 3 . The household then extracts the amount x* from the forest, reducing the amount of resource remaining.
Norms, Household Interactions, and Social Networks. Household agents assess (and create) community norms by interacting with agents in their social networks. In rural India, a household’s social network primarily reflects interactions with spatially proximate households. In our model households are embedded in a 2D grid, one household per cell, such that a household’s social network includes its Moore-neighbor households 4 .
Households also may interact with more distant households, as a result of various social relationships (e.g., family ties, friendships, etc.). In order to study the effects of different social network structures resulting from varying combinations of adjacent and distant “neighbors,” our model includes a parameter, p, which controls the fraction of non-adjacent neighbors in each household’s social interaction network. In particular, after a household h is placed in the 2D grid and its social network is set to be the list of its Moore neighbors, each neighbor i on that list has probability p of being replaced on the list with a household j randomly selected from the community at large (other than the agent itself), so that h and i are no longer in each other’s social network, but h and j are<footnote>. Once created, the social networks remain fixed for the model run.
In our model each household agent uses its social network to assess the community norm regarding extraction levels. In particular, each step the agent computes the average extraction level (from the previous step) of the other agents in its network. That average is taken as the extraction level the agent prefers to match when calculating utility N(x) as described for equation 2, above. Thus the dissemination of information among household agents provides an indication to each agent of how much resource other agents are using, information that is then factored into their own decision making (in Equations 1 and 2).
Note that when p is 0 the interaction network of each agent is its adjacent neighbors, so that clustering is high (many of h’s neighbors are neighbors of each other) and the average path length (following the agents’ links to their neighbors) through the community is long. At the other extreme, when p is 1, each agent has a social network based on neighbors drawn randomly from the community, so that there are very few or no clusters but path lengths between any two agents are also short. And at moderately low p values, the social network has “small world” properties
(Watts and Strogatz, 1998), i.e., there are clusters but the average path lengths are short. Thus varying p alters the overall interaction patterns and the flow of information about resource use in a community, which in turn can affect the dynamics of norm formation and stability. By varying p across experiments, we can explore how these social network structures and the dynamics they induce in the spread and stability of norms can alter the effectiveness of institutional rules designed to alter agent behavior.
The Formal Institution Agent. The formal institution agent represents a branch of the Indian government that manages the forest resources and aims to maintain both the ecological quality of the forest and its ability to function as a common-pool resource for fuel-wood harvest. The formal institution agent determines the sustainable per capita harvest for a given time-period by dividing the net growth of the forest by the population size and weighting it for each household based on its size and estimated fuel-wood requirements. It then informs each household of its allowable
(sustainable) extraction level for that time step, which the household uses to calculate utilities for the extraction levels it is considering, as described above.
Thus household agents also interact with the formal institutional agent, but unlike the bi-directional inter-household interactions, this interaction is unidirectional in that the institutional agent sends each household a signal indicating the prescribed level of resource extraction that is deemed sustainable, based on the institution’s assessment of the state of the forest. In contrast, the inter-household interactions are bi-directional, and the signals sent reflect the level of resource extracted by the interacting households.
Forest Resource. The forest resource is assumed to be a closed-canopy maturing mixed pine and oak forest. The model represents the resource aspatially, as a total amount of biomass for the entire forest, which grows at a specified rate per year. We introduce some variability around the mean growth rate of 2.7% per year (0.01% per month) to incorporate stochastic climatic conditions. Household agents use forest fodder and lop off branches for fuel-wood. In a given time step, they can extract fuel-wood until a specified minimal amount of forest biomass remains. Observations of above-ground biomass and carbon allocated to individual tree components (e.g. stem, bark, branches, and foliage) vary widely. Jenkins et al.
(2003) demonstrated that a range of 7-30% of biomass for softwood species and 15-95% for hardwood species is allocated to branches, which is the biomass of use to villagers for fuel-wood. For our model, we divided the above-ground biomass and carbon values in half to estimate the amount found in branches.
The fraction of the initial forest resource remaining after some period of resource extraction is the primary outcome of interest in our analyses.
We use this value as an indicator of the sustainability of extraction levels generated by various household preferences and network structures, and of the influences of rules, norms, and their interactions on resource sustainability.
