Dec 1, 1999 - Bowles, Jeff Carpenter, Elinor Ostrom, John Stranlund, James Walker ... Hernandez at Humboldt, Carmen Candelo at WWF and Juan Gaviria, ...
“Overcoming Asymmetries in Local Commons Dilemmas: Evidence from Field Experiments” Juan Camilo Cardenas1 December, 1999
Abstract: This paper explores through a set of field experiments the effects of asymmetric payoff structures in a local commons dilemma by varying the individual wage on the effort allocated outside the commons and observing the individual’s behavior in asymmetric and symmetric wage groups. In both treatments groups of eight subjects go through a first set of rounds under no communication and a second stage with group discussions before each round. The results confirm that non-binding communication is effective in fostering cooperation and reducing free-riding. We found higher levels of group efficiency achieved by heterogenous groups, but contrary to theoretical predictions, the gains in efficiency were due to the high co operation by the low o utside wage players while the high wage players remained clo ser to their Nash best response which was, however, less detrimental to group efficiency. Further, face-to-face communication induced changes in behavior mainly for the low wage players but not for the high wage one s. However, those groups w ho achieved the h ighest social efficiencies, particularly after communication was allowed, did it by developing a shared n orm of equal effort across the high and low w age types, despite the fact that the social optimal solution called for differentiated strategies for “rich” and “po or”. Such a se cond-b est strategy yielded hig her gains and was easier and less costly to monitor and reinforce b y the group. The results sugge st that, contrary to co nvention al wisdom , poverty may not le ad inevitably to o verextracting of common-pool resources. The results also contribute to qualify the propositio ns by Olson (1965) and Bergstrom , Blume an d Varian (198 6) that income and wealth inequalities could increase cooperation in collective action dilemm as.
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This research has been possible because of the ideas and support at different stages from Samuel Bowles, Jeff Carpenter, Elinor Ostrom, John Stranlund, James Walker and Cleve Willis. Errors remain on the author’s. In Co lombia I mu st thank the field practitioners an d fellows from H umbo ldt, WW F and Fun dacion N atura who he lped pre-te st and con duct the experimen ts. Very special than ks are due Lu is Guillermo Baptiste and Sarah Hernande z at Humb oldt, Carme n Cand elo at WW F and Juan Gaviria, Nancy Vargas and Danilo Salas at Natu ra. Financial support for the field work was provided by the MacArthur Foundation, the Instituto de Investigacion de Recurso s Biologic os Alexande r von Hum boldt, the WWF Colom bian program , and Fund acion Natu ra - Colomb ia. Also thanks to Resources for the Future for financial support at the last stage of this research.
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1.
Introduction. Many communities use local commons resources as an important component of their income
sources2. People allocate individual effort between extracting common-pool resources and an outside option given by their private opportunities and based on their physical or human capital. One of the common ways group heterogeneity can play a role in the use of these resources is by having asymmetries in their outside options. Some users may have different possibilities for allocating their effort outside the commons, making their marginal benefits from using the commons asymmetric. Unequal land ownership, access to credit, or education provide some group members better income sources outside the commons. Intuitively, some might argue that people with better exit options should extract less from the local commons, while others worse off should extract more as their incomes depend more on extraction. Others might reason that those with fewer outside alternatives might be more interested in sustainable extraction of the resource as their marginal gains from conservation are higher. In either case, the social outcome will depend on the individuals’ rationality determined by the incentives to free-ride (over extract) and the possible Pareto improvements from cooperation by group members. The literature on group heterogeneity and the possibilities of cooperation and collective action in groups is vast but inconclusive, ranging from those who believe heterogeneity fosters cooperation and public goods provision by the rich, to those who stress the detrimental effects of inequality and social distance on cooperation. How these asymmetric outside options affect the possibilities for cooperation or free-riding in the use of the resource is the matter
2
‘Local commons’ is assumed here to be a situation in which a group has access to a common-pool resource, and where there is partial excludability and partial rivalry or subtractability (Ostrom, 1990). In this sense, the local comm ons shares the subtractability feature with private goods and th e nonexludab ility from private goods, but it do es no t nec essar ily me an a re sou rce o wne d co mmu nally.
