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A Simple Mechanism for the Efficient Provision ofPublic Goods: Experimental Evidence

By JOSEF FALKINGER, ERNST FEHR, SIMON GÄCHTER, AND RUDOLF WINTER-EBMER*

Free-riding incentives are a pervasive phe-nomenon of social life. In case of private pro-visions of public goods, free-riding leads toinefficient underprovision. Economic theory ex-plains this by viewing contributions to a publicgood as strategies in a noncooperative game(Theodore C. Bergstrom et al., 1986; Richard C.Cornes and Todd Sandler, 1986). Experimentalevidence suggests that subjects are sometimesmore cooperative than predicted by economictheory (Robyn M. Dawes and Richard H.Thaler, 1988; Douglas D. Davis and Charles A.Holt, 1993; John O. Ledyard, 1995). Yet, thesame evidence shows that underprovision of thepublic good relative to the efficient level ofcontributions is also pervasive. This holds truefor one-shot interactions as well as in case ofrepeated interactions. The tendency to under-provide is particularly strong towards the end ofa finite number of repetitions of a voluntarycontribution game (R. Mark Isaac et al., 1984;Ledyard, 1995).

Economic theorists have reacted to the free-riding problem by designing sophisticatedmechanisms for the implementation of an effi-cient allocation of public goods (e.g., EdwardH. Clarke, 1971; Theodore Groves, 1973;Groves and Ledyard, 1977; Jerry R. Green andJean-Jacques Laffont, 1979; for a survey, seeLaffont, 1987). This literature has greatlyincreased our knowledge about the incentive-compatibility requirements for the Pareto-optimal provision of public goods. However, ashas been pointed out by the proponents of thisliterature, the proposed mechanisms are fre-quently rather complicated and, hence, difficultto implement. In his survey on “Incentives andthe Allocation of Public Goods,” Laffont (1987p. 567) writes, for example: “(...) any real ap-plication will be made with methods which arecrude approximations to the mechanisms ob-tained here (...) considerations such as simplic-ity and stability to encourage trust, goodwill andcooperation, will have to be taken into account.”

Recently, several authors have proposed in-centive mechanisms which induce efficient con-tributions to the public good and seem to meetthe requirements of simplicity. Varian (1994a),for example, examined a simple two-stage gamein which agents have the opportunity to subsi-dize the other agents’ contributions. This mech-anism relies on the concept of subgameperfection.1 Earlier, Mark Bagnoli and BartLipman (1989) have presented an attractivelysimple sequential voluntary contribution gamethat implements the core of the economy. How-ever, the implementation requires a rather

* Falkinger: Department of Economics, University ofRegensburg, D-93040 Regensburg, Germany (e-mail: [email protected]); Fehr and Gächter: In-stitute for Empirical Research in Economics, University ofZurich, Blümlisalpstrasse 10, CH-8006 Zurich, Switzerland(e-mail: [email protected];[email protected]);Winter-Ebmer: Department of Economics, University of Linz, Alten-berger Strasse 69, A-4040 Linz, Austria, and Centre forEconomic Policy Research (London) (e-mail: [email protected]). Financial support from the Swiss NationalScience Foundation (Project Number 12-43590.95) is grate-fully acknowledged. We also would like to thank two anony-mous referees for their helpful comments. Comments by JamesAndreoni, Axel Ockenfels, by seminar participants at the Uni-versity of California-Berkeley, the University of Dortmund,the University of Frankfurt, the Massachusetts Institute ofTechnology, the University of Regensburg, the University ofZurich, at the Workshop for Experimental Economics atRauischholzhausen, and at the European Economic Associa-tion Meeting in Prague, the ESA Meeting in Houston, theASSA Meeting in San Francisco, and at the Meeting of theVerein für Socialpolitik in Rostock are also gratefully ac-knowledged. Valuable research assistance has been providedby Katja Cavalleri and Beatrice Zanella. We are particularlygrateful to Urs Fischbacher for writing the computer program.

1 Varian (1994b) generalizes the mechanism to othereconomic environments involving externalities. Joel M.Guttman (1978, 1987) and Leif Danzinger and Adi Schny-tzer (1991) consider a similar game in which individualschoose subsidy rates in the first stage and decide in thesecond stage about their contributions to the public good,given the subsidy rates chosen in the first stage. A criticalassessment of their analysis is provided by WilhelmAlthammer and Wolfgang Buchholz (1993).

247

complex and particular refinement of the Nashequilibrium.2 Other recent proposals deal withmechanisms in which the government tries toincrease contributions to the public good bysuitable tax-subsidy schemes. Such mechanismsare not purely private since they require a cen-tral authority which can enforce taxes. The rel-evant question is whether a government with noinformation about private characteristics candesign a tax-subsidy scheme which inducespeople to contribute more to the public good.The literature on the neutrality of lump-sumpayments (Peter G. Warr, 1982, 1983) or in-come taxation (B. Douglas Bernheim, 1986)shows that this is not a trivial task.3 Andreoniand Bergstrom (1996) put forward an interest-ing model of tax-financed government subsidiesto private contributions which definitely in-crease the equilibrium supply of public goods.4

Falkinger (1994) has shown that the privateprovision of public goods increases signifi-cantly if people value the relative size of theircontributions positively. In Falkinger (1996) asimple tax-subsidy scheme is designed whichinduces people to take into account the relativesize of their contributions in such a way that anincreased or even an efficient level of publicgood provision is achieved as a Nash equili-brium.5 This tax-subsidy scheme works as fol-lows: For each given income class, deviationsfrom the average contribution of this incomeclass are rewarded or penalized. More specifi-cally, if an individual’s contribution is bi unitsabove the mean contribution of the other mem-bers of her income class, she gets paid �bi. She

gets thus a subsidy of � for a marginal increasein her contribution. In contrast, if her contri-bution is bi units below the average of othermembers, she has to pay a tax of �bi. Thus, amarginal increase in her contribution reducesher tax payment by �. It can be shown that, inequilibrium, this strikingly simple incentivescheme produces an efficient amount of thepublic good if � is chosen appropriately. Inaddition, the mechanism is fully self-financ-ing, irrespective of whether subjects are in orout of equilibrium.