Computational Experiments
We conducted four sets of computational experiments. The experiments allow comparisons among model runs with alternative parameter settings. The experiments were designed to explore how (a) the relative weight agents place on adhering to rules and norms, (b) the proportion of the population with a high preference for consumption, (c) social network structure and (d) the proportion of the population with a high preference for adherence to rules, all affected resource outcomes. The model was run thirty times for each combination of parameter values, and the average and variance of resource remaining were computed. This metric best captures our concern with the sustainability of resource extraction.
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3 In other experiments, the candidate extraction levels were chosen from a uniform distribution over the allowed range for x; results were qualitatively similar and therefore not reported.
4
Since the agents are in a bounded 2D grid, agents have 8, 5 or 3 adjacent neighbors.
5 Other metrics such as the distribution of agent consumption levels, and XXXX were also examined, and were found to correlate strongly with the amount of forest remaining at the end of the simulation.
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Each model run was composed of 625 household agents and was run for 600 time steps (i.e. 50 years). Initialization of a model run involved creating and placing household agents on a grid (25 x 25), with one household agent per cell. Households varied in size, with an average size of
4.75 based on rural household survey data (Misra et al. 1988). After all households were created, they established a social network that remained stable for the entire model run.
In each time step, resource grows and the formal institution tells each household a prescribed sustainable extraction level. Each household uses the social capital ties in its network to determine the current norm for extraction, combining that information with the prescribed level from the institution to calculate utilities for candidate levels of extraction as described earlier. Each household selects the candidate extraction level with maximum utility and extracts that amount from the forest (or as much as is remaining above the minimum forest resource level). The forest remaining and other measures are recorded after all households have had a chance to extract resource. The formal institution re-calculates sustainable extraction levels every 12 steps (once a year). Agents are activated asynchronously, in a different random order each step.
Experiment 1: Weight on rules versus norms. In this experiment we tested the effects of altering the weight agents place on adherence to rules over norms. We performed this experiment to test whether the amount of forest remaining would increase as the population placed greater emphasis on adhering to rules set by the formal institution. Increasing the importance of rules in our model can be interpreted as an increasingly good reputation of the formal institution among the population of agents, or increasingly strict enforcement or sanctions that make rule noncompliance more costly to the agents. We set up a series of cases where the weight the on rules (r in Equation 2) of all agents was varied from 0.0
(no attention to rules, complete attention to norms) to 1.0 (complete attention to rules, no attention to norms). For this experiment, agents were each given preference weights of  C =  L =  A = 0.33 (Equation 1) and social networks composed of their spatially adjacent neighbors (p=0).
Experiment 2: Agents with high preference for consumption. In the second experiment, we evaluated how households with a higher preference for consumption altered how varying the weight, r, on adhering to institutional rules versus social norms, affected resource outcomes. Households were divided into two groups: (1) households with equal preferences for consumption, leisure and adherence (equal  values) as in Experiment 1, and (2) a group of “high consumer” 6 agents that had a weight on consumption that was twice that placed on leisure and adherence to rules or norms (  C = 0.5;  L =  A = 0.25). We varied the proportion of the population composed of high consumers from 0% to 100%, for each of the values of r used in Experiment 1. The landscape was divided into two sections with one sub-population on each side of a single shared boundary.
Experiment 3: Network Structure. In the Experiments 1 and 2, interaction among agents was constrained to the spatially adjacent neighbors of each household (p=0). For this experiment, we replaced social interaction network connections to adjacent households with connections that extended beyond immediate neighbors as described earlier. The objective was to examine how different social network structures affected the dissemination of information and the formation of norms that, along with institutional rules, influence aggregate fuelwood extraction behavior. We implemented this experiment by varying the parameter p from 0 (only adjacent neighbors) to 1 (only randomly selected neighbors).
Experiment 4: Agents with high weight on rules. In Experiments 1,2 and 3 all households within a model run were given the same value for r, the weight placed on adhering to institutional rules (versus the weight on norms, 1-r). To evaluate the degree to which a small number of agents with a high r might be able to influence norms sufficiently to yield desirable resource outcomes, we created two groups with different levels of r: (1) ‘rule adherents’ weight rules much higher than norms (r=0.9); and (2) ‘norm adherents’ have the opposite weights (r=0.1). In this experiment, we varied the relative proportion of rule adherents (0% to 100%) and the network structure parameter (p, from 0 to 1). Like Experiment 1, household agents’ preference weights were  C =  L =  A = 0.33.
Results
Experiment 1: Weight on rules versus norms. Altering the level of rule adherence (r) among agents in the different model runs resulted in a nonlinear response of the amount of forest remaining (the 0% line in Fig. 2). At very low values of r much of the forest was consumed. However, at low to medium levels (i.e. 0.2 to 0.4) households dramatically altered their extraction behavior, which led to much higher levels of forest resources remaining.