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of this paper. We have addressed such questions by developing a model of a group of individuals who use a forest that provides multiple benefits to them. Besides the benefits from use and non-use values of the forest, their incomes also depend on an outside private alternative represented by a marginal rate (wage) on effort not allocated to extracting resources. In other words, income depends on the allocation of time between extracting the forest which poses a group negative externality (e.g. water quality) and from the alternative outside the forest which yields a private marginal rate. We introduce heterogeneity by assigning asymmetric wages within the group, that is, some in a group earn a much higher rate on their best private alternative; others earn a much smaller rate. Therefore, although all may benefit equally from extracting the forest, the opportunity cost of labor on extracting it is dependant on their next best alternative. The model generates two benchmark solutions. One is the social optimal benchmark, where the group’s outcome is maximized through perfect coordination of individual actions, and the other is a Nash (sub optimal) equilibrium where individuals maximize their income assuming no coordination of their actions with others. To test for the effects of these asymmetric payoff structures, we compared the asymmetric treatment to a baseline symmetric wages case. In both treatments the groups had to go through a first set of rounds where no communication was allowed among the eight group members, and then a second set of rounds with group discussions before each round. These experiments were undertaken with the participation of 120 real local commons users in three rural villages in Colombia where communities have access to a common-pool of forest that provides firewood, food, and fiber. As with other similar experimental evidence, our results confirm that people do not behave according to the free-riding prediction and, rather, they are willing to cooperate, but they cannot 3
achieve the full social optimum. Also we confirm that face-to-face communication, even though it is not binding, acts as an effective mechanism, to the community to foster a group-maximizing behavior and move it away from the Nash benchmark. Compared to the baseline symmetric case where all eight members have the same outside wage, the heterogeneous groups achieved, on average, higher levels of social efficiency. The asymmetric structure of the payoff functions did induce different behaviors in the two types (high and low outside wages), and different behaviors from the symmetric case, but the gains in social efficiency were achieved mostly by a combination of two processes. First, the actions of the subgroup of six low wage members attempted a cooperative strategy more compatible with the group maximization, and secondly the two high wage members behaved more closely to the Nash prediction, which at the levels of cooperation of the other sub-group was more helpful to the group outcome. However, the group efficiency among the asymmetric groups varied enough to analyze the data further, given that some symmetric groups achieved higher levels of efficiency than asymmetric ones. We found that the asymmetric groups who achieved the higher levels of efficiency after communication was allowed did by attempting to develop a shared norm of equal appropriation of the forest, despite the fact that the social optimal solution asked for a differentiated strategy where the two high wage members do not use the forest at all, and the six low wage participants use it at a low level. These groups found it more effective to develop a second-best but simpler strategy to increase group and individual earnings by calling for a homogenous level of effort across the two types. Additional data analysis and video/audio tape recordings confirm that the capacity of groups for self-governance and monitoring of individuals’ actions was more effective for simpler norms such 4
as “let’s play lower numbers” rather than trying a more complex set of rules.
2.
Asymmetries, inequality and group heterogeneity How heterogeneity affects cooperation remains open to debate (Varughese and Ostrom,
1999). Much of the arguments in the literature regarding heterogeneity as a positive factor in collective action dilemmas are based on the view that the wealthier group members would be the main or sole providers of the public good, while the poorer would free-ride on such contributions (Bergstrom, Blume and Varian,1986; Olson, 1965). Such propositions have been challenged by experimental, theoretical and field evidence. Bardhan, Bowles and Gintis (1998) survey the effects of wealth inequality on economic performance, and they show the problems induced by asset inequality in the case of fishermen dilemmas, given the asymmetric information nature of the problem. Other works on the problems of heterogeneity and inequality in local commons settings can be found in Baland and Plattteau (1997, 1998), Bardhan, (1993, 1999), Dayton-Johnson and Bardhan (1998) and De Janvry et.al (1988). In most of these works the heterogeneity introduced in the utility function of group members could take multiple forms and therefore the variety of results leave open the question of whether heterogeneity affects cooperation positively or negatively. Ostrom and Gardner (1993) also study heterogeneity in local commons for the case of physical asymmetries in the appropriation of a resource, for instance, in the location (tail-ender, head-ender) of the users of an irrigation system. In fact, Sandler (1996), developing further Olson’s arguments and model, suggests that depending on the technology of the externality and the kind of inequality being studied, the relation between heterogeneity and cooperation may go from negative to positive. On the experimental evidence, Ledyard’s (1995) survey finds heterogeneity to be one of the 5
