Grosse, Stefan; Putterman, Louis; Rockenbach, Bettina. Working Paper Monitoring In teams: A model and experiment on the central monitor hypothesis

Transcription

1 econstor Der Open-Access-Publkatonsserver der ZBW Lebnz-Informatonszentrum Wrtschaft The Open Access Publcaton erver of the ZBW Lebnz Informaton Centre for Economcs Grosse, tefan; Putterman, Lous; Rockenbach, Bettna Workng Paper Montorng In teams: A model and experment on the central montor hypothess Workng Paper, Brown Unversty, Department of Economcs, o Provded n Cooperaton wth: Department of Economcs, Brown Unversty uggested Ctaton: Grosse, tefan; Putterman, Lous; Rockenbach, Bettna (007) : Montorng In teams: A model and experment on the central montor hypothess, Workng Paper, Brown Unversty, Department of Economcs, o Ths Verson s avalable at: utzungsbedngungen: De ZBW räumt Ihnen als utzern/utzer das unentgeltlche, räumlch unbeschränkte und zetlch auf de Dauer des chutzrechts beschränkte enfache Recht en, das ausgewählte Werk m Rahmen der unter nachzulesenden vollständgen utzungsbedngungen zu vervelfältgen, mt denen de utzern/der utzer sch durch de erste utzung enverstanden erklärt. Terms of use: The ZBW grants you, the user, the non-exclusve rght to use the selected work free of charge, terrtorally unrestrcted and wthn the tme lmt of the term of the property rghts accordng to the terms specfed at By the frst use of the selected work the user agrees and declares to comply wth these terms of use. zbw Lebnz-Informatonszentrum Wrtschaft Lebnz Informaton Centre for Economcs

2 Montorng n Teams Usng Laboratory Experments to tudy a Theory of the Frm tefan Grosse, Lous Putterman **, Bettna Rockenbach * DRAFT Mar Abstract. Alchan and Demsetz s (97) nfluental explanaton of the classcal busness frm argues that there s need for a concentrated resdual clam n the hands of a central agent, to motvate the montorng of workers. We model montorng as a way to transform team producton from a collectve acton dlemma wth strong free rdng ncentves to a productvtyenhancng opportunty wth strong prvate margnal ncentves to contrbute effort. In an experment, we have subjects experence team producton wthout montorng, team producton wth a central montor, and team producton wth peer montorng, then vote on whether to employ the central montor, who gets to keep a fxed share of the team output, or to rely on peer montorng, whch entals a coordnaton or free rdng problem. Our subjects usually prefer peer montorng but they swtch to the specalst when unable to successfully self-montor. We provde evdence for stuatons n whch team members resst the appontng of a central montor and succeed n overcomng coordnaton and free rdng problems as well as for a stuaton n whch an Alchan-Demsetz-lke frm grows n the laboratory. JEL Codes: C9, D0, D70, H4, J54, P, P3 Keywords: montorng, team producton, free rdng, cooperaton, experment. Unversty of Erfurt, ordhäuser tr. 63, Erfurt, Germany ** Brown Unversty, Provdence, Rhode Island, UA.

3 . Introducton What accounts for the structure of the captalst frm, n whch equty supplers or ther agents hre and supervse workers gven few or no resdual clams? In an nfluental paper about the theory of the frm, Alchan and Demsetz (97) characterzed team producton by the followng four propertes:. there exst several nput provders,. the combned output s larger than the sum of the outputs that the ndvdual nput provders can acheve by workng alone, 3. there s an observable team output but no observable output of the ndvdual nput provder, and 4. t s possble but costly to measure the amount of nput contrbuted by each ndvdual provder. The central dlemma of team producton, they argued, s that the benefts of workng as a team (e.g. benefts from economes of scale or of specalzaton) may be undercut by the ncentve that each team member has to free rde f compensated accordng to team output rather than personal nput. To mtgate ths problem, team members rewards must be ted to ther contrbutons, but that requres another costly nput montorng and ths n turn gves rse to another collectve acton problem f montorng s to be suppled by the team members themselves. The classcal captalst frm solves ths problem, they argue, by makng one specalzed agent the montor of the other team members who pays them accordng to ther observed nputs. The central agent s motvated to montor by the fact that he keeps all team revenue above hs contractual oblgatons to the nput provders. We understand Alchan and Demsetz s depcton of team producton n the absence of montorng to be an example of the famlar problem of collectve acton or ncentves n teams that has been studed by expermental economsts n recent decades under the headng Voluntary Contrbuton Mechansm (VCM) or Publc Goods Game (PGG). In a VCM or PGG, subjects are grouped wth others and each decdes how much of a certan endowment to contrbute to a group project and how much to hold for herself. Contrbutons to the project are scaled up by the expermenter, such that there s a socal optmum of contrbutng. However, snce the resultng revenues are dvded equally among team members, the ndvdual optmum s contrbutng nothng. We nterpret Alchan and Demsetz as sayng that f a suffcent nvestment s made n montorng ndvduals contrbutons, then they can be pad accordng to ther contrbutons, rather