All of the above-mentioned mechanisms aredesirably simple and do well in theory. It is, how-ever, important to note that the fact that a mech-anism does well in theory, does not tell us muchabout its effectiveness in the laboratory or in prac-tice. In principle, it could well be the case thatalthough the Nash equilibrium in the presence ofthe mechanism implies an efficient provision ofthe public good, subjects’ actual behavior willgenerate significant under- or overprovision. Sincethe pioneering experimental work of Vernon L.Smith (1979a, 1979b, 1980) and Ronald M. Har-stad and Michael Marrese (1981, 1982), it is clearthat laboratory tests are in order to provide reliableevidence on whether the empirical properties of aproposed mechanism deviate from the theoreticalpredictions. For example, in a recent paper by YanChen and Charles R. Plott (1996) it turns out thatthe performance of the Groves-Ledyard mecha-nism critically depends on the size of a so-calledpunishment parameter. Theory says that a Pareto-efficient solution can be implemented as a Nashequilibrium if this parameter is positive. There-fore, according to the theory, the size of this pa-rameter should not affect the performance of themechanism. In fact, however, the size of the pun-ishment parameter is crucial. A further examplefor the importance of laboratory tests is providedby Bagnoli et al. (1992). They show that Bagnoliand Lipman’s mechanism “does not appear (...) togenerate core allocations or even somethingclose” in case of multiple units of the public good(p. 97).

Deviations of actual behavior from the equi-librium predicted by theory can be due to coor-dination problems or to bounded rationality ofsubjects. They also can arise because subjects’motivations differ from the theoretically as-sumed preferences. That deviations from equi-librium are potentially relevant is also indicated

2 Bagnoli and Michael McKee (1991) and Bagnoli et al.(1992) tested this mechanism experimentally.

3 See Johann Brunner and Falkinger (1999) for a generalcharacterization of neutral and nonneutral taxes and subsi-dies in an economy with private provision of public goods.Georg Kirchsteiger and Clemens Puppe (1997) discuss is-sues of uniqueness and stability. James Andreoni (1993)tested the neutrality of lump-sum taxes experimentally andfound that neutralization is incomplete.

4 Robin Boadway et al. (1989) and Russell D. Roberts(1992) have also considered games in which the state sub-sidizes the individual contributions to the public good sothat an efficient allocation is realized in the Nash equilib-rium. Their analysis rests on the assumption that individualsdo not anticipate the taxes by which the subsidies arefinanced.

5 For an application of the mechanism to the reduction ofglobal CO2 emissions, see Falkinger et al. (1996).

248 THE AMERICAN ECONOMIC REVIEW MARCH 2000

by the stylized facts of finitely repeated volun-tary contribution games.6 In these experimentsthere seem to be many factors at work which arenot well understood and about which standardtheory is silent. One factor which has recentlyreceived increasing attention is the possibilitythat subjects are “confused,” i.e., that individualchoices reflect some fundamental randomness(see Andreoni, 1995; Plott, 1996; Thomas R.Palfrey and Jeffrey E. Prisbrey, 1997). Can webe sure that factors like, for example, “confu-sion” do not impede adjustment towards theefficient outcome in the presence of an incentivemechanism?

In this paper we report the results of a largeseries of experiments which have been designedas a test of the practical tractability and effective-ness of the incentive mechanism proposed byFalkinger (1996). We implemented treatmentswith and without the mechanism. In our Controltreatment there was no mechanism so that subjectsfaced strong free-riding incentives. In the so-called Mechanism treatment we implemented theFalkinger mechanism. Everything else was thesame in both treatments. Therefore, we can exam-ine the impact of the mechanism by comparingcontribution behavior under the two treatments.To allow for learning the basic stage game in boththe Control treatment and the Mechanism treat-ment was repeated several times.

We studied the impact of the mechanism indifferent economic environments. In particular,we varied group size and players’ payoff functionsso that the Nash equilibria differed systematicallyacross environments. In some environments theNash equilibrium was at the boundary of the sub-jects’ strategy space while in others it was in theinterior. Also, in some environments all individu-als had identical preferences while in others theywere different. The results of our experimentsindicate that the proposed incentive mechanism isvery promising. In each of the implemented eco-nomic environments the mechanism caused animmediate and large shift towards an efficient

level of provision of the public good. This sug-gests that little practical experience with the mech-anism is necessary to induce a large increase incontributions. This property of the mechanism isprobably due to its simplicity.

A further remarkable fact is that the Nashequilibrium is a rather good predictor of behav-ior under the mechanism. If the Nash equilib-rium lies at the boundary of subjects’ strategyspace, a vast majority of individuals plays ex-actly the equilibrium strategy. If the Nash equi-librium is in the interior of subjects’ strategyspace, contributions are relatively close to theequilibrium. In contrast, in the Control treat-ments there was, in general, considerable over-contribution relative to the equilibrium in theearly periods. Towards the end, however, be-havior was very close to the Nash prediction inthe Control treatments, too.

The paper is organized as follows: Section Iintroduces the mechanism to be examined. Sec-tion II discusses the experimental design, and inSection III the empirical results are presented.Section IV interprets these results and providesa summary.

I. The Mechanism

Consider an economy of n individuals withincomes yi , i � 1, ... , n. They have prefer-ences over private consumption ci and a publicgood G represented by a strictly quasi-concaveand differentiable utility function

(1) ui�ci , G�.

The public good is provided by voluntary con-tributions that is,

(2) G � �i � 1

n

gi � gi � G�i ,

where gi denotes the contribution of individuali and G�i � ¥j � i gj. It is assumed that theprice of ci equals one. pG is the price of thepublic good. Thus, without taxes and subsidiesthe individual budget constraint is given by

(3) ci � pG gi � yi , i � 1, ... , n.

6 In these games the Nash prediction frequently involveszero contributions. Nonetheless, there is initially a relativelyhigh rate of contributions. Towards the end, the Nash equi-librium is approached for reasons which are not well un-derstood. For a recent attempt to explain this evidence, seeFehr and Klaus M. Schmidt (1999).

249VOL. 90 NO. 1 FALKINGER ET AL.: THE EFFICIENT PROVISION OF PUBLIC GOODS

The standard approach to the private provi-sion of public goods is based on Nash behavior.The members of the economy choose their con-tribution gi under the assumption that the con-tributions of the others are given. In case of aninterior solution, maximization of (1) subject to(2) and (3) gives us for a fixed G�i

(4) MRSi � pG , i � 1, ... , n

with MRSi � (�ui/�G)/(�ui/�ci). Under theassumption that both the private and the publicgood are normal goods for all individuals, equa-tions (3) and (4) describe a unique Nash equi-librium c1, ... , cn and g1, ... , gn (seeBergstrom et al., 1986). In contrast to (4), theefficient provision of the public good requiresthat the rule (Paul A. Samuelson, 1954)

(5) �i � 1

n

MRSi � pG

is fulfilled. By comparing (4) and (5) one ob-tains the known fact that public goods are un-derprovided in a private equilibrium.