‘weak’ factors that seem to affect contributions in public goods experiments. Two major types of heterogeneity are discussed, heterogeneity in the “environment” variables such as payoffs and endowments and variance in the “systemic” variables among which he mentions economics training, beliefs, and gender. The review of evidence, he suggests, seems to show a generally negative relation between heterogeneity and contributions, although the evidence is not strong. Chan et.al. (1996) recently tested the theoretical predictions by Bergstrom, Blume and Varian (1986), henceforth BBV, on the effects of income redistributions on private contributions to a public good, and found that although the more unequal groups did increase the level of aggregate contributions, it was by heavier contributions from the poorer and lighter contributions from the richer players. Therefore, the higher social efficiency of the heterogenous groups could not be attributed to the higher cooperation by the wealthier players. In an attempt to explore the same issue, Hackett, Schlager and Walker (1994) studied the effect of communication in solving commons dilemmas by introducing heterogeneity in the initial endowment to be allocated in the private and public goods investments under a CPR design. They found that despite heterogeneity, communication remained effective in inducing cooperation. However, homogeneity made the development of rules simpler and easier to endorse and enforce. Their findings also suggest that the complexity introduced by heterogeneity leads to confusion and difficulties on maintaining the agreements discussed in the communication stage: “Face-to-face communication is a powerful tool. It is handicapped significantly, however, in situations in which group members are unable to develop or sustain the social capital necessary for enduring commitments (1996: 123)”. In fact we have tested these claims using same experimental data by examining how the actual characteristics of the subjects in these groups affected the experimental outcomes and have found that the heterogeneity of the group in 6
terms of actual wealth and economic activity of the eight players decreased social efficiency, perhaps because of the social distance and less familiarity with local commons dilemmas created by ownership of wealth and a production system less dependent on social relations with neighbors (Cardenas, 1999).
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Experimental design The methodological approach for the model and experiment follows substantially that of
Ostrom, Gardner and Walker (1994), henceforth OGW, which has become the main point of departure for experiments on common-pool resources dilemmas. We try to isolate one type of inequality and study how it affects the outcome of solving a commons dilemma in the following manner. When allocating available labor between extracting from a forest and a private alternative (e.g. work on own land or in the wage market), households find it in their best interest to equalize the marginal benefits from using the forest to the marginal value of their next best alternative outside it. The marginal value from the forest, however, depends negatively on the allocation of labor by the entire community. As the forest becomes more heavily extracted, the individual household should find it better to allocate more labor into their best private alternative, which should provide higher yields. However, it also depends on the rate that labor produces outside the forest. Therefore, the unequal set of outside wages will create unequal levels of extraction at both the optimal solution and the Nash sub-optimal equilibrium.
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3.1
The payoff model. The payoffs for our experiments were generated by a simple model of a fixed number of
