Common Pool Resource with Free Mobility: Experimental evidence from Mongolia Dolgorsuren Dorj

∗ †

April 5 2009

Abstract We conduct experiments for the CPR game in which people freely choose between two localities that differ by governing structure: unregulated and sanctioning mechanism. Our no sanctions with free mobility setting investigate the effect of free mobility, while our asymmetric institutions (sanctions in one locality and no regulation in other) setting with free mobility investigates effect of institutions on the resource use efficiency. We compare the result to the benchmark with no free mobility. We found that (a) under free mobility conditions efficient resource use is attainable if the sanctioning system adjusts to the population level; (b) sanctioning system increases the appropriation efficiency in the neighboring community not only because of the migration induced by higher efficiency in community with sanctions, but also regulated community serves as a role model to follow for unregulated community; (c) subjects monitor each other only if there are free riders hence, in the absence of free riders sanctioning institution has no deadweight loss. JEL classification codes: C70, C91, Q2, R5. ∗

Corresponding author. Department of Economics, University of Hawaii at Manoa, 2424 Maile Way, Honolulu, HI 96822. Email: [email protected] † Thanks to Katerina Sherstyuk for her guidance in this research. I appreciate funding through the Arts and Science Advisory Council Award at University of Hawaii at Manoa. I am grateful to Academy of Management (Mongolia) for providing facilities to conduct experiments.

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1

Introduction

It has been accepted that users of the CPR will overexploit the resource, because private benefits of resource extraction outweigh the social costs of extraction, which results the appropriation beyond the social optimal level. In CPR experiments with no institutions subjects appropriate more than the Nash predictions (Walker et. al, 1990). Communication was introduced as an information given to subjects that describes the harvesting level that will generate the socially optimal outcome in Ostrom et al. 1992 study. They show that monitoring alone without sanctions may worsen the resource depletion while sanctions improve efficiency. Another set of experiments report that decentralized mechanisms such as sanctions do not alter Nash equilibrium because it is costly decision for selfish players (Walker, Gardner, and Ostrom 1994). Different story is in place when sanctions become the revenue-generating device for the selfish players instead of pure costly activity (Casari and Plott 2003). Mutual monitoring and sanctioning opportunity in Italian Alps allowed villagers successfully manage the commons in 13th and 19th century. Much of the study on sanctioning institutions in common pool resource environment including above experiments deals with incentive problem within one community (Moir 1999, Fehr and Gachter 2000, Walker et al. 2000). This research extends above studies incorporating free mobility issue. Present work differs from existing literature on the CPR. If the previous work focuses mainly on one locality CPR problem, our model more emphasizes on migration issue between localities, where free entry is possible with no cost. Here we extend existing research to allow for two communities, in which citizens in localities are free to choose the place to live. First, we use a Nash type free mobility equilibrium concept, a partition of population that is stable against any unilateral deviations to existing and new jurisdictions. Hence, in equilibrium all localities are inhabited and no citizen wants to move to any other jurisdiction. Second, we explore different institution structures under two-community economy with free mobility. In particular, institutions are: (i) unregulated locality, (ii) sanctioning system (Casari and Plot 2003). We study the effects of the different institutions on the spatial distribution of herders in a two-community economy. The objective of this paper is to test conditions for cooperation in CPR game with free mobility. We test predictions of several models with different institutions (sanctions and no sanctions) under the migration pressure condition. 2

Why do we care about multiple localities? The extensive grazing that requires high mobility within the large territory of grassland motivates our interest in multiple localities context. Next, spatial proximity of herders plays significant role in the selection of proper institution with monitoring. Therefore, our focus is on availability of cooperation in the mobile production activity when sanctions are introduced. Section 2 contains predictions of the model. Section 3 explains experiment design. Sections 4 and 4.2.1 will report the results of the experiment on free mobility equilibrium. In section 5 we discuss and conclude. Instructions and consent form are attached. We ask whether a sanctioning system can survive, when free mobility allows individuals to choose between communities that differ by institutions governing them.

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Theoretical Predictions

We adopt a sanctioning model with selfish herders from Casari and Plott (2003)1 . We assume that community adopts sanctions and in the case of migration entry locality adjusts sanctions to the increased population level. Also we assume that all subjects are selfish and identical. We assume that benefit of adopting sanctions outweighs the cost of institution. Community of herders set up rules among themselves and monitor each other. Subjects who discover the violators will receive transfer from violated agent as a fine. The fine is predetermined in proportion to the violation level. Threat to be monitored keeps herder’s grazing level at appropriate level. Second, we allow free mobility between two localities, where citizens in each area are free to choose the place to live and appropriate the resource. Third, we introduce different institutions in localities. Fourth, we found following predictions of different game models:

2.1

No Sanctions in one locality, classical model

Standard common-pool resource game by default has no institutions; the physical environment and institutional environment coincide. This model is classical in a sense that players are selfish and identical; players have no parameters attached to the utility of other decision makers. In a standard common-pool resource game (e.g. Falk, Fehr and Feschbacher 2002) finite n 1

Casari and Plott have a sanctioning model with heterogeneous population as well

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number of herders with endowment, e, simultaneously decide on the amount of appropriation from the common pool denoted as xi . Here we focus on symmetric equilibria where herder’s strategies are the same within the locality, xi = x. Let X be the sum of all herder’s appropriation and f (X) is total revenue of all herders, where f (X) = aX − bX 2 is a concave function with parameters a > 0 and b > 0. The cost of maintaining one animal denoted by c is independent of every other member’s decision while the revenue for each member will depend on grazing choice of all members. The share of each individual in total grazing is, xi /X. Then each herder profit is given by πi = e − cxi + [xi /X]f (X). From first order condition we find the equilibrium appropriation by each herder. Proposition 1 Selfish Nash equilibrium in one locality with homogeneous types and complete information determines the appropriation by each herder: a−c . Total appropriation in selfish Nash equilibrium is given by X ∗ = x∗i = b(n+1) n · a−c , which is higher than the social optimum. n+1 b

2.2

Sanctions in one locality: competing theories

Classical model with sanctions 2 assumes that users of the resource set up rules among themselves in such a way so that total appropriation in locality is at social optimal level. In particular, community agrees and restricts appropriation to certain amount, threshold, λ. All players are free to monitor each other with respect to the threshold. Harvesting beyond this threshold costs individual a fine payment if any other member of community would discover her violation. For each excess harvesting unit violator pays unitary cost, h. The fee the violator pays is a transfers to inspector who discover the violation. Monitoring is a costly decision for anyone who decides to inspect any other member. With a unitary cost, k, inspector may obtain exact information about the harvesting decision of any other member. The payoff P for each agent is given by πi = xXi f (X) + e − cxi − Ii mi + i6=j Iij rij , where mi = h(xi − λ) is the total fee paid by violator, rij = mj − k, is the revenue generated by agent i from monitoring of agent j. I = 1 if inspection occurs. Note that there are no multiple fee payment for violator. If more than one inspections requested for person one of agents will be randomly selected as an 2

See Casari and Plott 2003.