The problem of underprovision of publicgoods can be overcome by the following simpleincentive scheme (Falkinger, 1996): Each indi-vidual gets a reward or has to pay a penaltydepending on the deviation of its contributionfrom the mean contribution, where the mean towhich an individual’s contribution is comparedmay be the average contribution of the wholepopulation or the average contribution of theincome class to which the individual belongs. Adifferentiation according to income is not im-portant if clubs with more or less equal incomeearners are considered or small-sized publicprojects are to be provided, for which the shareof the contribution to the public good in thehousehold budget is small even for a poor con-tributor. However, if more substantial publicprograms should be supplied, the differentiationis essential. Suppose, for instance, that averageincome earners contribute one third of theirincome to the public good and that a poor indi-vidual earns only one-fourth of the mean in-come. Then the poor individual would have topay a penalty even if he contributed all his

income to the public good. This problem isavoided by matching each individual only withother members of the same income class. Noticethat the partitioning of individuals into incomeclasses does not imply that people who are inthe same income class have identical prefer-ences. The mechanism allows heterogeneouspreferences within and across income classes.

Formally, let k � 1, ... , m be the incomeclasses in the economy and let Ik be the set ofindividuals in class k. The government imposesthat an individual i belonging to income class kgets a subsidy (or has to pay a tax) ri accordingto the rule

(6) ri � �pG�gi � 1nk � 1 G�ik � ,where nk � n is the number of people belong-ing to income class k, and G�i

k � ¥j � Ik� {i} gjis the sum of all contributions of members ofthis income class minus the contribution of in-dividual i. � is a constant subsidy rate.

For the government, this rule has the advan-tage that the budget is balanced whatever theprice of the public good and whatever the con-tributors decide to do. (¥i � 1

n ri � 0, since bydefinition for each income class, ¥i � Ik G�i

k �(nk � 1) ¥i � Ik gi). For individual i belongingto income class k, the budget constraint be-comes:

(7) ci � pG gi � yi � �pG�gi � 1nk � 1 G�ik �i � 1, ... , n.

Maximization of (1) subject to (2) and (7) yieldsfor given values gj , j � i:

(8) MRSi � �1 � ��pG , i � 1, ... , n.

Thus, reward scheme (6) implies that the priceof the public good is subsidized from pG to(1 � �) pG. As a consequence, contributions gito the public good will increase for � � 0compared to a situation with no mechanism(� � 0). Moreover, if � � 1 � (1/n), thefirst-order conditions in (8) imply that the Sam-


uelson rule ¥i � 1n MRSi � pG for an efficient

level of provision of the public good is fulfilled.It is shown in Falkinger (1996) that (7) and (8)define an efficient equilibrium for � � 1 �(1/n). This means that an efficient level ofcontributions to public goods can be achieved asa Nash equilibrium by using the incentivescheme defined in (6). The intuition behind thisresult is as follows: The private benefit of anadditional unit contributed to the public good isMRSi , which is on average 1/n of the socialbenefit ¥i � 1

n MRSi. This leads to underprovi-sion if people are confronted with the full costof contribution, pG. The mechanism with � �1 � 1/n reduces the marginal cost of contrib-uting to the public good to (1 � �) pG � pG/n.This matches the 1/n share of the social benefitand, hence, an efficient level of contributions isachieved. The budget-balance problem is solvedby using the fact that deviations from averagesum to zero.

While the above scheme rewards and penal-izes deviations from the average contribution,others proposed to pay subsidies bound to thelevel of contribution. Roberts (1987, 1992) andBoadway et al. (1989) discuss a system ofmatching grants in a model in which contribu-tors do not take into account that the grants haveto be financed by taxes. Andreoni andBergstrom (1996) showed that contributions topublic goods can be increased by subsidies tothe level of contributions if the contributorshave no budget illusion. With our incentivescheme (6) the contributors are also free frombudget illusion. If they fully account for theimpact of their action on the government bud-get, they see that it is always balanced. There isan important additional advantage of scheme(6). By subsidizing deviations from the averagecontribution instead of the level of contribution,the size of the required public budget transac-tions is substantially reduced. Consider, for in-stance, the case of identical contributions by allindividuals. Then actually no subsidy and taxpayments are paid, and contributions to the pub-lic good are increased without involving anypublic budget transactions.

Does the proposed scheme, which works intheory, and which has rather attractive propertiesfrom an economic policy point of view, also workin practice? The experiments described in the nextsection put the theoretical proposal to the test.

II. Experimental Design

To investigate the empirical properties of themechanism we implemented two basic treat-ments—a Control treatment and a Mechanismtreatment.7 In the Control treatment the tax-subsidy parameter � was always zero, i.e., therewas no mechanism, while in the Mechanismtreatment � � 0 was chosen. Within these basictreatments we varied the economic environmentin a systematic manner. We varied, in particu-lar, the group size n, the payoff function, i.e.,the marginal rate of substitution (MRSi) be-tween ci and G, and the tax-subsidy parameter�. Across all treatment conditions and eco-nomic environments the price of G, pG, was setequal to one. The characteristics of the differentexperimental designs are summarized in Table1. We discuss first the treatments C1 to M3 inwhich the equilibria were at the boundary of theindividuals’ strategy space. After that we turn totreatments C4 to M5 which implemented inte-rior equilibria.

In the Control treatments C1, C2, C3 and theMechanism treatments M1, M2, M3 each playeri was endowed with y � 20 tokens and themonetary payoff from investing gi tokens intothe public good was given by

(9) ui � ci � aG

� y � gi � ��gi � G�i /�n � 1�

� a�gi � G�i �,

where a � 0 is a given constant. The secondline of (9) results after substituting (2) and (7)for ci and G, respectively.

8

Both in C1 and M1 the group size was n � 4and MRSi was given by a � 0.4. However,while � � 0 in C1, � is set equal to 0.7 in M1.According to (9) the total marginal return of giis a constant. It is equal to �1 a � �0.6 inthe Control treatment C1 so that complete de-fection is a dominant strategy. In contrast, inM1 the total marginal return of gi is given by�1 � a � 0.1. As a consequence gi �

7 The instructions are available on request.8 Note that we have assumed only one income class.


y � 20 is a dominant strategy for every player.Since ¥i � 1

n MRSi � na � 1.6 � pG � 1,efficiency requires that the whole endowment isinvested into the public good. Thus, while theMechanism treatment implements an efficientsolution, the Control treatment implements anequilibrium with full defection. The advantageof implementing linear preferences and a cornersolution is that the results of the Control treat-ment C1 are easily comparable with the stylizedfacts of many similar experiments. This pro-vides us with information about whether thereare any peculiarities in our data.

During the experiment each of the n subjectssimultaneously chose a contribution gi. To al-low for learning this constituent game was rep-licated ten times. By backward induction, tocontribute nothing (everything) to the publicgood is the subgame-perfect equilibrium strat-egy in the Control treatment C1 (Mechanismtreatment M1). At the end of each period sub-jects were informed about the average contribu-tion of the other group members, their ownincome from ci , as well as their income fromthe public good aG. Group members did notknow with whom they formed the group andthey were informed that they will never learn it.The tenfold replication makes our control ex-periment comparable to similar experiments de-scribed in the literature (see Davis and Holt[1993] or Ledyard [1995]). In addition, the rep-lication enables us to study the evolution ofbehavior over time. From many public goods ormarket experiments it is known that subjects

seldomly jump directly into the equilibrium.Instead, contributions converge more or lessquickly to the equilibrium.