homogenous individuals that exploit a local forest for firewood. In each round of the games, each individual is given an endowment of time e that can be allocated to collecting firewood or to allocating labor into a private alternative such as the wage market or working on her own land. Let xi denote the amount of time individual i spends collecting firewood from the common, and let w denote the prevailing wage for that outside private alternative. Then, i’s decision to provide (e - xi) units of labor to the private alternative yields a payoff of w × (e - xi). As one can expect, within a community some individuals will have higher and others lower w wages according to their skills or assets. We will call “rich” those individuals with higher wi rates, and “poor” those with lower. In our experimental design, we will introduce asymmetries within groups of a community by varying this wage rate w across individuals in a group. Time spent collecting firewood from the forest yields a private benefit, which we assume takes the quadratic form g(xi) = ( xi - N (xi)2 /2, where ( and N are strictly positive and are chosen in part to guarantee g(xi) > 0, for xi 0 [1, e]. The strict concavity of g(xi) indicates diminishing marginal private returns to time spent collecting firewood. Subjects were told explicitly that their decision to spend time extracting firewood would also affect water quality in the area adversely, for instance, because of erosion and sedimentation at the upper watershed. We assumed that water quality q is a quadratic function of the aggregate amount of time individuals in the community spend collecting firewood; specifically, q(3xj) = q0 - (3xj)2 /2, where q0 is interpreted to be water quality in the absence of firewood extraction. Again these parameters are chosen in part to guarantee q(3xj) > 0 for all feasible 3xj. An individual’s valuation 8
of water quality is f(3xj) = q(3xj). Define u(xi, 3xj) to be the sum of the sources of utility for an individual exploiter of the local forest. Parameters were chosen, in part, to guarantee that u(xi, 3xj) > 0 for all possible xi and 3xj. To facilitate scaling individual payoffs, we take an individual’s payoff function to be a positive, monotonic transformation F of u. In particular, F(u) =k(u)0 , where k and 0 are all positive constants. An individual’s payoff function is then
U i(xi, 3x j) = k[(q o -(3x j)2 /2) + ((x i - N(xi)2 /2) + w i×(e-x i)] 0
[1]
Each group consisted of n = 8 subjects, and each subject was allocated e = 8 units of time in each round. Pre-testing of the experimental designs at the University of Massachusetts and at the Humboldt Institute for Biodiversity in Villa de Leyva, Colombia, led us to denominate units of time as months per year. Scale concerns led us to choose the following remaining parameter values: k=(4/16810), 0 =2, qo=1372.8, ( =97.2, N =3.2, and e=8. For the case of wi, we assigned three different wage rates for our experimental design. For the case of symmetric or homogenous groups, all individuals receive a wage rate of wS=30. For the case of asymmetric payoff groups, we assigned a much higher rate of wH=60 to two of the group members (the rich) and wL=20 to the remaining six (the poor)1. Individual payoffs were therefore calculated from the payoff function: Ui(xi, 3xj) = (4/16810) [(1372.8 - (3xj)2/2) + (97.2 xi - 3.2(x i)2/2) + wi × (8-xi)]2
[2]
where wi = 20,30 and 60 for i=S,H,L players.
1
Notice that at group levels we have maintained an equal average wage for the symmetric and asymmetric cases of w=30, it is the distribution that has changed.
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The three resulting payoffs tables S, H and L are included in the appendix2, and these were handed to the participants without the shading of some of cells. Therefore, for each participant her payoffs are a function of individual choices and the choices of all other participants. Asymmetric vs symmetric group composition. The focal interest of this paper is to study how the introduction of asymmetric payoff structures -for the particular case of the marginal return on an outside wage- differs from a baseline homogenous case where all individuals face the exacts same payoffs. For doing this we will form groups of eight participants each. Participants in the symmetric groups will receive an S table (See appendix), while those in asymmetric groups will receive either an H or a L table. The assignment of tables for the latter case was totally random, where two participants got H tables and the remaining six L tables. For all cases each player knew exactly which table she had, and what tables had the other seven participants in her group; further, all payoff tables were displayed in large posters size in the walls of the field lab. In other words, payoff structure was common knowledge. Nash Strategies and the Balance Between Self-Interested and Other-Regarding Behavior. Because extracting firewood generates a pure public bad in the form of lower water quality, standard theory predicts that purely self-interested individuals will spend more time harvesting firewood than is socially optimal. Indeed, one common reference point for experiments of this type is the one-shot, complete-information Nash equilibrium (the standard model of purely self-interested strategic behavior) and another is the outcome at which group welfare is maximized. Individuals when making their Xi decision will balance their self-interest with the effects of Xi on the rest of the group. From
2
The payoffs tables values are in Colombian pesos and correspond to earnings in one round. At the time of the field experiments the exchange rate was of approx. $1,300 pesos/US$. The average earnings for a player after participating in a session of about 18 round s was equal to 1 to 1.5 m inimum rural day wages.