Experiment 2: Agents with high preferences for consumption. When we repeated Experiment 1 but with a population of agents that had a greater preference for consumption (the 100% line in Fig. 2), we found that it took a much higher weight on rule adherence over norms (r) to achieve nearly the same level of remaining forest. In addition, with high level consumers the nonlinear response to r was damped both in the rate at which it altered agent behavior and the amount of forest remaining. Including a mix of agents from the two subpopulations (i.e. agents with high versus moderate preference for consumption) produced similar, intermediate responses of forest remaining to varying levels of r (Fig. 2). For all proportions of agents preferring higher levels of consumption, low values of r resulted in the lowest levels of forest remaining. Increasing the proportion of high consumer agents decreased the amount of forest remaining and flattened the non-linear response to r. As the proportion of agents with higher weight on consumption increased, agents must have more weight on rules (higher r) before improvements in forest resources were realized.
6 Note that agents with a high preference for consumption, i.e., agents with a high

C relative to the other
 ’s, will not necessarily be high consumers---what they actually consume depends on other factors such as resource availability and current norms. However, other things being equal, agents with higher

C values will consume more than agents with lower

C values, so for brevity we will refer to them as “high consumer” agents.
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1.2
1.0
0.8
0.6
0.4
% High Preference for Consumption
100%
75%
50%
25%
0%
0.2
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Weight on Rules (r)
0.7
0.8
0.9
1.0
Fig. 2.
Results from Experiments 1 and 2 show the effect on forest remaining of changing the weight placed on rules and the relative number of agents with a high preference for consumption. Error bars represent 95% C.I.
Experiment 3: Network Structure. Figure 3a shows the amount of forest remaining as the relative number of high-consumer agents is increased, for different social structures (p) and r = 0.3, For p >= 0.05, i.e., for social networks with even a few long range ties, forest consumption is reduced
(relative to p=0, no long-range mixing) for populations with intermediate (25% to 75%) proportions of high consumers. This suggests that even a small level of social mixing reduces the proportion of agents preferring high consumption required to create a high-consumption norm. On the other hand, Figure 3b shows the effects of social mixing when the agents place higher weight on following institutional rules (r=0.5). In this case, for p >= 0.05 forest consumption is increased (relative to p=0, no mixing) for populations with intermediate (25% to 75%) proportions of high consumers. This suggests that for agents that place more weight on adhering to formal institutional prescriptions, even a small amount of social mixing increases the proportion of high-consumer agents required to establish higher-consumption norms. Note that when the proportion of agents with high preference for consumption was very low (0%) or high (100%), the network structure had no effect on forest remaining. Similarly, when values of r were less than or equal to 0.2 or greater than 0.5 (not shown), the network structure had little effect. In these cases the effect of increased propagation of information (norms of behavior) through a social network with long-range ties was overwhelmed by extremes in preferences (for rule adherence or consumption).
Experiment 4: Agents with high weight on rules. When we increased the proportion of rule adherents (high r in the population) the model produced a near-linear increase in forest remaining outcomes when agents social networks consisted only of adjacent households (Figure 4, p = 0).
As we altered the network parameter p from a highly clustered network (p = 0) to a randomly connected network (p = 1), the amount of forest remaining increased, for all proportions of rule adherents less than 100%. At moderate levels of social mixing (p = 0.25), strong non-linearity in relative outcomes of forest remaining were evident. In particular, small numbers of rule adherents made large differences when household networks had a small number of distant non-adjacent connections. The effect of additional rule adherents tapered off strikingly beyond 20%. These results were achieved despite rule adherents not having a special place in the network (such as a higher degree of connections). This is consistent with the explanation for the effect of social mixing advanced above, i.e., a small number of long range connections enables information to propagate rapidly across a population.
100%
P - value
0.00
80%
0.05
60%
0.10
1.00
40%
20%
0%
0.00
0.25
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0.75
% High Preference for Consumption
1.00
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Fig. 3.
The effect on forest remaining by network structure (p), weight placed on rules (r
1
= r
2
= 0.3) and the relative number of agents with high preference for consumption. Error bars represent 95% confidence intervals.
1.2
1
0.8
0.6
0.4
0.2
P=1.00
P=0.50
P=0.25
P=0.15
P=0.10
P=0.05
P=0.00
0
0% 20% 40% 60% 80% 100%
% Rule Adherents
Fig. 4.
