Characterizing Heterogeneous Behavior of Non-Point-Source Polluters in a Spatial Game under Alternate Sensing and Incentive Designs

Non-point-source water pollution is characterized by individual agents whose behavior impacts downstream water quality conditions, but the pollution contribution of any one agent cannot be accurately determined. The design of the experiment is motivated by a situation where a regulator seeks to reduce damages caused by water pollution generated by a group of producers situated along a river reach, where the pollution contribution of each individual producer cannot be detected. This section presents important highlights of the basic design and the experimental treatments that define the implemented experimental game. The Supplemental Material presents the complete technical details of the game design (also discussed by Miao et al. 2016). The theoretical decision framework that underlies the experiment is based on Segerson (1988)’s non-point-source pollution model, and the basic payoff functions and parameters are similar to those of Spraggon (2002). Spatial differences and a nutrient transport model (QUAL2K) are incorporated into the experiment to simulate the physical environment (Chapra et al. 2008) (also discussed in Supplemental Materials S2.3).

A session of the experiment is composed of multiple groups. Each group is composed of six student participants who play the role of agents making production decisions in a common watershed. The production by agents occurs on specific parcels, which are located linearly along a river: Parcel 1 is the farthest upstream and Parcel 6 is the farthest downstream (Fig. 1). The spatially explicit positioning of the agents has parallels to lab and field experiments that have explored the differences in water-use decisions of upstream and downstream irrigators (D’Exelle et al. 2012; Bell et al. 2015).

The agents in the experiment make decisions over a series of rounds, using a web-browser-based interface built into the Python package Willow (Weel and McCabe 2015). In every round, the six agents simultaneously make production decisions that determine their private incomes. Agents’ production creates byproducts (pollution) that enter a river and cause damage to hypothetical downstream users. A principal, representing an environmental regulator, penalizes or rewards each agent based on the measured ambient (group) pollution level at a downstream monitoring point (sensor) that results from the production decisions of all upstream agents.

The measurement of the pollution level occurs at specific sensors and is assumed to be measured over an interval of time, referred to here as a sensing window. The sensing window in a given round occurs after the production decisions of each of the agents are complete. Specifically, the sensing window starts from the time the pollution enters the stream and lasts until pollution concentrations at the sensors reach a steady state. The effect of an individual production decision on the observed concentration at the sensors depends on all agents’ production decisions, their locations, and the frequency of the sensing measurements. Given the non-point-source pollution motivation for the study, the agents cannot observe the behavior of other agents and the regulator cannot observe the individual agents’ actions, just the ambient level of pollution measured at the sensors.

Each agent’s profit in a round is composed of the income they earn from production, adjusted by any tax or subsidy imposed by the principal according to pre-established policy rules. These rules are communicated to the agents in the experiment instructions (Supplemental Material). The income functions of the six agents are identical (indexed by $n=1,\dots ,6$). The income function is quadratic in the agent’s production level, which is the decision variable, $x_n$, and takes the form of Eq. (1)where $I_n$ = private income of agent $n$ in a given round. The decision variable, $x_n$, can take on values between 0 and 50.

The amount of pollution byproduct generated by the agent is proportional to their production level (it is assumed that 1 unit of production leads to $\mathrm{1,000}\mathrm{\mu gN}/\mathrm{L}$ emissions of nitrite), and the pollution concentration over time at one point in the river is determined jointly by all agents’ decisions. Each round is independent, and pollution concentrations do not transfer across rounds. The tax/subsidy that applies in each round is a linear function of the measured pollutant concentration and is therefore contingent on the production decisions of all agents. The tax/subsidy takes the form of Eq. (2a) if there is only one sensor placed just downstream of the last parcelwhere $\mathrm{TS}(x_1,\dots ,x_6)$ = tax/subsidy that is charged on an individual agent; and $C(x_1,\dots ,x_6)$ = measured concentration of pollution. However, if there is one additional sensor placed between Parcels 3 and 4, the tax/subsidy takes the form of Eq. (2b)where ${\mathrm{TS}}_{\mathrm{up}}(x_1,x_2,x_3)$ = tax/subsidy that is charged to an individual agent from Parcels 1 to 3; $C(x_1,x_2,x_3)$ = measured concentration of pollution from the sensor between Parcels 3 and 4; ${\mathrm{TS}}_{\mathrm{down}}(x_4{x}_5,x_6)$ = tax/subsidy that is charged to an individual agent from Parcels 4 to 6; and $C(x_4,x_5,x_6)$ = measured concentration of pollution from the downstream sensor. The thresholds in Eqs. (2a) and (2b) are exogenous concentration levels determined by the principal (regulator). The thresholds are different across treatments and are designed such that average TS is approximately zero when each agent chooses a production level of 25. The target production level of 25 is assumed to be determined exogenously and is not a product of the economic model. When TS is negative, the agents pay a tax; otherwise, they receive a subsidy.