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the individual’s standpoint an appropriate benchmark is her pure Nash strategies—that is, individual payoff-maximizing choices taking the choices of the rest of the group as fixed. In fact, we take the difference between an individual’s Nash best-response to the choices of the other players in the group and his or her actual choice to be an indicator of how that individual balances self interests and those of the entire group. To illustrate the point, let us take the case of the S payoff table, i.e for the middle wage case 3. Suppose there are eight players and each of seven players choose to spend two months collecting firewood from the surrounding forest. Since the sum of the seven players’ choices is 14 months, Table S indicates that the eighth player’s payoff-maximizing response – the individual’s Nash bestresponse – is to spend eight months collecting firewood. [We have highlighted the cells that indicate an individual’s pure Nash strategy for each level of “their months in the forest”]. This choice is made purely out of self-interest, without regard for the welfare of the others in the group. Note that his or her payoff in this outcome is 776 points, while each of the other seven receive 535 points [for each of them, the sum of the others’ choices is 20 months, while they choose 2 months]. Now imagine that the eighth player chooses 3 months instead of 8, while the other seven players continue to choose 2 months. We consider this to be a significantly more group-oriented choice – it is costly because that player’s payoff is now 652 points instead of 776; however, each of the other players’ payoffs increase from 535 points to 606 [for each of them, the sum of the others’ choices is now 15 months, while they choose 2 months]. Much of our analysis that follows is based upon the differences between the players’ actual choices and their Nash best-responses: choices that are close to Nash responses indicate relatively self-interested behavior, while those that are further 3
The same rationale follows for the players facing an H or L payoff structure.
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away indicate stronger other-regarding or cooperative behavior. As for the standard benchmarks, it is straightforward to show that in our design the optimal amount of time each individual should spend collecting firewood is one month4. On the other hand, since a pure strategy Nash equilibrium requires that every player’s choice be a best-response to every other player’s best-response, in this context the Nash equilibrium is reached if every individual decides to spend 6 months collecting firewood from the nearby forest. It is worth noting that at the Nash equilibrium, subjects earn only about 24% of the payoffs attainable in the efficient outcome. In the case of the asymmetric groups, the pure Nash and social optimal solutions are slightly more complicated to derive although they are calculated the same way we derived the benchmarks for the symmetric case 5. For the group to achieve a Pareto optimal outcome, they require that the two rich players choose XoptH=0 and the six poor XoptL=1 yielding respectively $801 and $602 pesos. On the other hand, we can calculate a pure Nash strategy for each payoff table, assuming symmetric behavior within payoff types, and find that the six poor will devote their entire endowment of labor to the forest while the two rich players none of it and invest their labor entirely into their outside alternative The following table summarizes for the symmetric and asymmetric cases the choice variable
4
Since the player’s payoffs are identical, optimality requires symmetric individual choices. Let x denote the com mon am ount of tim e each ind ividual spen ds collectin g firewood in any symmetric ou tcome. Us ing [1], the joint w elfare function is W (x) = n(k)[(q 0 - (nx)2 /2) + ((x - N(x)2/2) + w×(e - x)]0 . The first-order condition for the maximization of W(x) requ ires -xn2 + ( - Nx – w = 0. Solvin g for x and substituting the actual parameter values yields optimal individual amounts of time spent harvesting firewood, x* = (( - w)/(N + n 2 ) = 1. 5
The Nash and social optimal benchmarks are in fact mostly corner solutions to the problem. We made this d eliberately to ind uce a case wh ere the rich d id not have to use the fore st and the p oor prop ortionally mo re than the baseline case. Thus, the Nash equilibrium required the poor to devote all their labor to the forest while the rich none while the optimal solution required the poor to use some of the forest and again the rich none.
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and outcomes for the two benchmarks of comparison for our analysis. Table 1. Benchmarks for the symmetric and asymmetric games. Two Benchmarks for equilibria in the commons game Social optimal solution (GroupMax strategy)
Nash solution (IndivMax strategy)
Symmetric game (All 8 players)
Asymmetric game Two H players
Six L players
Individual decision (Xopt)
XSopt = 1
XHopt = 0
XLopt = 1
Yields ($) per round per player
YSopt = $645
YHopt = $801
YLopt = $602
Group yields
SUMYSopt = $5,160
Individual decision (Xnash )
XSnash = 6
XHnash = 0
XLnash = 8
Yields ($) per round per player
YSnash = $155
YHnash = $117
YLnash = $191
Group yields
SUMYSnash = $1,240
SUMYHLopt = $5,214
SUMYHLnash = $1,380
Notice the differences in the individual choices depending on the treatment. In the homogenous case, at a social optimal the group needs to devote only a small amount of labor into the forest and the rest in their best private alternative. However one can see in the payoffs tables the incentive for any individual to increase xi if the group is close to such solution (i.e at the upper rows of the tables). Such an incentive is what creates part of the dilemma and what drives the group as a whole towards Pareto inferior solutions when decisions are made in a decentralized way.