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inspector. We will use following parameters throughout the paper: a= 14.5, b=1/30, c= 2.5, N= 10, k=7 and λ = 18. 3 Next consider alternative hypotheses of competing theories on sanctioning mechanism. First, we test hypothesis of a classical model where full social optimal appropriation is supported by Nash equilibrium. Here threshold is set little bit lower than the social optimal grazing level for each agent. In equilibrium everyone violates little bit and everyone would benefit from inspecting each other; hence we obtain social optimal grazing level for all agents. Second, alternative hypothesis states that once the threshold is set up to some level, people will obey the rules and stick to that number. Therefore, to get the social optimal grazing level for everyone, we set the threshold equal to the social optimal level. In this case, we will have little bit overgrazing and equilibrium appropriation per person is little bit higher than the social optimal. However, efficiency stays at high level close to full social optimal. Third, we test hypothesis that some agents follow the rules and choose grazing level exactly equal to the social optimal while others violate the rules. We propose model with two types: violator vs. non-violator. Predictions of all three hypothesis are stated in the following propositions. Classical model with sanctions: λ = 16. Proposition 2 Suppose locality has a sanctioning mechanism, where the threshold and punishment levels are set as λopt = xopt − k/h − ε and h = a − c − xopt (n + 1) · b, respectively. Then this sanctioning mechanism supports the socially optimal level of harvesting as Nash equilibrium, X ∗ = X opt . Also in this equilibrium every one inspects each other, p∗ = 1. Efficiency level in community is equal to 100 percent 4 if the monitoring cost equals zero. However, it is less than 100 percent if we count monitoring cost, 93.5 percent. 3

A fine (h) varied with the population size in the following way h=0 if n=1 ; h=3 if n=2; 4 if n=3; 4.50 if n=4; 4.80 if n=5; 5 if n=6; 5.14 if n=7; 5.25 if n=8; 5.33 if n=9; 5.40 if n=10. Q∗ Qopt Q Qopt 4 E = / ·100 = ( −N e)/ ·100. One can also say sanctions restore efficiency, yet not without a loss, a monitoring cost is a waste of the resources. We characterize an outcome in terms of efficiency as an optimality of appropriation level and overall efficiency, which includes a monitoring cost. Efficiency and an overall efficiency coincide when a monitoring cost is equal to zero).

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Model with sanctions and one type: λ = 18. Proposition 3 Suppose in sanctioning system the threshold is set exactly equal to social optimal λopt = xopt and punishment level is set as h = a − c − xopt (n + 1) · b. In selfish Nash equilibrium with one type all agents violate and appropriate at xi = hk + λ. Since threshold is set to social optimal level in symmetric equilibrium xi = 19.3 > xopt . In this equilibrium monitoring is not full but close to complete, p = 0.928 < 1. Appropriation efficiency including monitoring cost is at 93.5 percent. Model with sanctions and two types: non-violator and violator, λ = 18. There are v violators and n − v non-violators, where n is the total population of a community. We assume a symmetric behavior within the type. Proposition 4 Selfish Nash equilibrium in one locality with two types and R −1) + complete information determines the appropriation by violators: xvj = k(n h(v−1) nv λ and xi = λ. Total appropriation in selfish Nash equilibrium is given by R −1)v + nR λ, which is greater or equal than the social optimum but X ∗ = k(n h(v−1) much lower than the harvesting level in unregulated locality, X opt ≤ XR∗ < (a−c)(nR −1)−bλ(n2R −1) XU∗ . Equilibrium probabilities are: pnv = 1, pv ∈ (0, 1), − hv kb(nR −1)2 h2 (v−1)

−

nR −v−1 v

≤ pv ≤

(a−c)(nR −1)−bλ(n2R −1) h(v−1)

−

kb(nR −1)2 h2 (v−1)

−

nR −v . v−1

See Appendix 6, Tables 1, 2 for the derivations and summary of predictions. First model considers pure strategy equilibrium while the next two theories have mixed strategies in monitoring. The classical model and the model with one type may support social optimal grazing as a Nash equilibrium when the threshold is set little bit lower than the social optimal level. Model with two types requires sufficient number of violators to obtain social optimal level. In the first two models all agents are violators; the model with two types has violators and non-violators. In terms of appropriation efficiency all three models predict 93.5 percent including monitoring cost.

2.3

Social Optimal in two localities, classical model

Proposition 5 In two-community economy with homogeneous agents, socially optimal level of grazing in each community is the same as the social 6

optimal level where only one locality is present, Xsopt = (a − c)/2b, and it is independent of number of people in the locality. Per person-grazing level in each locality is determined by xs = X opt /Ns depending on the number of people within the locality.

2.4

No Sanctions in two localities, classical model

Consider the case where both localities are unregulated. Proposition 6 Free mobility equilibrium in two neighboring, unregulated pastures with identical herders is characterized by the symmetry of outcomes. Half of herders graze in locality one and half of them choose locality two, N1∗ = N2∗ . Also total grazing level in each locality is the same as the selfish ∗ Nash equilibrium in one locality, Xoneloc. = X1∗ = X2∗ . Both localities’ grazing levels are above the social optimal level, X1∗ = X2∗ > X opt . Thus, free mobility equilibrium efficiency level in unregulated pastures is lower than the efficiency at social optimal level.

2.5

Sanctions in one and No sanctions in other locality with free mobility

Suppose community in one locality adopts sanctioning system as in Casari and Plott (2003) and the other locality is unregulated. Below we consider predictions for the alternative models: classical model, model with one type, and model with two types.

Classical model Proposition 7 (1) Total appropriation level in community with sanctions will remain at the social optimal level and equal to XR∗ = X opt . Efficiency of sanctioning system is at maximum. (2) Efficiency of unregulated pasture improves as compared to the case where there is no sanctioning system neighboring the unregulated pasture. Here migration to regulated locality reduces the population in unregulated locality, hence the externality, yet appropriation is above social optimal level, XU∗ > X opt . (3) The appropriation levels across localities are as follows, X opt = XR∗ < XU∗ . The locality with the sanctioning system has a higher number of individuals than the unregulated locality, NR∗ > NU∗ . 7

Model with one type Proposition 8 (1) In Nash equilibrium with one type, total harvesting level in locality with sanctions is given by, X ∗ = v( hk + λ). (2) Harvesting level U > a−c and there is small in unregulated locality is given by XU∗ = (a−c)n b(nU +1) 2b overgrazing, however efficiency improves compared to case with two localities that have no regulation. (3) The appropriation levels across localities are as follows, X opt ≤ XR∗ < XU∗ . Population split between localities is such that nR > n U .

Model with two types Proposition 9 (1) In Nash equilibrium with two types, total harvesting level R −1) + λ) + (nR − v)λ. in locality with sanctions is given by, X ∗ = v( k(n h(v−1) U (2) Harvesting level in unregulated locality is given by XU∗ = (a−c)n > a−c b(nU +1) 2b and there is little bit overgrazing. Efficiency in unregulated locality improves with migration to locality with sanctions. (3) The appropriation levels are as follows, X opt ≤ XR∗ < XU∗ . Population split between localities is such that nR > n U .

See the summary for each treatments in Table 1. To test hypothesis of competing theories on sanctioning mechanism we construct two treatments with sanctions, where threshold is set to social optimal level. Treatment ”S” has one locality with sanctions while treatment ”NS” simulates two localities case where one locality has sanctions and the other does not have regulation.