The profit earned by an individual participant in a given round is the sum of private income [Eq. (1)] and the tax/subsidy in that round [Eq. (2)]. When the measured pollution concentration is greater than the threshold, TS is negative and therefore the participants’ realized profits in that round are lower than their private income.

The amount of pollution generated by each agent is assumed to enter the river simultaneously and then mix together, flow downstream, and dissipate. In other words, the pollution becomes less concentrated as it spreads across a larger area. Although based on the sum of pollution generated by each agent, there are nonlinear effects that can increase pollution concentrations as contaminates flow downstream through nitrification. The nutrient transport model QUAL2K is here calibrated to simulate water flow and the diffusion of the nitrite that is produced by agents and other background nutrients (details can be found in Supplemental Materials S2). In this specification, a nitrification process is observed that causes upstream parcels to have a large effect on the measured concentration, whereas downstream parcels have smaller effects. This specification simulates river ecosystems with larger residence times of nutrients, such as the Delaware River and lower Mississippi River systems.

Due to the model’s complexity, experiment participants were not provided with the specific analytical relationship between the concentration of the pollutant in the river and their production decisions. However, the instructions provided numerical examples, and the computer screen included a calculator to help the participants understand the effects of their decisions. The participants were given ample time to use the calculator to enter hypothetical production levels for each parcel and then observe the resulting measured concentration, tax/subsidy, and profits.

The pollution damage (social cost) was assumed to happen immediately downstream from Parcel 6, and the degree of damage is determined by the maximum concentration of the pollutant that is observed during the sensing window. Specifically, the damage function takes the form of Eq. (3)where $D(x_1,\dots ,x_6)$ = economic damage; and $C_{\max }(x_1,\dots ,x_6)$ = maximum concentration, within the sensing window, just downstream of Parcel 6. The net social benefit takes the form of Eq. (4)

Table 1 describes the four treatments, which differ in terms of the number of sensors and frequency of sensing. In the first two treatments, there is one sensor located just downstream of Parcel 6; in last two treatments, there is a sensor located just downstream of Parcel 6 and another located just downstream of Parcel 3. In terms of sensing frequency, the two low-frequency treatments involve the least monitoring—one time during the sensing window—and the tax/subsidy is calculated based on the measured pollutant concentration. In the two treatments with high-frequency sensing, sensors measure the pollutant concentration four times randomly chosen during the sensing window, and the tax/subsidy is determined based on the maximum concentration measured. A status quo (control) treatment is also included in the experiment in which there is no policy or sensor intervention. Two additional treatments with continuous sensing were also played but are excluded from the analysis in this paper due to the possibility of multiple Nash equilibria.