3.2
The subjects and the field lab setting
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The experiment followed most of the convention in CPR experiments (OGW, 1994); it involves groups of 8 subjects who participate in a set of rounds where they make their individual decisions, xi 0 [0,8], according to the payoff table. The subjects sat at individual desks that were distributed in a circle with enough separation between the desks so they could not look at another’s work. Except in periods when communication was allowed, the desks faced away from the center of the circle. In each round, each subject would choose how many units of time, xi 0 [0,8], to spend collecting firewood from a local forest. Subjects were given the payoff table as described before. Thus, although individuals could not know in advance what the others would choose, they knew the payoffs table their decisions were based on. Once a subject made a decision for a particular round, this decision was written on a slip of paper. When all subjects had made their decisions, a monitor collected each slip of paper and gave them to another monitor who recorded the individual decisions and calculated the total for the group. This total was announced to the subjects, who then determined their own payoffs from the payoff table. Subjects kept a record of their own payoffs as a check on the monitor’s record. Each session began with some welcoming remarks within which the subjects were told that the session would last approximately two hours. A monitor would then read the instructions to the participants. [The instructions are available from the author]. Results from pre-tests of the experiment led us to decide not to give the subjects written instructions because of the wide variation in levels of literacy among them The instructions explained the basic setting of the game, how points were earned, how these points were converted to cash at the end of the session, and the procedures of the game. The instructions included three different examples to familiarize the subjects with the payoffs and the procedures. Two practice rounds were conducted. The monitor asked for questions 14
at several points, and when there were no further questions the game began with round 1. Large, readable posters of the payoff table, the forms the subjects used during the game, and the examples from the instructions were placed on one wall of the ‘field lab’. For this experiment we recruited 15 groups of 8 participants each. The groups played 7-10 initial rounds of the game, without knowing exactly how many rounds the game would last, nor what kind of new rules would be played afterwards. During these initial rounds individuals made their choices without communicating with the others or the monitors. After this first stage the monitors would stop the game and announce a new set of rules for the forthcoming rounds. The monitor read a new large poster announcing that from now on the group would be allowed to have a five minute open discussion before the decision for the next round. The discussion should be about anything they wanted on the game, but could not include any kind of threats or promises of transfers of points or cash after the game. After the decision in each round, the participants should return to their individual desks and make their individual, and still private, choice for xi. The groups played this sequence [discussion -> individual decision] for about 9-12 rounds, and again, the subjects did not know when the last round was going to be. The participants. In total, 120 subjects from 3 villages participated in the experiments. They were distributed in 15 groups, 10 of which were under the symmetric (baseline) payoff tables, and 5 under the asymmetric case. In the case of the asymmetric groups, the assignment of H and L tables was done randomly by having the players pick a bag that had the six L and two H cases. The invitation was made to all adults who lived in that village. We avoided having close relatives play within the same group. They were told that they were to participate in a set of games from which they could earn some prizes. Two days after the end of the sessions, they were all invited to participate 15
in a community workshop to discuss the results of the games, without revealing the individual gains. All players received a show-up prize (a household item --e.g. lamp, table set, machete), and their points earned were converted into cash. The average gain for a player was, as planned, the equivalent of 1.5 days of work at the minimum local wage which was aimed at compensating them for participating in the game and in the workshop two days later. Also, they had to fill out a exit-survey questionnaire after the game with follow-up questions about the game, and household data on their economic activities, participation in social life, and preferences about certain issues related to our study.
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Experiments results The results of the set of experiments performed in the field are consistent with field
observation and other experimental evidence as regards the power of face-to-face communication to overcome partially the commons dilemma. But there were surprises as well. These results are described in several categories below. 4.1
The “months in the commons” decision (Xi) Figure 1 shows the evolution of the average choice variable (xi) for each type of player H,L
in the five asymmetric groups, and S for the ten symmetric ones. The graph is divided into the two stages, the first set of rounds where no communication is allowed (from rounds 1-7) and where communication is allowed (from rounds 11 to 19)6. Recall Table 1 for the benchmarks provided by the social optima and the Nash solution. The figure shows the two types of treatments, symmetric
6
Some but not all groups played rounds 8 to 10 during the first stage. We deliberately stopped the first stage at different rounds in order to avoid anticipation of the final round.