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Experiment Design

Total 80 inexperienced subjects who were engaged in a post diploma training activity recruited from Academy of Management. Ten participants are invited to each session. All participants were given a number from 1 to 10 and were seated separately from each other in a room with overhead projector facing the screen. No communication was allowed. Instructions were read aloud to everyone. After the instructions were read, the quiz was given. Subjects had one practice period to insure that they understood instructions clearly. Also at the end of the experiment questionnaire was submitted to the subjects asking for the strategy they followed. The instructions are appended. 8

The CPR problem is described as an abstract decision-making situation, where exists opportunity to make a money by ”investing” in market(s). Each of ten subjects had chosen investment level without knowing others’ investment (appropriation) levels within the group. Investment level is expressed in ”tokens” and payoffs are in terms of ”francs” 5 . Each subject have been paid in cash at the end of experiment. An experiment lasted from 2 (no sanctions experiments) to 5 hours (sanctions experiments). Individuals earned on average 12.7 USD. In total there were eight experimental sessions; two sessions with (i) no sanctions design and six sessions with (ii) sanctions design. No sanctions design had two parts: (a) all ten subjects invest in one single market with no sanctions and (b) in the second part there is opportunity to invest in one of two markets that had no sanctions. Sanctions design had three parts: (a) all have opportunity to invest in a single market with no sanctions; (b) then all may invest in a single market with sanctions; (c) lastly, exists opportunity to invest in one of two markets where one market had no sanctions and the other had sanctions. Each experimental session consists of 20 to 30 periods. The experimental part with two markets is designed to capture essential elements of the CPR with free mobility game and had ten periods each having two stages in no sanctions environment and three stages in a sanctioning environment. In two markets design subjects have to choose the location and grazing level if there are no sanctions while inspection game includes monitoring decision in addition to the location choice and the investment. First, herder chooses the market (locality) to invest for. When the number of people in each market known, in the second stage subjects submit request for a number of tokens that they wish to put in the market chosen. The choice of tokens can vary between 1 and 100. The investment decision is submitted simultaneously in all designs. In the market with inspection game when everyone completed submission of tokens, total group investment level and total group return becomes public information. Next step allows subjects to inspect any person within the group whom he suspects is in violation of the publicly known amount of investment. Monitoring per person requires 7 francs, while each extra token discovered gives the reward of 5.4 franc for the inspector when locality has ten people. 5

laboratory artificial currency that are converted into domestic currency, togrogs, at the end of experiment

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The period payoff computed by subjects and checked by experimenter contains three elements: results of investment decision by agent, total investment and results of inspection. Past history is available including each locality threshold level, participant own investment level and cumulative payoffs, total group investment and gross group return, and individual investment levels of subjects that were violated and inspected.

3.1

NO SANCTIONS with FREE MOBILITY EXPERIMENTS

After ten periods of basic one-market no sanctions experiments (N), participants experienced ten periods of symmetric two-market treatments (N N ). The latter environment differs from no sanctions treatments by free mobility condition. Each participant was free in choosing her preferred market for investment; two markets were identical in terms of parameters. However, depending on a population level and the choices made by participants they may end up with the different returns on investment. In two-market treatments when the number of people in each markets (MARKET A and MARKET B) is known subjects decide on investment levels. Each subject had 4 tokens as an endowment. The range of tokens that were allowed to order in Market A was [1, 100]. Each token that the subject orders costs him c= 2.5 experimental francs. Gross group return and return on tokens invested was presented in Table 1 in the instruction (N). Return per token invested depends on a gross group return, f(X), and total group investment, X. The shape of gross group return is depicted in Figure 1. The market period ends after all participants submit their investment orders on a slip of paper or after 3 minutes (whichever occurs first). Subject orders are entered into the EXCEL spreadsheet that computes the payoffs. Then the person running experiment records those payoffs for each participant and returns to the subjects in private. The participants then record their payoff on a payoff sheet. Then after each period each participant had following information on a big screen : Total group investment, X, in the market(s); Return per token invested, F(X)/X, in the market(s); Gross group return, F(X), in the market(s).

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3.2

SANCTIONS with FREE MOBILITY EXPERIMENTS

This treatment differs from previous treatment in two ways: (i) there were ten or six periods of no sanctions (N) in MARKET A ; (ii) ten periods of a single MARKET B with sanctions (S) followed. After everyone made the investment decisions and the total group investment was discovered, participants had opportunity to monitor each other. Each subject may benefit from monitoring others’ activities, which costs him 7 francs per person; (iii) lastly, ten periods of two distinct markets were conducted, where subjects are free to place tokens in either MARKET A with no sanctions or MARKET B with sanctions. Monitoring: If subject ordered tokens in MARKET B, based on the total group use discovered after the investment decisions, she had an option to earn money by monitoring others. All participants submit their inspection orders anonymously to the assistant on a slip of paper even if you are not ought to monitor. The slip contains the ID of inspector, ID(s) of person(s) she want to monitor and option to leave blank. After all subjects submit their slips on monitoring decision, inspections are realized and ID(s) of violator(s) with the number of exceeded tokens become available on a big screen. A decision consists of three pieces of information: (i) choice of a market; (ii) level of investment; (iii) inspection decision (in only Sanctions experiments).

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Result

Results of no sanction experiments 4.1

No Sanctions in one locality

We use the classical Nash model in one locality as a benchmark and compare with the experimental results where no sanctions were introduced. Result 1 With no sanctions the resource extraction is high and close to the classical Nash equilibrium (i.e. with homogeneous, selfish players) from below. Average efficiency is low and no different from Nash prediction.

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4.1.1

Support

Group Use: (Table 8, Row 1. The overall average group appropriation for the eight experiments was 306.2 which is below the Nash level of 327.3 at a 5 percent level ( p-value for t-test is 0.0250). 6 . 79.7 percent of data falls into 25 percent bandwidth around the predictions where 15.6 percent of data are below and only 4.7 percent are above the Nash level 327.3. Individual use: Individual decisions were highly dispersed in the action space varying from 1 at minimum to 100 at maximum. Out of 640 individual decisions only 8 were exactly at Nash equilibrium (5 actions at 33 tokens and 3 actions at 32), with Nash predicted value of 32.7. Overall 35.6 percent of data are within the 25 percent bandwidth (i.e. in the interval [25, 41]) around the predicted value. 20.2 percent of individual actions are above 41 and 44.2 percent of actions are below 25. Efficiency: Table 9, Row 1. On average efficiency was 42.52 percent of the maximum surplus available as compared to the Nash equilibrium level of 33.1 percent(p-value= 0.1474). Efficiency ranged across sessions from minimum of 24.95 to maximum of 61.6 percent. In five out of eight sessions the efficiency level was higher than predicted, but in three out of eight are below than prediction.

4.2

No Sanctions in two localities

With two unregulated localities the classical Nash model predicts overgrazing in both localities. Result 2 As predicted the experiments with two unregulated localities demonstrate overuse of the resource beyond the social optimal use. In line with prediction free riding exists and full surplus has not been absorbed. 4.2.1

Support

Group Use: In two experiments overall average group use scored 249.2 and 247.6 respectively. Group use varies across periods ranging from minimum of 140 to maximum of 347. The 77.5 percent of data on total group use demonstrate appropriation that is below the classical Nash predictions. 6

The Nash equilibrium value of X=327.3 has not been recorded in any of 64 periods. The group use below the Nash equilibrium recorded in 62.5 percent of periods

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Individual use: Individual use levels were dispersed ranging from minimum at 10 to maximum at 100. Only 3.8 of all data do confirm the classical Nash equilibrium of xi =60. The 16.3 percent of data are within the 25 percent bandwidth around the predicted value (i.e in the interval [45, 75]). That is 74 percent of data are below and 9.8 percent of data are above the 25 percent bandwidth. Efficiency: Table 9, Row 3. The resource use average efficiency per locality in each sessions reached 78.7 and 76.5 percent respectively, while theory predicts 55.6 percent from maximum rent. Population split: Table 9, Row 4. As predicted the Nash split of population across localities in a 5 : 5 fashion recorded in 30 percent of data. Overall 75 percent of data are within the 25 percent bandwidth (i.e. in the interval [3.75, 6.25]) around the predicted value. 5 percent of records are below and 25 percent are above the 25 percent range around the prediction.