Results from Experiment 4 illustrate the effect on forest remaining of relative number of rule adherents and network structure. Error bars represent 95% C.I.
Discussion
Formal resource-management institutions have a number of mechanisms at their disposal through which they affect collective resource use patterns, resource outcomes, and thereby, sustainability. These include communication of rules and their rationales and rule enforcement, sanctions, and adjudication. Because these management activities are carried out in the context of social interactions through information networks that generate norms for behavior, understanding the effects on resource outcomes of the choices a formal institution makes can be challenging. Although we cannot make claims about the magnitude of these effects in specific cases, our model reveals, qualitatively, the effects of household preferences, social interactions, and network norms on the effectiveness of an institution’s activities.
The results of Experiment 1 suggest that when households in a community have homogenous preferences for adhering to the rules of a formal institution that aims to maintain sustainable harvesting levels, the level of resource use decreases and remaining resource amount increases nonlinearly with greater weight on the preference to adhere to institutional rules. This non-linearity is governed by the process of norm formation in the community. We modeled norm formation through households seeking to match the level of extraction of their neighbors. Low levels of preference for adhering to rules in our model can be interpreted as representing low levels of (a) trust in the institution, (b) confidence in communications from the institution, (c) enforcement of institutional rules, or (d) sanctions for rule violations. In such cases, household decision making is influenced more by the behavior of neighbors and the utility households derive by balancing consumption and leisure.
Small increases in preference for rule adherence reduces consumption only by small amounts until a tipping point is reached such that the norms of the network are influenced by the rules used by the institution. One preliminary implication of this result is that common-pool resourcemanagement institutions should seek levels of investment in communication, enforcement, sanctions, and/or adjudication that are sufficient to influence the norms of a community and tip the behavior toward those desired by the institution. The good news is that once there is sufficient interest in rule adherence to affect the process of norm formation, little additional effort may be required to achieve levels of resource use consistent with institutional goals. A possible confounding factor is the degree to which agents preferences change in response to actions by formal institutions. For example, the imposition of institutional rules and associated sanctions to promote behavior in the group interest (i.e., reduce extraction levels to a sustainable level) may have the side-effect of “re-framing” how the agents see their preferences, such that they increase the weight they put on self-interest (Bowles 2008, Cardenas et al. 2000).
Our initial experiment was predicated on two key assumptions. The first was a homogeneous population, in terms of the importance households place on various contributors to their utility (i.e., consumption, leisure, and adherence to rules or norms) and the relative importance of adherence to norms versus rules. The second assumption was that there were no long-range ties within the agents’ social networks. In Experiment 2, we relaxed the first assumption to form two groups. The first group had equally balanced preferences for consumption, leisure, and adherence to sustainability rules and the second group had a greater preference for consumption. We find that as the number of agents with high consumption preferences increases, the effectiveness of institutional rules decreased in a linear fashion (i.e., relatively even spacing between lines in Figure 2).
The decreased effectiveness was evidenced by a decline in the amount of resources remaining, regardless of the level of preference for following rules versus norms. Additionally, increasing preference for following rules (r) versus norms produced a tipping point, where norms shifted towards more sustainable behavior, and more forest remaining (Fig. 2). These results suggest that an understanding of the diversity and types of preferences in a community is necessary for institutions to identify an effort level that is likely to be successful.
The results of Experiment 3, which evaluated the importance of long-range ties in the social network that influences the formation of social norms, indicate that, at moderate levels of rule adherence (0.3<= r <= 0.5), the presence of long-range ties results in a non-linear relationship between the number of households preferring consumption and forest condition. At these moderate levels of preferences for adhering to rules, a reasonably small number of households with greater preference for consumption can produce a relatively large decline (for r=0.3 or 0.4) or increase (for r=0.5) in the forest outcome, as these preferences have a greater influence on norms throughout the community because the social networks result in short path lengths between all agents. This effect of network structure enhances the sensitivity of the response of resource
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outcomes to rule adherence at just the levels of rule adherence of most interest to the institution, i.e., in the range of effort levels near the tipping point from little to great influence on outcome.