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(S tables) and asymmetric (H and L tables). The former with 10 groups of eight S players, and the latter with 5 groups of two H and six L players each.
[INSERT FIG. 1 HERE ]
The average choice for all players starts between 4 and 5 months7 and as rounds go by, there is a divergence of paths for each type where the H players are the ones reducing x the most, and the S and L participants not decreasing x as much. Table A1 in the appendix presents the means for X across stages and across payoff tables. To test for differences in the means of X over periods, see Table A.2, and for tests across payoff tables see Table A.3, where we compare these for the first and last 3 rounds before and after communication 8. Such a divergence of paths is expected due to the different incentives created by the payoff structures. It should be clear from the payoff table that at the high aggregate levels of effort in the very first rounds, the best response for the H players is to decrease X, despite their self-regarding or other-regarding preferences. However, the best response or Nash strategy for the L players at the same points was to increase X. When the six L players are allocating 4 months and two H players around 2 months, for an aggregate of 28 units, the Nash strategy for an L player should be 8. Yet, the L players do not increase X, but rather maintain it at an intermediate level, and there is a slight reduction if we compare the first and last rounds during the first stage. Something similar occurred for the symmetric
7
We believe m ost players start from this point because that is the X cho ice that was explained to all groups during the in structions sessions. 8
For statistical testing purposes the periods are labeled A for “before communication” and B for “with com municatio n”. A1=rou nds(1-3), A2= rounds(6 -8), B1=(1 1-13), B2 =(17-19 ).
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baseline groups. L and S players face the dilemma more clearly than the H ones. Increasing X gives the L and S participants higher individual gains, but as a group this brings the social efficiency down, thus affecting each of them. The introduction of the communication institution reduced the sum of X for each group. In the case of the symmetric groups, the average X decreased about one unit (See tests 2 and 4 in Table A.2.). This was also the case for the L players in the asymmetric case, but not for the H players, who maintained their average decision at around X=2 and stuck close to their best response Xnash. Although the average decision by S and L seems similar in the graph, we found that XLA2) (A2->B1) (B1->B2) (A2->B2) 0.084 0.110 0.930 0.007 0.110 0.616 0.005 0.000 0.500
0.492 0.035 0.006 0.057 0.035 0.002 0.010 0.013 0.000
0.775 0.443 0.387 0.929 0.443 0.309 0.443 0.846 0.674
0.751 0.006 0.001 0.025 0.006 0.000 0.003 0.017 0.000
(pool B1+B2))
Table A.3. Comparing across payoffs tables (H,L,S) Before communication p-values (WilcoxonA1=(1-3) A2=(6-8) Mann-W hitney test) Test 5 (H-L)
X XDEVIA Y$
Test 6 (H-S)
X XDEVIA Y$
Test 7 (L-S)
X XDEVIA Y$
0.040 0.000 0.054 0.124 0.000 0.157 0.144 0.922 0.199
0.004 0.000 0.014 0.000 0.000 0.000 0.410 0.071 0.000
After communication B1=(11-13) B2=(1 7-19) 0.031 0.000 0.000 0.000 0.000 0.000 0.083 0.021 0.003
0.264 0.000 0.000 0.025 0.000 0.000 0.087 0.033 0.011
Table A.4. Tests for "shared rules" (equal vs. proportional appropriation) Comparing X choices between payoffs tables (H L) Before communication After communication p-values (WilcoxonA1=(1-3) A2=(6-10) B1=(11-13) B2=(17B=(11-22) Mann-W hitney test) 22) 0.089 0.015 0.951 0.496 0.459
0.126 0.919 0.306 0.100 0.199
0.025 0.916 1.000 0.096 0.231
0.001 0.377 0.440 0.001 0.212
$2,752
$4,116
$3,640
$3,875
$3,757
$2,998 Group Earnings Equal p-value (t-test): 0.654
$3,491
$4,670
$4,515
$4,593
0.105
0.001
0.13
0.001
Test 8 (H vs L) by groups
Test 9: Y$
Group 1 Group 2 Group 3 Group 4 Group 5 Mixed
0.379 0.295 0.435 0.711 0.762
Result: => => => => =>
Different X Equ al X Equ al X Different X Equ al X
34