Results of sanctioning experiments 4.3

Sanctions in one locality

Model with one type and model with two types predict almost no overgrazing in locality with sanctions. See Table 4. We compare results with symmetric equilibrium with on type and model with two types. Result 3 With sanctions higher level of cooperation observed. 4.3.1

Support:

Group Use: In six experiments overall average group use scored 214.7, which is close to the Nash prediction with two types of 203.3, and statistically not different at five percent level (p-value for t-test is 0.2665). Overall 80 percent of group data are within the 25 percent bandwidth around the prediction, 16.7 percent stands above and 3.4 is below this range. Total group use on average drops from 303.1 in the unregulated to 214.7 with sanctions. Individual use: Exactly 30.8 percent of all actions do confirm to the Nash equilibrium prediction of xi =18 for some i non-violators. Overall, 45.7 percent of all actions are above 18. However, only 4.3 percent of actions are above the 40 tokens. In total 54.3 percent of all actions are xi ≤ 18.

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Efficiency: In terms of efficiency overall rent from resource use reached 88.4 percent which is statistically different from predicted 93.5 percent 7 at 1 percent significance level (t-test p-value= 0.0388). In one out of six experiments efficiency is higher than predicted that is 94.5 percent. Monitoring: More than half (63.8 percent) of all actions were inspected with sanctioning mechanism. Average monitoring cost of 44.3 is statistically different from predicted value of 61 at 5 percent level (t-test p-value= 0.0343). Therefore, monitoring that is less than 100 percent or not full, that requires less costs in one hand, however that prevents free riding had more survival feature. 4.3.2

Sanctions in one and No regulation in other locality

Result 4 As predicted with sanctions in one locality and no regulation in other locality, community with sanctions sustains the resource use close to efficient level. The appropriation efficiency in unregulated locality improves because of the migration to locality with the sanctioning system that prevents overgrazing. Moreover, the experiments demonstrate higher level of cooperation in unregulated localities because community with sanctions serves as a role model to follow that was not predicted by the model. 4.3.3

Support

Group Use Table 8: Locality with sanctions experienced overall low average group use of 169.9 which is marginally no different from symmetric equilibrium predicted value of 188 at five percent level (t-test p-value=0.0490). The group use varied from minimum of 145.6 to maximum of 187.6. Group use in the unregulated locality in all six experiments scored (233.4) on average that is lower than the predicted classical Nash equilibrium of 288 (one tailed t-test p-value=0.9975). The group use with no sanctions across experiments ranged from minimum at 190.4 to maximum at 263.5. As predicted in terms of direction the appropriation in the unregulated locality is higher than the resource use in the regulated locality (one tailed t-test p-value=0.9986). In 78 percent of data group use in the unregulated locality is above the social optimal level, while the regulated community exceeds social optimal level only in 25 percent of data. Unregulated locality neighboring with regulated community experienced lower appropriation than 7

where 6 percent of rent is a deadweight loss due monitoring cost

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unregulated community (two tailed t-test p-value==...check this). As predicted this is due to lower population level in unregulated locality because the regulated community accommodates more people than unregulated locality. Individual use: See Table 10In locality with sanctions the average individual use level across sessions was 34.42 with minimum at 30 and maximum at 43. Exact social optimal use level in the regulated locality was recorded in 45.4 percent of data while with no regulation only 5 percent of actions match this value. 53 percent of data is equal and below predicted level of 30. In the unregulated locality 80 percent of data recorded are below the predicted value of 72. Overall individual use level scored in unregulated locality on average 52.26 with minimum at 35 and maximum at 64 across six sessions. We believe that low level of appropriation in the unregulated community, in addition to the low level of population due to sanctions in neighboring locality, also caused by the fact that subjects in unregulated locality were imitating choices in regulated community by reducing their use level of the resource and increasing the return per token. That is investors in two different markets were competing with each other to get the crucial outcome, high return per token invested. Regulated market served as a role model for the unregulated market. Non-violator and violator: As predicted with sanctions percent of violating actions on average reduces to 24 compared to 70 percent in separate unregulated locality. Interestingly, on average violating actions in neighboring unregulated locality reduces as well to 64 percent. See Table ??. We believe that behavior in regulated locality shaped the behavior in other locality because the information between localities was free of charge and agents in unregulated locality tried to imitate the outcome in regulated locality where return per token was high when agents stick to rules. With sanctions 76 percent of population in regulated community and 36 percent of population in neighbor unregulated locality follows the social optimal harvesting level. With no regulation in one separate locality this number was 30 percent. Efficiency: Table 9, Row 5. In locality with sanctions efficiency ranged from minimum of 91.1 to maximum of 97.3. The range is very tight to the predicted efficiency of 96.1. The mean across six sessions was 95.26 which is statistically not different from prediction at five percent level (two tailed t-test p-value=0.3759). Average efficiency in the unregulated locality ranged from minimum of 69.85 to maximum of 94.21. The mean was 80.02 compared to the predicted 15

value of 64. Therefore, efficiency in unregulated locality was higher than predicted in all cases (one tailed t-test p-value=0.0066). Population split: The predicted split of population across localities of 4 : 6 recorded in 21.7 percent of data. Overall 67 percent of data are within the 25 percent bandwidth (i.e. in the interval [3, 5] and [4.5, 7.5]) around the predicted value. 33 percent of records are out of 25 percent range around the prediction. Monitoring: 64.24 percent of all actions were inspected in locality with sanctions. On average monitoring cost amounted 23.3 tokens while predicted value was 40 in symmetric equilibrium.

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Discussion

Much of the study in CPR literature suggests sanctioning mechanisms are used to overcome the incentive to overexploit the community resource. Previous literature finds that sanctions as a costly activity will not imposed by selfish players (WGO 1994) while in the inspection game developed by CP (2002)can improve efficiency. The present model adds a major innovation to Casari and Plott’s sanctioning model with selfish players, a multiple locality frame and counts a monitoring cost. Our framework extends CPR problem allowing free mobility between different localities. In the one-locality design behavior is compared to point predictions for the symmetric Nash equilibrium, asymmetric Nash equilibrium and the social optimal outcome. In the two-locality design behavior is compared to point predictions of the symmetric, asymmetric Nash Free Mobility predictions and social optimal outcome. We construct four treatments to test predictions of free mobility equilibrium model. In particular, with no regulation design locality overexploited it’s resources beyond the social optimal level. With sanctions the resource use efficiency increases. In two unregulated localities the efficiency reached 77.4 percent than the predicted value of 55.6 per locality. From here we can draw the conclusion that with the less number of people the resource use is lower. Interesting results derived from the design, where one locality adopts sanctions and the other does not have regulation. As predicted sanctions allows to keep the resource use at efficient level. Unregulated locality has improved efficiency to 80 percent which is higher than prediction of 64 percent. As predicted, improvement from 55.6 to 64 percent in efficiency is due to fact that the locality with sanctions can accommodate more people than the unregu16