In total, 11 groups participated in C1 sessionsand 18 groups in M1 sessions. Six groups par-ticipated in both C1 and M1. These groupsparticipated first in a C1 session upon whichthey played an M1 session. As we will discussin the next section, a typical result of linearpublic-good experiments with � � 0 is that inthe first periods subjects contribute 40 to 70percent of their tokens to the group account andthat the level of contributions drops to 5 to 20percent in the last periods. This means thatsubjects experience a lot of free-riding duringthese experiments. From a psychological pointof view the experience of free-riding may influ-ence behavior in the Mechanism treatment.Moreover, there is some experimental evidencethat experienced subjects contribute less to thepublic good (Isaac et al., 1984, 1991). The se-quence of C1-M1 sessions provides, therefore, arobustness test for the mechanism. By compar-ing the behavior of those M1 groups who firstplayed in a C1 session with the behavior of theother M1 groups who did not play in a C1session we can study the impact of free-ridingexperience on the functioning of the mecha-nism.

In the treatments C2 and M2 also payofffunction (9) was implemented. In contrast to C1and M1, however, we increased the group sizeto n � 8. This change allows us to investigateto what extent the functioning of the mechanism

TABLE 1—SUMMARY OF EXPERIMENTAL DESIGN AND PARAMETERS

Treatment

Numberof

groups

Groupsize(n)

Marginal rate ofsubstitution

between ci and G(MRSi)

Tax/subsidyparameter

(�)Endowment

(y)Equilibriumprediction

C1 11 4 0.4 0.0 20 gi � 0, @iM1 18 4 0.4 0.7 20 gi � 20, @iC2 9 8 0.2 0.0 20 gi � 0, @iM2 9 8 0.2 0.9 20 gi � 20, @iC3 2 16 0.1 0.0 20 gi � 0, @iM3 2 16 0.1 1.0 20 gi � 20, @iC4 18 4 [1/(5 � 0.1ci)] 0.0 50 gi � 10, @iM4 18 4 [1/(5 � 0.1ci)] 2/3 50 gi � 30, @iC5a 5 4 [1/(Ai � 0.1ci)] 0.0 50 gL � 11, gH � 9M5a 5 4 [1/(Ai � 0.1ci)] 2/3 50 gL � 39, gH � 21

a In C5 and M5 gH ( gL) denotes the equilibrium contributions of subjects with a “high” (“low”) valuation of the privategood. Subjects with a high (low) valuation of the private good have AH � 5.1 ( AL � 4.9).


depends on group size. To make the experi-ments with different group sizes comparable wemade the following adaptations: We adjustedthe MRS to a � 0.2 in order to keep ¥i � 1

n

MRSi � na equal to the C1 and M1 treatment.If we had instead kept the MRS constant at a �0.4 while increasing the group size to n � 8 wewould have doubled the aggregate gains fromcooperation (¥i � 1

n MRSi) relative to the C1 andM1 treatment. To render full contributions inM2 a dominant strategy equilibrium, we alsoadjusted � to � � 0.9. Note that with a � 0.2and � � 0.9 the return from a marginal contri-bution in M2 is given by �1 0.2 0.9 �

0.1 which is identical to the marginal return inthe M1 treatment. Subjects in M2, therefore,face exactly the same incentives as subjects inM1 although the group size differs. To investi-gate the issue of group-size effects further, weincreased n to n � 16 in C3 and M3. To keepthe aggregate gains from cooperation and themarginal return of gi equal to M1 and M2, weadjusted the MRS to a � 0.1 and � to � � 1.

In the previous treatments the equilibriumwas at the boundary of subjects’ strategy space.In the Control treatments full defection was theunique equilibrium while in the Mechanismtreatments full contribution for every player wasthe unique equilibrium. In addition, the aggre-gate gains were always maximized at the fullcontribution level. In more complex environ-ments the equilibrium is likely to be in theinterior of the strategy space. To test the effectsof the mechanism in such environments weconducted a series of experimental sessions inwhich individuals faced a nonlinear payofffunction. The features of these experiments aresummarized as treatments C4 to M5 in Table1. In all these treatments group size was n � 4.Each subject was endowed with y � 50 tokensand the payoff functions were given by:9

(10) ui � Ai ci � �1/2�Bi ci2 � G,

where Ai � 0 and Bi � 0 are constants.In the C4 and M4 treatments subjects were

homogeneous: Each subject’s payoff function

had the parameters Ai � 5 and Bi � 0.1. Theequilibrium strategy in C4 (with � � 0) isgi � 10 for all group members. In M4 weimplemented � � 2⁄3 so that the equilibrium isgi � 30 for all players. Remember that incase of an interior equilibrium the mechanismachieves an efficient solution if � equals � �1 � (1/n) which reduces for n � 4 to � �3⁄4.10 By choosing � � 2⁄3 we deliberatelyimplemented an inefficient equilibrium in M4because from many linear public-good exper-iments it is well known that, on average,subjects tend to overcontribute relative to theequilibrium (Ledyard, 1995). We conjecturedthat the gap between the efficient solution andthe equilibrium solution in our nonlinear en-vironment with � � 2⁄3 might also generateovercontributions relative to the equilibrium.From a game-theoretic viewpoint we thus ex-posed the mechanism to a particularly toughtest. Since an efficient solution is a potentiallystrong behavioral attractor the equilibriumpredictions are more likely to be violated inthis environment.

In C5 and M5 subjects were no longerhomogeneous. They valued private consump-tion differently. In each group two subjectshad a relatively low valuation of the privategood, i.e., Ai � AL � 4.9, while the othertwo subjects had a relatively high valuation ofci with Ai � AH � 5.1. For all group mem-bers Bi was again set equal to Bi � 0.1. Asbefore � was set to � � 2⁄3 in the Mechanismtreatment. In the Control treatment C5 theequilibrium strategy of subjects with AL isgL � 11 whereas for subjects with AH theequilibrium is gH � 9. In the Mechanismtreatment M5, equilibrium implies gL � 39for subjects with AL � 4.9 and gH � 21 forsubjects with AH � 5.1. Thus, the averageequilibrium contribution in the treatmentswith heterogeneous subjects (C5, M5) isequal to 10 (for C5) and 30 (for M5). It is,therefore, identical to the equilibrium contri-bution in the treatments with homogeneoussubjects (C4, M4). This gives us the opportu-nity to study the impact of heterogeneity bycomparing the average contributions acrosstreatments.