The results of Experiment 2 indicate that a small group of households with a preference for consumption can reduce the effectiveness of efforts by an institution to reduce resource consumption, through the influence on norms. The results of experiment 4 show how a small group of households with a strong interest in adhering to the rules of the institution, over norms, can have a strong positive influence on the community’s tendency to behave in ways consistent with those rules. The results of Experiment 4 indicate that (a) as the number of such rule adherents increases, the amount of resource remaining also increases and (b) as the social network includes more long-range ties, a smaller number of rule adherents are needed to reduce extraction levels and achieve a high-level of resource remaining. Although a formal institution may have little influence on the structure of the social network itself, these results suggest that resource-management institutions may be able to use the process of norm formation to enhance the effectiveness of rules. The most obvious way to do so would be to focus on rule adherence by a fraction of the community rather than all community members. Such commitments might be secured through greater participation in the institution within the community. In any case, these results suggest that knowing the structure of the social networks in a community is crucial to design effective resource governance institutions, and in consequence, for sustainable resource management.
In contrast to many studies of institutions and resource management that focus on specific institutional forms, this paper initiates an analysis of interactions between two major institutional forms that affect communal resource governance -- social networks and formal institutions. The paper finds considerable evidence for important interaction effects between informal social networks and formal institutions. The nature of these effects depends on the strength of agent preferences to sustain resources, network structure, and the length over which agents can form ties with each other. As the length of social ties among agents increase, there is stronger evidence for non-linear effects and tipping points with small changes in the proportion of agents who have strong preferences for high levels of consumption or conversely agents who have a strong preference for following institutional rules.
Materials and Methods
We developed theagent-based model (ABM) using the RepastJ 3.1libraries (http://repast.sourceforge.net). A gent-based modeling (ABM) is an approach to representing the properties, behaviors, decision-making strategies, and actions of interacting components in a dynamic system that is composed of actors and their environment. ABMs can be run to evaluate the aggregate system-level implications of individual behaviors, and the diversity and interactions thereof. Because ABMs derive system-level outcomes from component interactions, the approach can represent and model non-linear dynamics, positive and negative feedbacks, heterogeneity, learning and evolutionary decision-making strategies (i.e. adaptation), and a range of other analytically intractable processes (Holland 1995, PNAS-99 2002). Furthermore, the ABM approach can be used as a framework to integrate various sources of data, theories, and conceptual models (Janssen and Ostrom 2006; Robinson et al. 2007) and has replicated experimental commons dilemma results (Deadman et al. 2000). The supplemental text describes our ABM in detail.
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Supporting Information
Household Agent Utility
In our model, household utility is a function of its desire for three goods (consumption, leisure, and adherence to institutional pressures) and a resource extraction level. The extraction level chosen by the household is the level of resource depletion carried out by the household. Each time step, a household agent randomly selects 10 different levels of resource extraction and chooses the extraction level that maximizes the following utility function:
U(x) = C(x)
αC ·L(x) αL ·A(x) αA
[1] where U(x) is the utility for the household at a given extraction level x, C(x) is the utility derived from consumption, L(x) is the utility derived from leisure, A(x) is the utility derived by adhering to institutional pressures, and αC, αL , αA , are the weights that represent preferences for consumption, leisure, and institutional adherence, respectively. The three preference weights sum to one and ensure trade-offs among consumption, leisure, and adhering to institutional pressures.
C(
χ
) – Consumption
The consumption component of a household’s utility is a function of subsistence cooking requirements (s), fuelwood extraction (x), and the rate at which marginal utility decreases once subsistence has been met (ƒ in
[2]).
C(x) = s + ƒ · ( x – s ) , x ≥ s [2]
C(x) = x , x < s [3]
The utility derived by consumption for different preference weights applied to the consumption component are shown in Figure S1.
Figure S1: Consumption curves for different consumption preference weights (
αC
) and extraction levels, x.
The subsistence cooking requirements (s) for each household is calculated as a function of household size and per capita energy requirements: s = ( h s
· w ) / ( e · d ) [4]
9

where s is the subsistence wood requirement (m
3
), h s
is the size of household (i.e. number of occupants), w is the per capita energy requirement for cooking per month (240 MJ), e is the energy content of wood (16 MJ,
World Bank 2004), and d is the average density of oak and pine (600 kg·m -3 ).