lated locality. Additional 16 percent improvement in efficiency resulted from the fact that subjects in the unregulated locality were imitating the choices in regulated locality. Community with sanctions served as a role model for the locality without regulation. In terms of cost of administering the institution experiments demonstrate that subjects do not monitor when people do not violate. Hence, the efficiency of the sanctioning system improves when monitoring is not full. In particular, in one locality design only 64 percent of population has been inspected and average monitoring cost was at 44.3 instead of predicted 70 tokens. In two locality design again 64 percent of actions were inspected and monitoring cost amounted 23.3 tokens while prediction was 42. Our results draw several conclusions. Most importantly we find that the institution format under the free mobility condition may survive if it adjusts to the migration process. As predicted sanctioning system increases the appropriation efficiency in the neighboring community because of the migration induced by higher efficiency in community with sanctions. In addition, regulated community may become a role model to follow for unregulated community. In terms of welfare, in the absence of free riders sanctioning institution has no deadweight loss and community may reduce this loss by randomizing inspection. In our experiments subjects ”vote by the feet” for sanctioning system over unregulated regime by choosing the locality with sanctions; that is more people have chosen locality with sanctions. Note that this conclusion is true if the benefits of regulation outweigh the monitoring costs.

References [1] Aggrawal, 2002. Appropriating the commons: A Theoretical Explanation in The Drama of the Commons, Committee on the Human Dimensions of Global Change, Elinor Ostrom, Thomas Dietz, Nives Dolsak, Paul C. Stern, Susan Stonich, and Elke U. Weber ( eds), National Research Council, National Academy Press, pp.41-86. [2] Berliant Marcus, Edwards John H. Y. 2004. Efficient Allocations in Clubs, Journal of Public Economic Theory, 6(1): 43-63. [3] Berkes, 1989. Common Property Resources - Ecology and Community Based Sustainable Development, London: Belhaven Press.

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[4] Boadway Robin, 1982a. On the Method of Taxation and the Provision of Local Public Goods: Comment, The American Economic Review, Vol.72, No 4 (Sep.,), 846-851. [5] Boadway Robin and Frank Flatters, 1982b. Efficiency and Equalization Payments in a Federal System of Government: a Syntheisi and Extension of Recent Results, Canadian Journal of Economics, XV, No4, November, 613-633. [6] Buchanan, J., 1965. An Economic Theory of Clubs, Economica 32, 1-14. [7] Buchanan J. and Goetz Charles J., 1972. Efficiency limits of fiscal mobility: an assessment of the Tiebout model. Journal of Public Economics 1, April: 25-44. [8] Casari, Marco and Plott, Charles, R. 2003. Decentralized management of common property resources: experiments with a centuries-old institution, Journal of Economic Behavior and Organization, Vol. 51: 217-247 [9] Cheung, S.N. 1970. The Structure of a Contract and the Theory of a Non-exclusive Resource. Journal of Law and Economics, l13, pp.49-70. 16. [10] Chopra, K.C. Kadekodi, and Murthy, M. 1989. ”People’s Participation and Common Property Resources”. Economic and Political Weekly, (24) pp: A.189-A.195. [11] Dawes R.M 1973.”The commons dilemma game: an N-person mixedmotive game with a dominated strategy for defection”. Oregon research Institute Research bulletin 13:1-12 [12] Dawes R.M 1975. Formal Models of Dilemmas in Social Decision Making. In Human Judgment and Decision Process: Formal and mathematical Approaches, eds.M.F.Kaplan and S.Schwartz, pp.87-108 [13] Dawes, R.M. 1980. Social Dilemmas. Annual Review of Psychology 31:169-193. [14] Demsetz H., 1967. Toward a theory of property rights. American Economic Review 57: 34759

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[15] Flatters Frank, Henderson Vernon and Mieszkowski Peter, 1974 Public goods, efficiency, and regional fiscal equalization. Journal of Public Economics 3(May): 99-112 [16] Farrel Joseph, Scotchmer Suzanne ”Partnerships” QJE Vol. 103 (2): 279-297. [17] Falk Armin, Fehr Ernst, and Fischbacher Uhs, 2002. Appropriating the commons: A Theoretical Explanation in The Drama of the Commons, Committee on the Human Dimensions of Global Change, Elinor Ostrom, Thomas Dietz, Nives Dolsak, Paul C. Stern, Susan Stonich, and Elke U. Weber (eds), National Research Council, National Academy Press, pp.157-192. [18] Fehr, E., Gchter, S., 2000 Cooperation and punishment in public goods experiments. American Economic Review 90 (4), 980994. [19] Fehr, E., K. Schmidt 1999 A Theory of Fairness, Competition, and Cooperation. Quarterly Journal of Economics, 114: 817-851. [20] Greenberg, J. and S. Weber (1986): ”Strong Tiebout equilibrium under restricted preference domain,” Journal of Economic Theory, 38: 101-11. [21] Goren Hagel, Kurzban Robert and Rapoport Amnon. 2003. Social loafing vs. social enhancement: Public goods provisioning in real-time with irrevocable commitments. Organizational Behavior and Human Decision Processes 90: 277-290 [22] Hardin, G., (1968). The Tragedy of the Commons. Science. 162: 124348. [23] Holmstrom (1983). Moral Hazard in Teams. Bell journal of Economics 13: 324-40 [24] Hoel Michael (2002) Interregional interactions and population mobility working paper [25] Jodha, N.S. 1986. Common Property Resources and the Rural Poor in Dry Regions of India. Economic and Political Weekly. 21 (27): 169-181. [26] Johnson, O.E.G. 1972. Economic Analysis, the Legal Framework and Land Tenure Systems. Journal of Law and Economics. 15: 259-276. 19

[27] Kopelman, Shirli, Weber, J. Mark and Messick, David M. 2002. Appropriating the commons: Factors Influencing Cooperation in Commons Dilemmas: A Review of Experimental Psychological Research in The Drama of the Commons, Committee on the Human Dimensions of Global Change, Elinor Ostrom, Thomas Dietz, Nives Dolsak, Paul C. Stern, Susan Stonich, and Elke U. Weber ( eds), National Research Council, National Academy Press, pp.113-156. [28] Levine, D. 1998 Modeling Altruism and Spitefulness in Experiments. Review of Economic Dynamics 1: 593-622. [29] Moir, R., 1999 Spies and swords: behavior in environments with costly monitoring and sanctioning. Manuscript, Department of Economics, University of New Brunswick, Canada. [30] Olson, M. 1965. The Logic of Collective Action. Cambridge, Mass: Harvard University Press [31] Ostrom E. 1990. Governing the Commons: The Evolution of Institutions for Collective Action. Cambridge University Press, New York. [32] Ostrom Elinor, James Walker, and R.Gadner, 1992. Covenants with and without a sword: self-governance is possible. American Political Science Review 86: 404-417 [33] Oates E. Wallace. 1969. The effects of property taxes and local public spending on property values: an empirical study of tax capitalization and Tiebout hypothesis. Journal of Political Economy, 77 (6 November/December): 957-971. [34] Oates E. Wallace. 1999. An essay on Fiscal Federalism. Journal of Economic Literature, 37 (3): 1120-1149 [35] Rabin, M. 1993. Incorporating Fairness into Game Theory and Economics. American Economic Review 83(5): 1281-1302. [36] Sato, K. 1987. Distribution of the cost of maintaining common resources, Journal of experimental Social Psychology, 23: 19-31 [37] Smith, R. 1981. ”Resolving the Tragedy of the Commons by Creating Private Property Rights in Wildlife”. CATO Journal, (1), pp.439-468. 20