9 A similar design was used by Claudia Keser (1996) andMartin Sefton and Richard Steinberg (1996). 10 With � � 3⁄4 the equilibrium is gi � 40 for all players.


III. Results

In total, 240 subjects—who formed 45 inde-pendent groups—participated in our controlsessions. In the mechanism sessions we had 268subjects in 52 independent groups.11 An exper-imental session lasted between 1.5 and 2 hours.Subjects received a fixed fee of CHF 15 (about$11) for showing up on time plus their earningsin the experiment. The average subject earnedabout CHF 36 in an experimental session. Theseearnings surely covered the opportunity costs ofparticipating in the experiments. After readingthe instructions, subjects had to solve some hy-pothetical examples designed to ensure thatthey are capable to compute their earnings. Wedid not start the experiment before all subjectshad correctly solved all examples.

In reporting our results we proceed as fol-lows. We first document and compare the be-havior in the C1 and M1 treatment. Then westudy the impact of group size on the mecha-nism and, finally, we investigate the empiricalproperties of the mechanism in the environmentwith interior equilibria.

A. The Mechanism in a Linear Environment(Corner Equilibria)

In the C1 and the M1 treatment we imple-mented payoff function (9) and a group size ofn � 4. Figure 1A provides an illustration of thebehavior in these treatments. It shows the aver-age contribution to the public good in all C1groups and the 12 M1 groups which were notexposed to C1. A common characteristic ofthese groups is that they did not have priorexperience with another treatment. In additionto the average contribution, Figure 1A alsoshows the 95-percent confidence bounds for thegroup averages.12 It is worthwhile to mentionthat all confidence bounds have been computedwith nonparametric methods, i.e., we did not

make assumptions about the nature of the un-derlying distribution.13

Basically, the Control treatment replicates theresults of similar voluntary contribution exper-iments reported in the literature (see Dawes andThaler, 1988; Davis and Holt, 1993; or Ledyard,1995). Voluntary contributions are initially rel-atively far above the Nash equilibrium predic-tion of zero contributions to the public good.However, as it is typical for this kind of public-goods experiments, contributions sharply de-clined towards the end. In the last three periodscontributions dropped to an average level of 6.7tokens. In the last period, contributions de-creased to 3.4 tokens on average. A division ofthe ten periods of C1 into the first half (periods1–5) and the second half (periods 6–10) revealsthat all 11 groups contributed less to the publicgood in the second half of the experiment (Wil-coxon signed ranks test, p � 0.0017, one-

11 The students were from different fields, most fre-quently from the sciences. Economists were excluded.

12 Note that due to a common history the individualcontributions within a given group are—except in periodone—not independent from each other. However, the aver-age contributions of groups are independent and, therefore,they represent the proper unit of observation for statisticaltesting and the computation of confidence bounds.

13 To calculate confidence bounds we used the method ofbootstrapping. This method is appropriate if one has arandom sample from an unknown distribution (see BradleyEfron and Robert Tibshirani, 1993). The bootstrap uses onlythe sample information to calculate the standard error of themean. In our data we used bootstrap samples of N � 1,000drawn randomly (with replacement) from the independentobservations (i.e., group averages) of a given treatment. Wehave calculated the confidence bounds by using the 95-percent trimmed range of the bootstrap sample means.

FIGURE 1A. THE EFFECTIVENESS OF THE MECHANISM—MEAN CONTRIBUTIONS (AND CONFIDENCE BOUNDS) IN

MECHANISM TREATMENT M1 (GROUPS 1–12) ANDCONTROL TREATMENT C1 (ALL GROUPS)


tailed). In the last period 57 percent of thesubjects contributed zero. This indicates that,finally, the Nash equilibrium had substantialdrawing power.

Figure 1A also provides a first indication towhat extent the mechanism reduces free-riding.It shows that the incentive scheme indeed sub-stantially increased contribution levels relativeto the C1 treatment. In all periods, mean con-tributions in M1 are above the contributions inC1. Moreover—and contrary to C1—contribu-tions are increasing and approach the Nashequilibrium of full contribution. A division ofthe ten periods of the Mechanism experimentinto the first half (periods 1–5) and the secondhalf (periods 6–10), with group averages asobservations, shows that contributions to thepublic good were significantly higher in thesecond half of the experiment (Wilcoxon signedranks test, p � 0.0014, one-tailed). “Experi-enced” subjects reduce their contributions in theControl treatment but increase them under theMechanism.

Table 2 contains further information aboutthe behavior under the mechanism. It reportssome descriptive statistics for each of the 18independent groups participating in M1. Themean contribution in groups 1–12 of M1 wasvery close to the Nash equilibrium. On average,subjects contributed 90.5 percent of their en-dowment (as compared to 50.5 percent in C1).In the last three periods the average contributionwas 18.6 tokens (i.e., 93 percent of the equilib-rium) and the median contribution of all sub-jects of groups 1–12, as well as in 10 out of the12 individual groups, equaled the equilibriumcontribution of 20 tokens. Also in the last period(not shown in the table) the median contributionof all subjects was 20 tokens. This shows thatequilibrium contributions are the prevalent be-havior in the Mechanism treatment in most ofthe groups. The mechanism is, however, notonly capable of inducing high provision levelsthat are at or close to the full contribution equi-librium. It also substantially reduces the vari-ability of behavior relative to C1. This becomesapparent from a comparison of the confidencebounds in Figure 1A.

Formal tests of the difference between the C1and the M1 treatments confirm the picture. Us-ing the independent group averages over allperiods as observations, we can reject the null

hypothesis that group averages in both treat-ments are equal in favor of the alternative hy-pothesis that mean contributions are higher inthe Mechanism treatment (Median test, p �0.001, one-tailed).14

An interesting test of the power of the

14 The Median test is a distribution-free test which testswhether two independent samples are drawn from a popu-lation with the same median. It is a particularly robust testsince it only tests for central tendencies and makes nofurther distributional assumptions. For our data this test isappropriate since the observations in the two treatments areclearly differently distributed (Kolmogorov-Smirnov test,p � 0.033). Moreover, observations cluster at the corner ofthe strategy space. [See Sidney Siegel and N. John Castel-lan, Jr. (1988 pp. 124–28) for a discussion.] The Mediantest also confirms that group standard deviations are lower

TABLE 2—SUMMARY OF GROUP BEHAVIOR (�TOKENCONTRIBUTIONS TO THE PUBLIC GOOD) IN THE MECHANISM

TREATMENT M1

Group

Mean Mean Median

Period 1–10 Period 8–10 Period 8–10

1 18.2 19.2 202 19.1 20 203 17.1 20 204 16.4 17.3 205 16.0 16.5 186 18.4 17.8 207 19.0 17.5 208 19.6 20 209 19.4 20 2010 19.2 18.3 2011 15.9 16.4 19.512 19.1 20 20