The socially optimal production is a vector of production decisions at each parcel $x_1,\dots ,x_6$ that maximizes the net social benefit in Eq. (4) and is displayed in the last row of Table 2. The Nash equilibria (NE) for each parcel for the control (status quo) and the four treatments are also presented in Table 2. The Nash equilibria are calculated based on the assumption that every agent will maximize their private expected payoff given the decisions of other agents. In every equilibrium, each agent has no better strategy (production decision) to maximize the expected payoff given the behaviors of other agents. Since a numeric nutrient transportation model is used in this study, it is not possible to get analytical Nash equilibria solutions, and therefore solve for the Nash equilibria numerically (Supplemental Materials S2.2 provides the method). As illustrated in Table 2, the NE primarily differ due to the frequency of sensing, which determines the expected magnitude of the tax/subsidy. By design, the number of sensors does not have a large impact on the NE, but the number of agents that can impact the tax/subsidy is influenced by the number of sensors. Under the calibrated stream and pollution dynamics, the optimal total emissions across all agents is 200, with heterogeneity across agents based on spatial location. Specifically, emissions from upstream parcels have a larger effect on the maximum concentration than downstream parcels. Optimally, the farthest downstream parcel (Parcel 6) has the highest emissions whereas the parcel farthest upstream (Parcel 1) has the lowest emissions.

A total of 108 undergraduate students (18 groups of six) participated in six experimental sessions at an experimental laboratory at the University of Delaware. Each student was randomly assigned to a computer station before entering the lab. The assigned computer determines their initial group membership and their parcel location along the river.

In the experiment, each agent faces every treatment (a within-subject design) and each treatment consists of six rounds. In each round, agents make one production decision, and then they are shown a screen with the measured level of pollution, the tax/subsidy, and their total profit. Each subject’s location (Parcels 1–6) changes randomly between treatments, and the groups are rearranged between treatments to reduce group experience effects. The order of the treatments is also varied across six experimental sessions to reduce potential order effects. At the beginning of the session, subjects are allowed 15 min to read the first part of the instructions (Supplemental Material). Next, they watch a PowerPoint presentation to ensure their comprehension of the tax/subsidy and underlying pollution-diffusion model. Additional instructions and presentations are offered at the beginning of each treatment. For the results reported in this study, sessions lasted approximately 90 min, and participant earnings were directly determined by the profits that they earned over the course of the sessions. On average, participants received $29 in earnings at the end of the experiment.

The objective of the experiment is to observe behavioral responses to differences in the placement and frequency of sensors, when used in conjunction with financial incentives related to water quality. Cluster analysis is used to classify participants into distinct behavioral types. Then, using the behavioral types identified by the cluster analysis, MMNL models, described in the next subsection, are used to analyze how the treatment conditions impact the behavioral types. The results from the MMNL modeling allow the three introduced hypotheses to be empirically addressed.

Cluster analysis is a method for identifying heterogeneous classes/groups among subjects where subjects within each class/group display similar behavior and subjects between classes/groups exhibit distinct behavior (Anderberg 1973; Hastie et al. 2001; Johnson and Wichern 2002; Berry and Linoff 1997; Everitt 2011). It is particularly useful when a priori knowledge regarding the number of behavioral types or the type structure is not available. To explore heterogeneity of agent behavior, cluster analysis is applied to segment the agents into distinct behavioral types using the difference between an agent’s actual production decision and the NE as a measure of the agent’s behavior in each round, shown in Eq. (5)where $t$ = round in which the decision is made. Thus, six observations are obtained for each subject in each treatment, designated ${\mathrm{diff}}_1$, ${\mathrm{diff}}_2$, ${\mathrm{diff}}_3$, ${\mathrm{diff}}_4$, ${\mathrm{diff}}_5$, and ${\mathrm{diff}}_6$ representing the differences in each of the six periods. The cluster analysis is then implemented based on the six observations together to segment the subjects. That is, the distance matrix between two subjects used in the cluster analysis is calculated with all six observations. This allows for possibly capturing subjects’ changing behavior over time, although the empirical results show that agent decisions are largely consistent over the six rounds.