L( x ) – Leisure
Markets for fuelwood are largely non-existent in the locations studied. The primary expense incurred by household agents’ fuelwood extraction is time - invariably, the cost of time in leisure (or other activities) forsaken to extract forest resources. The leisure component is calculated based on the gathering time required for fuelwood collection, the amount of labor available for fuelwood collection. The function takes the following form:
L(x) = 1 – T / h l
, T ≤ h l
[5] where T is the time spent gathering fuelwood per month (as calculated in the section titled fuelwood collection, below) and h l
is the total household labor endowment. We set h l
at 5hrs per day as a representative value of the total number of fuelwood collection labor hours provided by the female household head and young children. A maximal valueof 1 for L(x) represents all household time spent in leisure; L(x) declines as shown in Figure S2 below, demonstrating the reduction in utility obtained by the leisure component (equation 5) of equation [1] for different levels of household fuelwood extraction when forest resources and preference for leisure (αL = 0.33) are fixed.
Figure S2. NEED A CAPTION HERE
A( x ) – Adherence to Institutional Pressures
The last factor in the household agent’s utility function, A(x), represents the utility derived by adhering to institutional pressures. A(x) is a weighted function of two factors that represent the relative importance the agent places on adhering to institutional rules or community norms:
A(x) = r · R(x) + (1 – r) · N(x), 0 <= r <= 1 [6]
10

R(x) increases to the extent the household’s extraction level x is less than the amount prescribed for that household by the formal institution’s rules (designed to maintain a sustainable forest):
INSERT R(x) equation here
N(x) increases to the extent the household’s extraction level x matches the level of extraction suggested by community norms, x*:
INSERT equation for N(x) here where x* is the average extraction level of the household’s neighbors during the previous time step. The weighting factor r, which can vary across households, determines the degree to which a particular household places more importance on adhering to institution al rules (larger r) or on community norms (smaller r). Both the institutional rule and social norm values are added together and weighted by the household’s preference for adhering to institutional preferences (αA) versus its preferences for consumption (αC) and leisure (αL).
Fuelwood collection
Fuelwood and community forests are perceived as a free common pool resource for use by local households.
Therefore, markets for fuelwood are non-existent in the study region and instead the cost of fuelwood is a function of collection or gathering time, which is typical for fuelwood and minor forest products in rural areas in India (Heltberg et al. 2000). However, as households extract fuelwood resources they degrade the forest from the edge inward and are forced to spend more effort and time in subsequent fuelwood collections (Kumar and
Hotchkiss 1988; Baland et al. 2004). We use a simplified approach to model time spent collecting fuelwood and assume that when fuelwood is abundant, a minimum of 2 hrs is required to make a single fuelwood gathering trip. However, gathering time increases exponentially as the resource is depleted (Fig. S2). The rate of increase in gathering time is a function of the initial and remaining size of the forest, proportion of the forest in branches, the population of the village, and average biomass per square meter. The average head-load carried by an adult individual in a single trip approximates 30 kg (Bembridge and Tarlton 1990, Irfanullah 2002, Adhikari et al.
2004). Since households must make several trips to satisfy their subsistence cooking requirements, we calculate the overall time allocated to fuelwood collection per month using the following equation:
T = min (χ · c max
· d/p · t , h l
) [8] where T is the gathering time per month, χ is the extraction level of the household, c max
is the maximum consumption level of the household (which is 3·s in equation 4), p is the average head load per trip, d is the average density of oak and pine (600 kg·m -3 ), t is the gathering time for a single trip (a function of forest remaining, as shown below in Figure S3 and equation [9]), and h l
is the total available labor for fuelwood collection or leisure (and other activities) to each household.
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Figure S3: Time spent for a single trip gathering fuelwood based on the available resource level.
INSERT EQUATION [9] FOR S3 SOMEWHERE AROUND HERE.
References
Adhikari, B., Falco, S. D. Falco & J. C. Lovett (2004). Ecological Economics 48 (2): 245-257.
Baland, J. M., Bardhan, P., Das, S., Mookherjee, D. & R. Sarkar (2004). "The Environmental Impact of
Poverty: Evidence from Firewood Collection in Rural Nepal,’." Commons in an Age of Global Transition:
Challenges, Risks, and Opportunities. The Tenth Conference of the International Association for the Study of
Common Property, August: 9-13.
Bembridge, T. J. & J. E. Tarlton (1990). South African Forestry Journal 154 : 88-93.
Heltberg, R., Arndt, T. C. & N. U. Sekhar. (2000). Land Economics 76(2): 213-232.
Irfanullah, S. (2002). Nomadic Peoples 6 (2): 99-110.
Kumar, S. K. & D. Hotchkiss (1988). Consequences of Deforestation for Women's Time Allocation,
Agricultural Production, and Nutrition in Hill Areas of Nepal, Int Food Policy Res Inst.
12