Total forgroups1–12a

18.1 � 90.5percentb

18.6 � 93percent

20 � 100percent

13 18.8 19.8 2014 18.3 19.9 2015 14.5 15.7 17.516 17.8 19.8 2017 17.1 17.9 17.518 15 17 18.5

Total forgroups13–18c

16.9 � 84.5percent

18.3 � 91.5percent

20 � 100percent

a Groups 1–12 did not experience a C1 treatment prior toM1.

b Percentage rates are calculated with respect to the equi-librium of 20 tokens.

c Groups 13–18 played a M1 treatment after a C1 treat-ment.


mechanism is the first period. Higher contribu-tions in M1 compared to C1 would indicate thatnot much learning is necessary for the mecha-nism to be effective, even with completely in-experienced subjects. The null hypothesis thatpeople start contributing to the public good atthe same level as in the Control treatment has tobe rejected (Median test, p � 0.0178).15 Inother words, the difference in the average con-tributions in period 1 across treatments exhib-ited by Figure 1A is significant. Taken together,the evidence shows that with the mechanismone can achieve significantly higher contribu-tion levels at less variability than with voluntarycontributions alone—even without repetitionand learning possibilities.

How effective is the mechanism if peoplealready have free-riding experience? A keyfinding in a recent paper by Haig G. Nalbantianand Andrew Schotter (1997) is that the perfor-mance of different group incentives is stronglyaffected by the previous history of thegroup—in particular by its previous contribu-tion “norm.” This suggests that prior free-ridingexperience might well inhibit the performanceof the mechanism. Figure 1B and Table 2 showthe average contributions of groups 13–18 ofM1. These six groups participated in M1 afterthey experienced C1. Subjects in C1 did notknow that they will be in a M1 session after-wards. As one can see in Figure 1B, the C1 dataexhibit the usual declining pattern althoughcontribution levels are rather high (on averageabove 50 percent). There is a very pronouncedendgame effect of 30 percentage points fromperiod 9 to period 10. Despite this severe de-cline in contribution levels in the last period,subjects in period 1 of M1 (“period 11”) imme-diately “jump” to higher contribution levels.Subjects in the first period of M1 contributed onaverage more than 14 tokens to the public good(compared to 4.2 tokens in period 10 of C1before). The mean contribution in M1 was ineach period above the mean contribution in thecorresponding period of C1. The confidence

bounds in Figure 1B also indicate that groupbehavior is considerably more stable under themechanism.

In the second part of Table 2 we give asummary description of groups 13–18 of M1.As a comparison with groups 1–12 reveals, av-erage contributions over all ten periods areslightly lower in groups 13–18 but the differ-ence is not significant (Median test, p � 0.62).In the last three periods average (and median)contributions are almost identical to the contri-butions in groups 1–12. In particular, equilib-rium play is again the prevalent behavior. Thus,groups 13–18 basically replicate the behavior ofgroups 1–12 of M1, i.e., the performance of themechanism is not inhibited by the free-ridingexperience.

Before we consider questions of group sizewe take a closer look at the behavior of indi-vidual subjects. So far we mainly concentratedon average behavior within and across groups.From a policy viewpoint the group seems to bethe most important unit of observation becauseone would like to know how the mechanismaffects collective performance. Yet, from agame-theoretic perspective it is also interestingto know whether individual subjects are farfrom the Nash equilibrium prediction orwhether they are close. That average and indi-vidual behavior may differ significantly is, forexample, indicated by the experiments of James

in the Mechanism treatment than in the Control treatment( p � 0.0001, one-tailed).

15 For this test we used individual decisions in C1 andgroups 1–12 of M1 as observations (N � 44 in C1, andN � 48 in M1) since in the first period they are allindependent.

FIGURE 1B. THE ROBUSTNESS OF THE MECHANISM—MEANCONTRIBUTIONS (AND CONFIDENCE BOUNDS) OF GROUPS

13–18 OF M1 AFTER THE EXPERIENCE OF C1


M. Walker et al. (1990). Their data show thatthe average behavior of all groups together isreasonably well described by the Nash predic-tion although the Nash equilibrium has no draw-ing power at the individual level. With regard toour experiments, Table 2 already provides a firstindication that individual equilibrium play oc-curred quite frequently. During the last threeperiods in 13 of the 18 groups which partici-pated in M1 the median contribution is exactly20 and the average contribution of all groupstogether is larger than 18 tokens. This alreadyindicates that a large fraction of subjects playedclose to the equilibrium of gi � 20.

To shed more light on this issue we havecomputed the relative frequency of subjectswho deviate by a certain percentage of theirendowment from the equilibrium choice. Thedeviation has been measured by the absolutevalue of the difference between the equilibriumstrategy and the average contribution of an in-dividual subject. The result of this computationis displayed in Figure 2. Sixty-four percent ofthe subjects deviate at most by 10 percent fromthe equilibrium, roughly 15 percent deviate be-tween 11–20 percent, while the rest of the sub-jects deviate by more than 20 percent. Thus, thebig majority of subjects play close to the equi-librium under the mechanism.

B. Does Group Size Matter?

In this section we report the results of theC2-M2 and the C3-M3 treatments in which weincreased the group size to n � 8, and n � 16,respectively. In all these treatments each group

participated first in the Mechanism treatmentwithout knowing that afterwards there will alsobe a Control treatment. After period 10 of theMechanism treatment, subjects were told thatthere will be a new experiment.

Figure 3 depicts the evolution of averagecontributions for group sizes of n � 8 and n �16. Table 3 shows the contribution behavior ofgroups 1–9 where group size was n � 8 andgroups 10 and 11 where group size was n � 16.As in the Mechanism treatment with n � 4 (seeFigure 1A) subjects in larger groups start inperiod 1 with an average contribution ofroughly 16 tokens. However, in contrast to then � 4 case there is no increase in averagecontributions over time when the group size islarger. Instead, there are small fluctuationsaround a contribution level of 16 tokensthroughout the ten periods. In period 10 theaverage contribution is 16.3 tokens if n � 8 and16.9 tokens in the n � 16 case. Figure 3 andTable 3 also show that contributions in groupswith n � 16 are roughly the same as those ingroups with n � 8.

In the first period of the Control treatmentsthere is a very large drop in contributions toapproximately 6 tokens. Contributions in theControl treatments continue to decline untilthey finally reach less than 2 tokens in period20. In the last period 75 percent of the sub-jects in C2 and 84 percent of the subjects inC3 play exactly the Nash equilibrium of gi �

FIGURE 2. RELATIVE FREQUENCY OF SUBJECTS WHODEVIATE FROM EQUILIBRIUM IN MECHANISM TREATMENT

M1 AT MOST BY X PERCENT OF THEIR ENDOWMENT

FIGURE 3. THE EFFECTS OF GROUP SIZE

Note: Solid (dashed) lines denote confidence bounds forgroup size 8 (16).