Three common clustering methods are considered: the Gaussian mixture model, $K$-means clustering, and hierarchical clustering. Because there is no objectively correct clustering algorithm for a particular problem, the most appropriate clustering method is typically selected, experimentally, based on the specific structure of the data (Estivill-Castro 2002; Keritino et al. 2015). After model diagnostics, it was found that the Gaussian mixture model does not satisfy the required normality assumption. Several statistics were then computed, such as the Calinski and Harabasz index (or variance ratio criterion, Calinski and Harabasz 1974), Krzanowski-Lai (KL) index (Krzanowski and Lai 1988), and Scattering and Dispersion (SD) validity index (Halkidi et al. 2000), to evaluate the goodness of fit of the hierarchical and $K$-means methods. For example, the Calinski and Harabasz (CH) index measures the ratio of between-group variation to within-group variation. A good clustering method will create within-group subjects as similar as possible and between-group subjects as dissimilar as possible. Therefore, a large CH index is indicative of good clustering. The Calinski and Harabasz index of the hierarchical clustering in this study is 208.94, which is higher than 38.76 of the $K$-means method, indicating that the hierarchical method has a better goodness of fit. The other statistics in general suggest similar results. Henceforth, only the key results derived from hierarchical clustering are described.

To study possible varying effects of sensor and incentive conditions on heterogeneous agent behavior and to test the Hypotheses 1–3, MMNL models are estimated using the results from the cluster analysis. The MMNL model was introduced by Boyd and Mellman (1980) and Cardell and Dunbar (1980) in the economic literature. Since then, various economic studies have improved or applied the MMNL model for data analysis (e.g., Beggs 1988; Enberg et al. 1990; Reader 1993; Jain et al. 1994; Revelt and Train 1998; Train 1998; Nevo 2001; Small and Verhoef 2007; Fiebig et al. 2010). The MMNL model is a generalization of the multinomial logistic model and thus it can handle multilevel categorical or discrete response variables. It measures the relationship between a multilevel categorical response and one or more independent variables (predictors) and can be used to predict the probabilities of the different possible outcomes of the response based on a logistic function of the linear combinations of the predictors. In addition, it can capture repeated measurement information and heterogeneity in the population by specifying random effects in model fitting.

In this study’s analysis, the data are fit with a categorical response $Y=\{1,2,\dots ,K\}$, representing the behavioral groups estimated from the hierarchical clustering algorithm, and then the conditional probabilities of the agents’ type of behavior are predicted given the experimental treatments (policy, sensors, and frequency of sensing) and array of spatial locations. The clustering algorithm (results described subsequently) identifies four groups, e.g., $K=4$. Interactions between the treatments and the locations (a full factorial design) are also considered when fitting the model. The experiment sessions and rounds are treated as random effects because there might be heterogeneous structures associated with the two variables.

The model is mathematically formulated by introducing the following notation. Parcels, policy, sensors, and monitoring frequency are all categorical variables. Dummy (indicator) variables are used to represent each category of the variables. Let $z_1,z_2,\dots ,z_5$ denote the indicator variables for Parcels 1 to 5. Let $z_6$ denote the indicator variable for policy and $z_7$ denote the indicator variable for two sensors and measure the additional effect due to two sensors. Let $z_8$ denote the indicator variable for high frequency, let $z_9,z_{10},\dots ,z_{13}$ denote the indicator variables for the interactions between parcel numbers and policy, let $z_{14},z_{15},\dots ,z_{18}$ denote the indicator variables for the interactions between parcel numbers and two sensors, let $z_{19},z_{20},\dots ,z_{23}$ denote the indicator variables for the interactions between parcel numbers and high frequency, and let $z_{24}$ denote the interaction for two sensors and high frequency. Parcel 6 is not in the model formulation because it is treated as a baseline.

In addition, let ${\beta }_{i,1},{\beta }_{i,2},\dots ,{\beta }_{i,24}$, $i=2,3,4$, denote the coefficients of the corresponding variables in the multinomial logistic model. For convenience, let [$Z$] be the predictor vector that contains elements $z_1,z_2,\dots ,z_{24}$, and ${\beta }_i$, $i=2,3,4$, be the coefficient vectors that contain elements ${\beta }_{i,1},{\beta }_{i,2},\dots ,{\beta }_{i,24}$, respectively. Let ${\mu }_i$, $i=2,3,4$, denote the intercepts. Eq. (6) describes the fixed-effect specifications. Random effects are omitted in the formulation because they mainly affect the variance but not the mean function