[38] Starrett A. David, 1980. On the Method of Taxation and the Provision of Local Public Goods: reply, The American Economic Review, Vol. 72(September): 852-853. [39] Starrett A. David, 1982. On the Method of Taxation and the Provision of Local Public Goods, The American Economic Review, 70 (3): 380-392. [40] Tiebout C. 1956. A Pure Theory of Local Expenditure, Journal of Political Economy 64, 416-424. Tenbrunsel, A.E. and Messick, D.M. (1999). Sanctioning systems, decision frames,. and cooperation. Administrative Science Quarterly, 44: 684-707. [41] Ellickson, Grodal, Scotchmer, and Zame. (1999) Clubs and the Market, Econometrica, 67 (5): 1185-1217. [42] MAria Alejandra Velez, John K. Stranlund and James J. Murthy 2005 What motivates Common Pool Resource Users? Experimental Evidence from the field. University of Massachusetts, Department of Resource Economics working paper No 2005-4. [43] Walker,James, R.Gadner,and Ostrom, Elinor, 1990. Rent dissipation in a limited-access common-pool resource: Experimental evidence. Journal of Environmental Economics and Management. 19: 203-211. [44] Walker,James and R.Gadner, 1992. Probabilistic Destruction of Common-Pool Resources: Experimental Evidence. The Economic Journal 102(September): 1149-1161. [45] Urs Fischbacher 2007, z-Tree: Zurich Toolbox for Ready-made Economic Experiments, Experimental Economics 10(2): 171-178.

6

Appendix Equilibrium with two types of herders

There are v violators and n − v non-violators, where n is the total population of a community. Let’s solve for all possible equilibria with two types ( violators and non-violators), assuming symmetric behavior within the type. v We need to solve for pnv , pv , with xnv i and xj . Probability to monitor others for non-violators and violators denoted by pnv and pv , respectively. By 21

assumption, the harvesting level for non-violator is given and equal to the threshold level, xnv = λ. For simplicity, we denote xj ≡ xvj - per person i harvesting level of a violator. If a combination of pnv , pv , xj and λ constitute an equilibrium, then the following incentive constraints hold: Non-violator’s incentive constraints for the harvesting level: EP nv (N otV iolate) ≥ EP nv (V iolate);

(1)

Violator’s incentive constraints for their harvesting level: EP v (V iolate) ≥ EP v (N otV iolate);

(2)

Further, there should be appropriate equilibrium condition on monitoring probabilities pnv , pv (to be discussed below). Monitoring probabilities should satisfy the following: pi = 1 if EP i (Inspect) > EP i (N otInspect); pi ∈ [0, 1] if EP i (Inspect) = EP i (N otInspect); pi = 0 if EP i (Inspect) < EP i (N otInspect), i = v, nv.

(3) (4) (5)

We start with the conditions 1 and 2 on harvesting. • Expected payoff from not violating for the non-violator is determined by: nv EP nv (xi = λ) = (a − c − bX−i )λ − bλ2 ; (6) nv where X−i is a total harvesting level of all agents other than one nonviolator i. It combines harvesting level for both types except one nonviolator i nv X−i = vxj + (n − v − 1)λ; (7)

and xj is the harvesting choice of violators. Expected payoff from violating the threshold, by choosing some xi > λ, for non-violator is given by pv v + pnv (n − v − 1) )(xi −λ); n−1 (8) It is sufficient to show that (1) holds for x∗i > λ that maximizes expression (8) over all xi ≥ λ. Maximum payoff is at x∗i where the FOC nv EP nv (xi > λ) = (a−c−bX−i )xi −bx2i −h(

22

holds: pv v + pnv (n − v − 1) ∂EP nv nv (xi = x∗i ) = (a−c−bX−i )−2bxi −h( ) = 0; ∂xi n−1 (9) which leads to v v+pnv (n−v−1)

x∗i

=

a − c − h( p

n−1

nv ) − bX−i

2b

;

(10)

From (6) and (8) incentive constraint (1) for non-violator becomes: pv v + pnv (n − v − 1) ∗ nv )(xi −λ) ≤ (a−c−bX−i )λ−bλ2 ; n−1 (11) ∗ where xi is given by (10). By substituting (10) into (11), we obtain that the incentive constraints (1) for non-violators holds if nv (a−c−bX−i )x∗i −bx∗2 i −h(

xj ≥

a − c − h(pv v + pnv (n − v − 1)) − bλ(n − v + 1) ; vb

(12)

• Violators harvesting level , xj , exceeds the threshold. For violators, the expected payoff from not violating equals to v EP v (xj ≡ λ) = (a − c − bX−j )λ − bλ2 ;

(13)

v is the harvesting level of all others except one violator j: where X−j v X−j = (v − 1)xj + (n − v)λ;

(14)

Violators expected payoff from violating is given by: pv (v − 1) + pnv (n − v) )(xj −λ); n−1 (15) It is sufficient to assume that exists at least one xj , where (2) holds. A necessary condition for such xj to exist is to have (2) hold at x∗j that maximizes (15). Solving for such x∗j , violator maximizes her payoff at x∗j ≥ λ: v EP v (xj > λ) = (a−c−bX−j )xj −bx2j −h(

pv (v − 1) + pnv (n − v) ∂EP v v = (a − c − bX−j ) − 2bxj − h( ) = 0; (16) ∂xj n−1 23

hence, v (v−1)+pnv (n−v)

x∗j

=

a − c − h( p

n−1

2b

v ) − bX−j

;

(17)

From (13) and (15) incentive constraint (2) for violator becomes: pv (v − 1) + pnv (n − v) ∗ v )(xj −λ) ≤ (a−c−bX−j )λ−bλ2 ; n−1 (18) By substituting (17) into (18), we obtain that incentive constraints (2) for violators holds if

v (a−c−bX−j )x∗j −bx∗2 j −h(

xj ≤

a − c − h(pv (v − 1) + pnv (n − v)) − bλ(n − v + 2) ; (v − 1)b

(19)

• We now turn to inspection decision. After the harvesting decision herders are free to inspect any other herder and generate revenue from monitoring activity. Agents monitor for sure if the expected revenue from monitoring others exceeds monitoring cost; they are indifferent between monitoring or not if expected revenue from monitoring equals monitoring cost; and they will not monitor if expected revenue from monitoring is less than monitoring cost. This implies following conditions for equilibrium monitoring probabilities for non-violator: pnv = 1 if EP nv (Inspect) > EP nv (N otInspect); pnv ∈ [0, 1] if EP nv (Inspect) = EP nv (N otInspect); pnv = 0 if EP nv (Inspect) < EP nv (N otInspect).

(20) (21) (22)

Note that EP (N otInspect) = 0, EP (Inspect) = ER(Inspect)−Cost(Inspect). Revenue from monitoring for a non-violating agent i depends on the percent of population that violates excluding i, v/(n − 1). Since, v · (xj − λ) · h, and Costnv (Inspect) = k we get: ERnv (Inspect) = n−1 v · (xj − λ) · h > k; n−1 v ∈ [0, 1] if · (xj − λ) · h = k; n−1 v = 0 if · (xj − λ) · h < k. n−1

pnv = 1 if

(23)

pnv

(24)

pnv

24

(25)

This implies that we may have pnv ∈ (0, 1) only if: k(n − 1) + λ; hv Equilibrium conditions on pnv are: k(n − 1) if xj > + λ, then pnv = 1; h·v k(n − 1) if xj = + λ, then pnv ∈ [0, 1]; h·v k(n − 1) + λ, then pnv = 0. if xj < h·v xj =

(26)

(27) (28) (29)

• Violator monitors with probability, pv ∈ [0, 1], and her decision is determined by the following conditions: pv = 1 if EP v (Inspect) > EP v (N otInspect); pv ∈ (0, 1) if EP v (Inspect) = EP v (N otInspect); pv = 0 if EP v (Inspect) < EP v (N otInspect).