0. This sharp contrast between the Mecha-nism treatment and the Control treatment in-dicates that the mechanism is very effective inan environment that creates an enormous free-rider problem in the absence of the mecha-nism.

Yet, the comparison between Figure 1A andFigure 3 as well as between Table 2 and Table3 also shows that the performance of the mech-anism is slightly lower at a larger group size. Toinvestigate whether these differences are signif-icant we conducted a nonparametric Mann-Whitney test with group averages in period 10of M1 (n � 4) and M2 (n � 8) as units ofobservation.16 There is weak evidence ( p �0.081, one-tailed) that the null hypothesis ofequal average contributions can be rejected infavor of the alternative that groups with n � 4contribute more. However, on the basis of amore conservative Median test the null hypoth-

esis of equal medians cannot be rejected ( p �0.21, one-tailed). Taken together we interpretthis as weak evidence that the mechanism’sperformance slightly decreases if the group sizerises from n � 4 to n � 8. Yet, Figure 3 alsosuggests that there is no further decrease in theperformance of the mechanism if the group sizerises to n � 16.

This interpretation is confirmed if we look atindividual subjects’ deviations from equilib-rium play (see Figure 4). It is still the case thatthe fraction of subjects who exhibit only smalldeviations (in the range of 0–10 percent) islargest. However, compared to subjects’ devia-tions in the M1 treatment (see Figure 2) thefraction which deviates by more than 10 percentfrom the equilibrium is now larger.

C. The Mechanism in a NonlinearEnvironment (Interior Equilibria)

In this section the results of the C4-M4 andthe C5-M5 treatments, in which interior equi-libria were implemented, are reported.Groups 1–12 of M4 and all groups of M5participated first in the Mechanism treatment(M4, M5). After the Mechanism treatment thesame subjects participated in the Controltreatment (C4, C5). Subjects in the Mecha-nism treatment did not know that they wouldplay another experiment afterwards. Forgroups 13–18 of M4 we reversed the order ofplay. This allows a robustness check of themechanism in this more complex environ-ment. Since we thought that in a nonlinearenvironment it might take longer to approach

16 Due to the small number of group observations in M3we cannot compare this treatment statistically with M1 orM2.


TREATMENT WITH GROUPS OF 8 AND 16 SUBJECTS

Group

Mean Mean Median


1 13.1 13.3 132 16.5 17.6 183 17.1 15.8 204 16.9 17.0 195 16.7 17.3 206 15.9 18.3 207 17.3 17.4 208 15.9 16.4 189 14.7 14.0 15

Total ofgroups 1–9a

16.0 � 80percentb

16.4 � 82percent

19 � 95percent

10 16.7 17.0 19.011 15.0 15.1 16.0

Total ofgroups10–11a

15.8 � 79percent

16.1 � 80.5percent

18.0 � 90percent

a Groups 1–9 (10 and 11) consist of 8 (16) group mem-bers.


FIGURE 4. RELATIVE FREQUENCY OF SUBJECTS WHODEVIATE FROM EQUILIBRIUM IN MECHANISM TREATMENTS

M2 AND M3 AT MOST BY X PERCENTOF THEIR ENDOWMENT


the equilibrium we increased the number ofperiods in both treatment conditions to 20.

Figure 5A shows the evolution of averagecontributions in groups 1–12 of M4 over time.The figure displays the remarkable fact thataverage contributions are very close to the equi-librium already from period 1 onwards.Throughout the M4 session they fluctuate a littlebit around the equilibrium of 30 tokens. Thesecond salient fact is that the 95-percent confi-dence bounds are rather small and contain theequilibrium in almost all periods. Hence, thenull hypothesis of equilibrium play cannot berejected. Thirdly, the evidence from C4 indi-cates that contributions drop immediately if themechanism is removed and approach, finally,the Nash equilibrium of 10 tokens. The averageand modal choice in period 20 of C4 was exactequilibrium play at gi � 10. A Wilcoxonsigned ranks test confirms ( p � 0.002, one-tailed) what Figure 5A already suggests,namely, that contributions are significantlyhigher in the Mechanism treatment.

Figure 5B presents the evolution of averagecontributions when subjects first play the Con-trol treatment C4. As in the Control treatment ofFigure 5A, there is slow convergence to theNash equilibrium of 10 tokens.17 In contrast to

this slow convergence in C4, contributions inthe Mechanism treatment again are close to theequilibrium from the early periods of M4 on-wards. A Mann-Whitney test shows that contri-butions in groups 1–12 are not significantlydifferent from the contributions of groups13–18 ( p � 0.302). This confirms our findingin subsection A where we have seen that themechanism also performs well when subjectshave previous free-riding experience.

Taken together, the behavior of groups in M4indicates that there is no overcontribution in theMechanism treatment. The average contributionover all 18 groups and all periods is 30.6 tokens,which is only 2 percent above the equilibrium.For the last five periods the average contributionis 29.6 tokens, which is only 1.3 percent belowthe equilibrium. The median contribution in thelast five periods is even exactly at the equilib-rium. This indicates that the Nash equilibrium isa remarkably good predictor of group behaviorin the Mechanism treatment with homogeneoussubjects.

In C5 and M5 we implemented an interiorsolution with heterogeneous payoff functions.Here the equilibrium required subjects tochoose different contribution levels. However,the mean equilibrium contribution of groupswas again 10 tokens for C5 and 30 tokens forM5. Figure 6 shows how contributions evolveover time under these conditions. The Nashequilibrium of 30 tokens is again a rather good

17 Our data in C4 replicate the results of the experimentsby Keser (1996) and Sefton and Steinberg (1996).

FIGURE 5A. EVOLUTION OF MEAN CONTRIBUTIONS (ANDCONFIDENCE BOUNDS) IN GROUPS WITH HOMOGENEOUS

PREFERENCES WITH AND WITHOUT THE MECHANISM(GROUPS 1–12 IN M4 AND C4)

FIGURE 5B. EVOLUTION OF MEAN CONTRIBUTIONS (ANDCONFIDENCE BOUNDS) IN GROUPS WITH HOMOGENEOUS

PREFERENCES WITHOUT AND WITH THE MECHANISM(GROUPS 13–18 IN C4 AND M4)


predictor of group behavior although not quiteas good as with homogeneous subjects. Duringthe first periods of M5 there is some overcon-tribution. However, if we take all periods to-gether the overcontribution is not statisticallysignificant. A �2 test reveals that mean contri-butions are not systematically above or below30 tokens ( p � 0.37). Moreover, contributionsin M5 are not significantly different from con-tributions in M4 (Mann-Whitney test, p �0.55). Towards the end of the Mechanism treat-ment M5 contributions come very close to theequilibrium (see Figure 6 and Table 4). Duringthe last five periods the average contribution is30.7 tokens, which is only 2.3 percent above theequilibrium. The median contribution in thistime interval is 31.5. In period 21, when themechanism is removed, there is a large drop incontributions. In C5, contributions finally alsoapproach the equilibrium value although withsome fluctuations around a decreasing trend.18

Information regarding individual play in thetreatments with interior solutions is presented inFigure 7. In the treatment with homogeneousplayers a little bit less than 40 percent of thesubjects deviate by less than 10 percent from the

equilibrium. A similar percentage of subjectsdeviates between 11 and 20 percent while therest exhibits larger deviations. In the treatmentwith heterogeneous subjects roughly 35 percentof subjects show only small (�10-percent) de-viations and 25 percent deviate between 11 and20 percent. Thus, at the individual level contri-butions are not as close to the equilibrium as in

18 With regard to C5 and M5 one has to keep in mind thatthe number of independent observations (groups) is consid-erably smaller than in C4 and M4. Therefore, confidencebounds are larger in C5 and M5.