Therefore, the predicted probabilities for the four behavioral group types can be calculated by Eq. (7)

The hierarchical clustering analysis provides a four-group partition, suggesting four agent behavior types. The group (cluster) mean difference in production relative to the NE are given in Table 3. An agent’s behavior is defined relative to the NE. The NE for an agent is their privately optimal production decision in the game, provided all other agents are also playing their own optimal production decision. That is, agents are best responding to others’ best response. The terms competitive and cooperative are used as labels to categorize agent behavior relative to the NE. As indicated in Table 3, Cluster 1 (competitive) behavior was, on average, closest to the NE. Clusters 2 (cooperative) and 3 (hypercooperative) chose lower than NE levels of production (and thus lower pollution), on average, and Cluster 3 tended to select the lowest production. Cluster 4 (hypercompetitive), on average, chose production decisions that exceeded the NE.

Fig. 2 looks further at the data distribution within each cluster. Because the agent decisions (differences from NE) are largely consistent over the six rounds, the data distributions are very similar over time. To make the graphical illustration simple, the information was averaged over time for each agent and the distribution of the averaged differences for each cluster are summarized by a boxplot in Fig. 2. The bold line in the middle of each boxplot represents the median value of the (averaged) differences from the NE for the group, the horizontal lines on the top and bottom of each plot represent the maximum and minimum values of the cluster excluding outliers, and the circles represent outliers.

It can be seen from Fig. 2 that Cluster 4 generally produces more than the NE because the differences of the cluster are above zero. This class of agents is therefore characterized as hypercompetitive. Cluster 1 agents are closest to the NE because the median value of the cluster is closest to zero. These agents are characterized as competitive/selfish. In contrast, Cluster 2 and Cluster 3 are generally below zero, indicating that the agents in these two groups produce consistently below the NE, and the agents in Cluster 3 fall the farthest below. Therefore, Cluster 2 and Cluster 3 agents are characterized as cooperative/altruistic and hypercooperative, respectively. The information shown in these plots is consistent with the average per-cluster values presented in Table 3.

Fig. 3 shows the probability density functions of the four behavioral groups distributed under experimental control (status quo) and treatment conditions. Although approximately 83% of agents chose a competitive behavioral strategy predicted by the NE under the control status quo condition, the treatments induce increases in cooperative behaviors. The four behavioral groups derived from hierarchical cluster analysis are then used as response variables in the multinomial logistic regression analysis to investigate heterogeneous covariate effects and are further predicted by tunable conditions represented in the experimental treatments, parcel numbers, and their interactions.

Table 4 presents the estimated results from the MMNL model, which was selected based on the minimization of the Bayesian information criterion (BIC) across a suite of six different model specifications shown in the Supplemental Material. Models with different random effects specifications are compared across and with a null model (no random effects), as indicated in Table S1. It is found that the multilevel model that controls for sessions as random effects and includes a full factorial of interaction effects of experimental treatments with parcels is the model that best fits the data. The estimated coefficients from this best-fit model are provided in Table 4. The results indicate that the spatial location (whether a parcel is upstream or downstream of a sensor), frequency of sensing, number of sensors, and policy all affect the likelihood of an agent playing cooperatively or competitively.

Fig. 4 shows MMNL predicted marginal probabilities for all four behavioral groups in relation to four experimental predictors—policy (whether the tax/subsidy policy is in place), parcel ID, sensors, and frequency of sensing—while all other predictor variables in the MMNL are held constant at their mean values. The existence of the incentive-based policy increases the probability of cooperative behavior. Agents in upstream Parcels 1, 2, and 3 are more likely to be competitive and less likely to be cooperative compared with the agents in downstream parcels. The addition of one sensor (with policy) increases the marginal likelihood of cooperative behavior but diminishes this likelihood with another sensor. Finally, low frequency of sensing induces a higher marginal likelihood of cooperative behavior than higher frequency of sensing.