(30) (31) (32)

v−1 We know that ERv (Inspect) = n−1 · (xj − λ) · h, Costv (Inspect) = k we get: v−1 pv = 1 if (xj − λ)h > k; (33) n−1 v−1 pv ∈ [0, 1] if (xj − λ)h = k; (34) n−1 v−1 pv = 0 if (xj − λ)h < k. (35) n−1

Violator may follow a mixed strategy in monitoring, pnv ∈ (0, 1) if: k(n − 1) xj = + λ; h(v − 1) Equilibrium conditions on pv are as follows: k(n − 1) if xj > + λ, then pv = 1; h · (v − 1) k(n − 1) if xj = + λ, then pv ∈ [0, 1]; h · (v − 1) k(n − 1) if xj < + λ, then pv = 0. h · (v − 1) 25

only (36)

(37) (38) (39)

We know that v > v − 1, therefore, conditions (26) and (36) cannot hold together, which implies that there is no way to have identical probability in monitoring for both types pnv ≥ pv (40) and the only possible cases are: either pnv = pv = 1; or pnv ∈ (0, 1], pv ∈ [0, 1), pnv > pv ; or pnv = pv = 0;

(41) (42) (43)

Equation in 42 reads as in the footnote8 . To summarize, it follows that in equilibrium incentive conditions (12), (19) and one of monitoring conditions (41), (42) or (43) must hold. Condition in (40) helps to eliminate multiple equilibria. Suppose xj < xnv j =

k(n − 1) k(n − 1) +λ< +λ hv h(v − 1)

(48)

then we would have pnv = pv = 0. But this is not an equilibrium with inspection game because conditions in (12), (19) are not consistent with (25) and (35). Suppose k(n − 1) +λ (49) xj > xvj = h(v − 1) then pnv = 1 and pv = 1. This is the case when all herders are identical and do violate such that monitoring is profitable. However, conditions (12), (19), (23) and (33) can’t be satisfied at the same time. When xj = xnv j =

k(n − 1) k(n − 1) +λ< +λ hv h(v − 1)

(50)

8

pnv pnv pnv pnv

= 1, pv ∈ (0, 1); = 1, pv = 0; ∈ (0, 1), pv ∈ (0, 1), pnv > pv ; ∈ (0, 1), pv = 0.

26

(44) (45) (46) (47)

pnv ∈ (0, 1), pv = 0. But this is impossible since IC in (12), (19) and (24), (35) do not hold. Suppose k(n − 1) k(n − 1) + λ < xj < +λ hv h(v − 1)

(51)

then pnv = 1, pv = 0. However, this is not an equilibrium since IC set in (12), (19) is empty to satisfy (23) and (35). Nash equilibrium exists with xj = xvj =

k(n − 1) +λ h(v − 1)

(52)

R −1) where pnv = 1, pv ∈ (0, 1) and X ∗ = vxj + (nR − v)λ = v( k(n + λ) + h(v−1) R −1)v (nR − v)λ = k(n + nR λ. Then equations in (12), (19), (23) and (34) do h(v−1) hold. If n = v, then we obtain a symmetric equilibrium (all agents violate). Table 4 below gives equilibrium xj , pv and pnv for each case v = 1, ..., 10. Table 6 has details of equilibrium in two-locality case.

27

Table 1: Equilibrium Predictions (excluding endowments) T reat N Social N ash M ax Eqlm ment Optimal eqlm Surplus Surplus opt (N) 10 X = 180 X = 327.3 Π = 1080 Π = 357.7 xopt = 18 x = 32.7 π = 35.77 (S) 10 X opt = 180 X = 193 Π = 1080 Π = 1010 P P opt v one x = 18 x = 19.3 λ = 18 = π− k type π v = 101 number of pv = 0.93 violations: 10 opt (S) 10 X = 180 X = [193.1, 203] Π = 1080 Π = 1010 P P opt nv two x = 18 x = 18 λ = 18 = π− k types xv = [19.5, 30] π v = 101 π nv = 101 pnv = 1 number of v p ∈ (0, 1) violations: 2-9 (N,N) 10 Xiopt = 180 X(n1) = 300 Π = 1080 Π1 = 600 i = 1, 2 X(n2) = 300 per loc. Π2 = 600 n1 = 5 per loc. n2 = 5 x(n1) = 60 x(n2) = 60 π(n1) = 120 π(n2) = 120 (N,S) 10 Xiopt = 180 X(N ) = 288 Π = 1080 Π(N ) = 691.2 one i = 1, 2 X(S) = 188.4 per loc. Π(S) = 1038 P P type n1 = 4 = π− k n2 = 6 x(N ) = 72 xv (S) = 31.4 λ = 30 π(N ) = 172.8 π(S) = 173 number of pv (S) = 0.95 violations: 6 opt (N,S) 10 Xi = 180 X(N ) = 288 Π = 1080 Π(N ) = 691.2 two i = 1, 2 X(S) = [188.7, 194] per loc. Π(S) = 1038 P P types n1 = 4 = π− k n2 = 6 x(N ) = 72 28 xnv (S) = 30 λ = 30 v x (S) = [31.8, 37] π(N ) = 172.8 π(S) = 173 pnv (S) = 1 number of v p (S) ∈ (0, 1) violations: 2-5 N- number of subjects; Eqlm-equilibrium; Eff-cy -efficiency. Efficiency in locality with sanctions is less than 100 percent due to monitoring costs.

Ef f − cy 33.1

93.5

93.5

55.6

64.0 (loc.N ) 96.1 (loc.S)

64.0 (loc.N ) 96.1 (loc.S)

Table 2: Summary of Experimental Sessions (Experimental design) Number of periods Date Session Code Design 1 : (N ), (N, N ) 10, 10 June7, 2006 N1 10, 10 June8, 2006 N2 Design 2 : (N ), (S), (N, S) 10,10 June2, 2006 S1 10, 10 June5, 2006 S2 6, 10 June6, 2006 S3 6, 10 June7, 2006 S4 6, 10 June8, 2006 S5 6, 10 June9, 2006 S6

Table 3: Efficient Outcome V ariable N otation V alue Total appropriation X 180 Harvesting level per person xi = xj 18 nv v Monitoring probabilities p =p 0 Monitoring Cost MC 0 Surplus 1080 Ef f iciency 100 percent

29

Table 4: Equilibrium predictions with two types (including monitoring profit) and sanctions in one locality(λ = 18) v xj xi X pv pnv Sur Ef f i N um M on. Sur = plus ciency ber of pro plus∗ λ w/o inspec f it with nv MP tions p/p M P nv 10 19.3 18 192.9 0.93 1010 93.5 9.28 1010 9 19.5 18 193.1 0.92 1 1009 93.4 9.28 0.87 1010 8 19.7 18 193.3 0.91 1 1008 93.3 9.26 1.00 1010 7 19.9 18 193.6 0.89 1 1007 93.2 9.24 1.17 1010 6 20.3 18 193.9 0.84 1 1004 93.0 9.22 1.39 1010 5 20.9 18 194.6 0.78 1 1001 92.7 9.19 1.75 1010 4 21.9 18 195.6 0.68 1 996 92.2 9.14 2.33 1010 3 23.8 18 197.5 0.68 1 986 91.3 9.03 3.49 1010 2 29.7 18 203.3 0.35 1 954 88.3 8.70 7.00 1010 1 v-number of violators; (n-v)- number of non-violators; Mon. cost, M C = k·n, v , is a monis a monitoring cost; Mon. profit, M Pinv = ((xj − λ) · h − k) n−1 itoring profit per non-violator( Note: it is zero for violator); Ef f iciency ∗ includes monitoring profit of non-violators.