FIGURE 6. EVOLUTION OF MEAN CONTRIBUTIONS (ANDCONFIDENCE BOUNDS) IN GROUPS WITH HETEROGENEOUSPREFERENCES WITH AND WITHOUT THE MECHANISM WITH

HETEROGENEOUS PREFERENCES (M5 AND C5)


TREATMENT WITH AN INTERIOR EQUILIBRIUM

Group

Mean Mean Median


1 36.5 40 402 24.9 27.3 20.53 28.9 26.3 29.54 26.7 25.2 225 30.6 35.7 43.56 30.7 28.6 307 24.8 28.1 318 33.2 29.9 359 32.7 35 3910 26.7 24.5 2511 32.2 26.8 2712 30.3 25.3 25


29.8 � 99.3percentb

29.4 � 98percent

30 � 100percent

13 30.4 27 33.514 37.1 32.4 2915 33.7 28.1 3016 30.1 30.9 35.517 30.1 31.5 3918 32.1 30.5 30


32.2 � 107.2percent

30.1 � 100.3percent

30 � 100percent

19 31.3 31.0 3520 35.8 32.8 4021 27.9 26.3 2522 28.6 26.8 2123 37.7 36.8 40


32.3 � 107.7percent

30.7 � 102.3percent

31.5 � 105percent

a Groups 1–18 (19–23) took part in the homogeneous(heterogeneous) treatment. Groups 1–12 (13–18) firstplayed M4 (C4), then C4 (M4). Groups 19–23 first playedM5 and then C5.



M1 (compare Figure 2 with Figure 7).19 How-ever, we find it remarkable that even in therather complex environment of M4 and M5 theNash equilibrium has a strong drawing poweralso at the individual level.

IV. Summary

In this paper we examined the performance ofthe Falkinger (1996) mechanism for the provi-sion of public goods. The results of our exper-iments indicate that the mechanism does quitewell in the laboratory. In each of the imple-mented economic environments the mechanismcaused an immediate and large shift towards anefficient solution. This suggests that little prac-tical experience with the mechanism is neces-sary to induce a significant and large increase incontributions. If one compares the long-run be-havior in the Control and the Mechanism treat-ments the impact of the mechanism is evenlarger: In the Control treatments we alwaysobserved a steady decline in contributions overtime and towards the end the free-riding equi-librium exerts a strong drawing power. Contri-butions in the Mechanism treatment remained

rather stable at high levels or increased overtime. Thus, in the long run the mechanism gen-erates even larger efficiency gains because it isable to overcome the strong free-rider problemobserved in repeated public-good experiments.

From a game-theoretic point of view the ma-jor difference between the Control treatmentand the Mechanism treatment concerns the factthat the Nash equilibrium is a much better pre-dictor of behavior in the Mechanism treatment.In general, deviations from the Nash equilib-rium are lower in the Mechanism treatments. Inthe Control treatments the Nash equilibrium isonly a good predictor for the final periods whilein the early periods we always observe substan-tial overcontribution. No such overcontributionoccurs in the Mechanism treatments.

This data pattern indicates that in the Controltreatment there are forces at work that inhibitquick adjustment to the Nash equilibrium. Inour view the differences in the deviations fromthe equilibrium have to do with the position ofthe equilibria. In the Control treatments the dis-tance between the Nash equilibrium and thewelfare-maximizing solution is much largerthan in the Mechanism treatments, where it iseven zero in many cases. Therefore, if subjectshave a behavioral drive towards cooperation,the adjustment to the free-rider equilibrium isinhibited. In contrast, in the Mechanism treat-ment such a behavioral drive speeds up theconvergence to equilibrium play.20

From a policy point of view it is also

19 Note that the strategy space in the treatments withinterior equilibria is gi � {0, 1, ... , 50} while in thetreatments with corner equilibria it is gi � {0, 1, ... , 20}.To render Figure 7 comparable to Figures 2 and 4 wealways computed the deviation from equilibrium as a per-centage of the total available endowment. Of course, inFigures 2 and 4 the total endowment coincides with theequilibrium contribution.

20 Since the fraction of groups and individuals that areclose to the equilibrium is relatively large in all of ourMechanism treatments, the question arises why we observeconsiderably more equilibrium play than, for example, inWalker et al. (1990). We are not capable of providing aprecise answer to this question. However, we conjecturethat part of the answer is due to the position of the equilib-rium. In the Walker-Gardner-Ostrom experiments the dis-tance between equilibrium behavior and welfare-maximizing behavior is larger than in our Mechanismtreatment. It is known from other studies (e.g., Jordi Brandtsand Arthur Schram, 1996; Fehr and Simon Gächter, 1998;Keser and Frans van Winden, 2000) that many subjects areconditionally cooperative, that is, they are willing to coop-erate if others cooperate but they tend to retaliate if they arehurt by others. If the distance between equilibrium behaviorand welfare-maximizing behavior is large, conditionallycooperative subjects are particularly tempted to achievecooperation, which contributes to individual deviationsfrom the equilibrium. Moreover, since these attempts atimplicit cooperation frequently fail, there will be retaliatory

FIGURE 7. RELATIVE FREQUENCY OF SUBJECTS WHODEVIATE FROM EQUILIBRIUM IN MECHANISM TREATMENTS

M4 AND M5 AT MOST BY X PERCENT OF THEIRENDOWMENT


interesting to know to what extent the publicbudget is actually involved under the mecha-nism. Although the public budget is alwaysbalanced by definition, it may be consideredas a further advantage of the mechanism if theactual tax and transfer payments per personare low. In reality, a mechanism may be moreeasily accepted if the implied payments fromand to the households are small. In our ex-periments the average tax or transfer paymentper person as a percentage of a subject’sendowment varies between 4 and 10 percent.This indicates that the volume of tax pay-ments that has to be enforced by a centralauthority is relatively small.

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