The results from the MMNL reveal that existence of policy (incentive manipulation) increases the likelihood of cooperative behavior. For example, when policy exists, the odds of cooperative behavior relative to competitive behavior are about 53 times higher as the odds without policy ($p<0.001$) for agents at Parcel 6 and about 7–53 times higher for agents at other parcels (multiplication of the coefficient of policy by the coefficient of interaction). But policy alone (without increasing the number of sensors and frequency of sensing) does not significantly affect the likelihood of extreme behavior (hypercooperative or hypercompetitive).

Most significantly, the effects of interactions of policy with the parcel dummy variables (Table 4) are significant for the cooperative group, indicating that policy has heterogonous influence among parcels. In particular, the odds of cooperative behavior relative to competitive behavior tend to be smaller for agents of Parcels 2, 3, 4, and 5 ($p<0.001$) compared with Parcel 6. However, the interaction terms are not significant for the extreme types of behavior (both hypercooperative or hypercompetitive).

These results support the conclusion that policy incentives generally induce cooperative behavior, but the effect also depends on the location of the agent’s parcel in the river network. Policy can induce competitive behavior in upstream agents, but the farthest downstream agents tend to display a greater likelihood of cooperative behavior.

After controlling for the location of agents, it is found that both the number of sensors and the frequency of sensing generally affect the likelihood of cooperative behavior. Adding one sensor (with a policy) has a relatively large effect on inducing cooperative behavior (the odds of cooperative behavior relative to competitive behavior are about 7–53 times higher than those without a policy across the six parcels). The size of the effect diminishes with the addition of a second sensor (the odds are reduced to about 40% for Parcel 6 and more or less for other parcels compared with the one-sensor case, although the odds are still higher than those without a policy). It is also found that one sensor (with a policy) in the river network does not significantly affect the behavior of the extreme types of agents (hypercooperative and hypercompetitive). However, adding a second sensor (low frequency) reduces the odds of hypercooperative behavior relative to competitive behavior for most agents except those at Parcel 5, whose odds are not changed much. Meanwhile, the additional sensor decreases the odds of hypercompetitive behavior for agents spatially close to the sensors (Parcels 3 and 6, $p<0.001$) but increases the odds for agents farther from the sensors.

Changes in the frequency of sensing produce some surprising results. A high frequency of sensing (four times) reduces the odds of cooperative behavior versus competitive behavior compared with a low frequency of sensing (once), especially for upstream agents (further reduced to about 22.7%–47.6% in comparison with Parcel 6), although it still increases the odds of cooperative behavior in comparison to the control group (no policy). Moreover, sensing frequency affects the behavior of the extreme types of agents. A high frequency of sensing increases the odds of hypercooperative behavior versus competitive behavior for farther downstream agents (e.g., a 2.1 times increase for Parcel 6) but decreases the odds of hypercooperative behavior for upstream agents. When high-frequency sensing is coupled with two sensors, the odds of hypercooperative behavior for downstream agents are further increased (e.g., about 5.7 times for Parcel 6), but the odds of the upstream agents are still lower than those under two sensors and a low frequency of sensing. On the other hand, a high frequency of sensing with two sensors reduces the odds of hypercompetitive behavior versus competitive behavior for agents spatially closer to the sensors (Parcels 3, 5, and 6) but increases the odds for agents farther from the sensors, again compared with two sensors and a low frequency of sensing.

From these results, it can be concluded that a minimal amount of sensing in addition to incentive manipulation can have large and statistically significant effects in increasing cooperative behavior. An increased number of sensors and frequency of sensing can reduce the likelihood of hypercompetitive behavior for agents closer to the sensors but is not as effective for agents farther from the sensors.