Ef f i ciency ∗

93.5 93.5 93.5 93.5 93.5 93.5 93.5 93.5 93.5 -

Table 5: Equilibrium Predictions with two types on Inspection decision, sanctions in one locality (λ = 18) EPjv Number of Number of M on. EPinv v xj xi EPinv w/o mon. with mon. Inspections V iolations cost prof it prof it 10 19.2963 18 0 101 101 9.27984 10 64.96 9 19.4583 18 100.13 101 101 9.27083 9 64.96 8 19.6667 18 99.99 101 101 9.25926 8 64.81 7 19.9445 18 99.83 101 101 9.24383 7 64.7 6 20.3333 18 99.6 101 101 9.2222 6 64.56 5 20.9167 18 99.25 101 101 9.18982 5 64.33 4 21.8889 18 98.67 101 101 9.1358 4 63.95 3 23.8333 18 97.5 101 101 9.02778 3 63.19 2 29.6667 18 94 101 101 8.7037 2 60.93 1 EPinv -expected profit of non-violator; EPjv - expected profit for violator. 30

Table 6: Equilibrium predictions with two types in locality with sanctions, two-locality economy (λ = 18). Total number of people: n = 6. v xj X pv pnv S Ef f N um. M Pinv M Pinv S∗ Insp. p/p total 6 31.4 188.4 0.95 1 1038 96.1 5.72 1038 5 31.8 188.7 0.94 1 1037 96.0 5.7 1.75 1.75 1038 4 32.3 189.3 0.92 1 1033 95.7 5.69 2.3 4.6 1038 3 33.5 190.5 0.88 1 1028 95.1 5.65 3.5 10.5 1038 2 37.0 194.0 0.77 1 1010 93.5 5.53 7.0 28 1038 1 ∗ ∗ S- surplus, Eff- efficiency; S and Ef f - surplus and efficiency including monitoring profit, Num.Insp.- number of inspections, M Pinv - monitoring profit of non-violator.

Ef f ∗ 96.1 96.1 96.1 96.1 96.1 -

Table 7: Equilibrium Predictions with two types on Inspection decision, sanctions in one locality and no sanctions in other locality (λ = 18) v xj xi = λ EPinv EPinv EPjv Number of Number of M on.Cost Inspections V iolations 6 31.4 30 0 173 173 5.72 6 40.00 5 31.75 30 171.5 173 173 5.7 5 39.96 4 32.3 30 170.7 173 173 5.69 4 39.8 3 33.5 30 169.5 173 173 5.65 3 39.55 2 37.0 30 166.0 173 173 5.53 2 38.70 1 Mon.Cost-monitoring cost.

31

Table 8: Average Appropriation Ses− sion All N1 N2 S1 S2 S3

S4

S5

S6

303.1 24.1

299 82.2

316.3 70.6

279.2 55.9

T reat ment (N )

P re dict 327

(S)

203

214.7 22.3

(N N )

300

230.5 17.1

242.6 218.4 57.6 50.1

0.1797

300

266.3 14.9

255.8 39.8

276.8 48.3

0.1797

per loca lity 288

248.4 25.3

249.2 247.6 9.3 41.3

0.0679

Ave− rage (N S)

317.0 37.8

331.9 29.2

233.4 28.0

283.3 329.5 74.5 46.8

268.8 53.2

174.8 208.9 28.8 41.2

210.9 231.8 235.2 14.0 36.5 45.5

190.4 263.5 251.5 72.7 55.7 46.2

188

208.7 238.5 34.2 58.2

p− value 0.0357

226.6 0.1730 36.7

247.5 68.9

0.0277

169.9 145.6 158.9 184.2 187.6 161 182.3 0.0277 17.1 33.7 15.5 23.9 24.4 12.6 24.2 Social optimal group use equal to 180 per locality. P-values are from the Wilcoxon signed ranks test on equality of experimental results with Nash predicted value

32

Table 9: Average Efficiency Ses− sion All

N1

N2

S1

S2

S3

S4

S5

S6

42.5 16.4

38.1 30.8

26.4 27.0

51.6 46.2

25 44.6

68.4 33.8

39.3 74.0

29.8 67.2

61.6 38.5

94.5 2.71

88.2 17.0

91.9 3.23

86.1 13.4

79.7 17.4

84.3 13.2

T reat ment (N )

P re dict 33.1

(S)

93.5

87.4 5.34

(N N )

55.6

83.57 6.92

78.68 88.46 27.8 25.3

0.1797

55.6

71.23 9.4

77.86 18.9

64.6 24.9

0.1797

per loca lity 5

77.4 25.2

78.27 76.53 23.1 27.3

0.0679

5.45 0.35 4.55 0.35 80.02 8.77

5.7 1.16 4.3 1.16

0.1797

Ave− rage Ave− rage split (N S)

5 64.0

5.2 1.14 4.8 1.14

p− value 0.2626

0.0464

0.1797 84.97 69.85 78.30 24.3 25.3 32.3

96.1

94.21 80.03 5.34 22.6

72.75 32.6

0.0277

95.26 91.1 95.4 96.0 97.3 95.7 95.96 0.2476 2.13 10.75 2.13 4.99 2.8 1.42 3.04 Ave− 4 4.73 5.2 4.5 4.8 5.3 4.4 4.2 0.0277 rage 0.45 1.23 1.78 1.32 1.49 1.26 1.4 split 6 5.27 4.8 5.5 5.2 4.7 5.6 5.8 0.0277 0.45 1.23 1.78 1.32 1.49 1.26 1.4 P-values are from the Wilcoxon signed ranks test on equality of experimental results with Nash predicted value

33

Table 10: Mean of individual use All S e s s i o 1 2 3 4 5 6 30.62 28.3 32.9 26.9 29.9 31.6 27.9 5.78 7.5 4.7 5.3 8.2 7.1 5.6

T reat ment N

P redict

S

19.3

21.47 17.5 20.9 3.95 2.8 4.1

NN

60

42.96 43.0 42.9 8.33 8.2 8.9 61.78 61.7 60.9 16.46 15.8 17.9

32.7

60

NS

72

21.1 1.4

n 7 31.7 3.8

8 p − value 33.2 0.0357 2.9

23.2 23.5 22.7 3.6 4.5 3.7

52.3 35.7 64.2 54.6 40.9 56.7 61.5 16.0 8.3 18.4 11.8 7.1 14.8 11.5 31.4 34.5 30.9 32.4 37.8 43.3 29.7 32.8 10.7 6.3 13.5 11.3 13.2 5.1 7.7 P-values are from the Wilcoxon signed ranks test on equality of experimental results with Nash predicted value

34

0.1159

0.1797 0.1797

0.0277 0.2489