The effects of the interaction between the sensing variables and the parcel dummy variables demonstrate that the spatial location of a non-point-source polluter relative to the sensors in a river network matters. Generally, it was found that when one or two sensors are added, agents of all six parcels are more likely to behave cooperatively, but the effect on inducing cooperative behavior is smaller for agents of upstream parcels than for agents of the parcels farthest downstream. Additionally, the interaction of a high frequency of sensing and the parcel location demonstrates the complex heterogeneity of the location effects for cooperative and hypercooperative agents. A high frequency of sensing tends to decrease the odds of cooperative behavior and hypercooperative behavior (versus competitive behavior) for upstream agents, but may increase or reduce less the odds for downstream agents (e.g., a 2.1 times increase of hypercooperative behavior for Parcel 6). This is likely because the NE level of production is significantly higher for downstream parcels in the high-frequency sensing treatments.

Overall, the authors conclude that sensors paired with incentives increase the likelihood of cooperative behavior in all parcels, but the size of the effect on inducing cooperation is slightly larger in downstream parcels compared with upstream parcels. Moreover, a high frequency of sensing is likely to reduce cooperative and hypercooperative behavior in upstream parcels although it might increase or reduce these behaviors in downstream parcels.

Overall, the incentive-based policy was found to induce cooperative behavior, and a low frequency of sensing with the incentives in place can have large effects on increasing cooperative behaviors. Minimal investments in setting up advanced environmental monitoring/sensing systems can potentially have large effects in improving water quality. The experimental data, however, also show that increasing the number of sensors (from one to two sensors) and frequency of sensing (from low to high) does not necessarily increase cooperative behavior. This finding suggests that additional sensors and frequency of sensing may diminish the likelihood of cooperative behavior in maintaining water quality; however, they may reduce the likelihood of extreme behavior.

This implication needs to be further tested in a more elaborate game design and with more levels of the frequency of sensing. More elaborate watershed-scale field experiments and agent-based models can be used in future studies to ascertain the extent and scale of these sensing effects, both with and without incentive manipulation. Such studies may enable identification of optimal environmental monitoring and sensor network designs in specific watershed management and policy design contexts. For enhanced ability to draw general conclusions, future research may change assumptions in the nutrient dynamics model that is used to simulate pollution concentration (and hence damages from pollution). For example, the model in this study assumes large constant background loadings into the surface water system. It may be interesting to modify the parameters to reduce the background loading; this may enhance the diffusion effect and alter how pollutants from different parcels diffuse over time, thereby changing polluters’ incentives across space.

Spatially explicit social dilemma and principal agent games, a variant of which has been presented in this study, can generate useful insights about the design of incentive mechanisms and sensor monitoring systems in the management and governance of human–environmental systems. Incorporation of spatially sensitive upstream and downstream dynamics in the management of non-point-source polluters, in particular design of environmental monitoring systems and incentive mechanisms, can be adapted to specific watershed topologies and stream networks. For example, the authors found that when one or two sensors are added (coupled with policy), agents of all six parcels were more likely to behave cooperatively, but the effect on inducing cooperative behavior was smaller for agents of upstream parcels than for agents of the parcel farthest downstream agents. Further, under a high frequency of sensing, agents of downstream parcels tended to perform more cooperatively than agents of upstream parcels. Conversely, a lack of sensing and absence of incentive manipulation likely leads to more predictable Nash/competitive behaviors.

Location of players vis-a-vis sensor locations matters significantly in inducing cooperative versus competitive strategies. More specific watershed-scale studies need to be designed to tease out the location-specific effects of installing environmental monitoring sensor systems across upstream and downstream gradients. Experimental results from this study confirm the value of installing cyberinfrastructure through monitoring and sensor systems, but more studies, ideally with spatially explicit dynamic social dilemma game structures, could improve current understanding of the location effects of sensors on non-point-source polluters in the management of watersheds.

The power of advanced in situ sensor networks to provide water quality data to support science-based decisions by stakeholders and resource managers appears intuitive and compelling. As discussed in terms of the results of this experimental study, other similar behavioral and game theoretical studies (mentioned in the “Introduction”) have suggested that the responses of private individuals and businesses to more detailed and accurate environmental information is variable and complex. Sensor-based water quality information can be gathered more often, accommodate a greater number of dimensions, have a higher resolution and/or accuracy, and cover a larger geographic and temporal environmental or social scope. Each of these factors can change human behavior, and the underlying premise may be that such changes in behavior will lead to a more sustainable use of natural resources. However, a behavioral change across the complex spatial terrains of watersheds in response to a given change in information is not guaranteed. Prior research, for example, has found that social information that can be interpreted as normative (such as choices of peers) can have strong and lasting effects on inducing cooperative behaviors (e.g., environmental conservation), perhaps stronger and longer lasting than the frequency or dimensional richness of scientifically measured environmental information (Dennis et al. 1990; Nolan et al. 2008; Peschiera and Taylor 2012). Location also matters, because the interaction effect of incentive mechanisms of resource users with sensor locations used by watershed managers has a strong effect in steering the multiscale environmental conditions.

Other studies in groundwater management, irrigation, and energy conservation domains investigating the effects of sensor information on strategic behaviors have found similar effects. For instance, greater availability of information regarding the condition of an aquifer could lead farmers to increase their water withdrawals in the short run at the expense of future water availability (Li et al. 2014). That could lead to lower seasonal water levels and overcapitalized farmers (e.g., Molden et al. 2003; Cosgrove and Rijsberman 2014). Similarly, provision of information that the level of pollution in a water body is low could encourage some farmers to forgo expensive pollution-abatement activities. In irrigation games, Bell et al. (2015) found that upstream players in the Indus Basin, whose water supply was unaffected by scarcity, did not change their competitive behavior in response to information that downstream players were not receiving adequate water. In contrast, D’Exelle et al. (2012) found that upstream irrigation players in Tanzania played cooperatively for enabling equitable sharing of water resources between upstream and downstream players. Studies of residential energy consumption have shown that more frequent provisions of usage and cost information can lead to declines in energy use (Petersen et al. 2007), but more frequent information often does not improve behavior or improves it only temporarily (Abrahamse et al. 2005).

Moreover, information that covers a larger spatial scale could have unintended spatial effects. For instance, information regarding high pollution levels in upper reaches of a watershed could discourage farmers in lower reaches from adopting conservation practices. Likewise, owners of lakefront homes could forgo adopting best management practices to control runoff or maintain septic systems if they view actions of their neighbors as making their individual actions irrelevant. People also sometimes misinterpret the risks associated with such information. For example, information that fosters new media reports regarding high levels of E. coli could lead to visitors shunning previously popular tourist destinations because they believe they are no longer safe even though the objective degree of risk has not changed. Broader decision behavior and game theoretic research in the future across a variety of watershed management conditions can explain the amplifying or dampening effects of strategic behavioral responses to incentive mechanisms and the placement of sensor monitoring systems.

The proposed clustering method to isolate behavioral strategies as a function of NE does not work well for situations that involve multiple Nash equilibria. In such cases, distance from the NE may yield nonunique solutions. In addition, both the NE and the production decisions can change across treatment settings. The cluster analysis is based on the distance between production choices and relevant NE, and therefore the observed changes in behavioral types across treatments and scenarios are due to both because of changes in production decisions and changes in the NE. Future research should evaluate the relative importance of each of these avenues. Another important limitation of the game concerns the theoretical assignment of cooperative behaviors to agents despite the fact that agents do not see each other’s moves or production levels. Treatments that enable communication between agents were not tested in this experiment but represent a fruitful area for future research (e.g., Guilfoos et al. 2019).

In addition, although logistic regression is a popular and effective approach for modeling categorical outcomes in classification problems, the method still relies on certain assumptions. For example, the model has a parametric formulation, and a linear relationship between the log odds and the predictors is assumed in the study. If these parametric assumptions are violated, the model could be misspecified. The model was diagnosed based on Pearson (chi-square) residuals, and severe violations were not observed. Because the dimension of the predictors in this study is relatively high, the authors consider that the linear assumption is relatively mild. Nevertheless, the conclusion is data-driven and model-based. There are other nonparametric techniques for classification problems, such as decision trees and random forests, which are worthy of future investigation. These methods are flexible and useful for the purpose of prediction but can be less effective for interpretation.