4 than an equal per capta share, as a result of whch there wll be an ncentve to contrbute and not to free rde. We present a smple theoretcal model correspondng to ths structure, and we nvestgate how real decson-makers respond to the structure by havng subjects make potentally rewardng/costly decsons under t n a laboratory experment. In the model and experment, montorng can ether be done by a specalzed agent, who s assgned a fracton of the team s jont output, or by the team members themselves, who are then compensated for ther contrbutons to producton but not for ther montorng tself. uppose that agents care only about ncreasng ther own earnngs, know one another to be of the same type, and are ratonal. Then f the only montorng were to be that done by the team members themselves, there would be a consderable possblty that montorng would not suffce and hence that the producton stage of the model would be a smple VCM, for whch there s a straghtforward predcton of zero contrbutons. If, nstead, a specalst were offered a suffcent fracton of team output and permtted to montor, t would be n the specalst s nterest to montor enough to make contrbutng to team producton ratonal for each team member. Wth approprate specfcatons of returns to team producton and of the share clamed by the specalst, team members earn more producng together wth a specalst montor than havng no montor and producng ndvdually. If allowed to vote at no cost a proxy for workers choce among organzatonal forms n a market economy the model predcts that team members wll vote to hre the specalst unless they manage to successfully montor themselves. We carry out expermental play of such a model. We vary the condtons under whch team members and specalsts can learn about ther tasks by varyng the order n whch play occurs (a) wth no montorng, (b) wth montorng (f any) by team members, and (c) wth montorng (f any) by a specalst, before havng several opportuntes to vote on whch knd of montorng to use, more perods of play, and opportuntes to vote agan. We also vary the costlness of montorng for team members versus specalsts, and whether or not there exst peer montorng equlbra on whch teams members can potentally coordnate. Ours s the frst experment we are aware of n whch a publc goods game wth ts well-known free rder problem can be converted nto a payment for effort envronment 3

5 wthout free rder problem by the free choces of subjects. It extends the recent nnovaton of studyng nsttutonal evoluton n the laboratory, applyng t to a key ssue n the theory of economc organzaton that has not prevously been addressed by such methods. Our results are strkng. In four of the sx treatments wth whch we experment, almost all teams are successful at self-montorng and thus choose not to hre a specalst. But when we make montorng by team members more costly than that by the specalst, and especally when we swtch to a model wthout a peer montorng equlbrum, peer montorng fals n many groups and a trend towards specalst montorng emerges. Our results thus accord wth expermental fndngs that a large number of subjects attempt cooperaton n the lab, but also wth the standard expermental fndng that n repeated dlemma games wthout devces such as punshment opportuntes or pre-play communcaton, cooperaton tends to flag over tme. For ths reason, the logc of Alchan and Demsetz s argument s supported n the lab n a partcularly clear fashon. The structure of the paper s as follows. ecton brefly dscusses the theory and lterature on the organzatonal form of producton n a market economy. ecton 3 presents our theoretcal model, and ecton 4 lays out ts mplementaton n our expermental desgn. ectons present the experment s results. ecton 5.4 ntroduces an alternatve model wth a unque equlbrum of free rdng n peer montorng, and presents results for the correspondng treatment. ecton 6 summarzes and provdes addtonal dscusson.. Lterature Why most frms n market economes exhbt certan common features, and n partcular why control rghts usually resde n a group of nvestor/resdual clamants, wth employees workng under the supervson of ther employers, has long been a central queston of the economcs of organzaton and comparatve nsttutonal analyss. Knght ee for example Ledyard (995) and Davs and Holt (993) for an overvew of older publc goods experments, Fehr and Gächter (000) for the effect of punshment and Brosg, Wemann, and Ockenfels (003) for the effect of communcaton. 4

6 (9) argued that the more confdent and less rsk-averse ndvduals become entrepreneurs whle others become workers who demand nsurance aganst rsk and who accordngly must be supervsed, snce ther fxed wages gve rse to moral hazard (see also Khlstrom and Laffont (979)). Alchan and Demsetz s explanaton of why workers are supervsed by a resdual-clamng central montor was summarzed n the ntroducton. Margln (974) argued that captalsts carved out the role of mposng dscplne on workers at the expense of workers welfare, by developng technologes that undercut the postons of ndependent workers. Holmström (98) suggested that the montorng of nputs could be rendered unnecessary by a forcng contract, but the contract envsoned s largely hypothetcal and has been argued to suffer from serous moral hazard problems (Eswaran and Kotwal (984), MacLeod (988)). Eswaran and Kotwal (989) and Banerjee and ewman (993) explan the assgnment of control rghts to fnancers by reference to unequal wealth and mperfectons n credt markets assocated wth the lmted lablty of borrowers. Kremer (997) argued that workers usually don t run frms because control by workers leads to a tendency to redstrbute earnngs among members, whch dstorts ncentves. Dow and Putterman (000) and Dow (003) vew Alchan-Demsetz s montorng hypothess as one of the leadng canddates to explan the conventonal employment relatonshp, alongsde theores of worker lqudty constrants and rsk averson, addtonal fnancng problems assocated wth mssng membershp markets, and potental decson-makng problems due to heterogenety of worker preferences. However, they pont out that contrary to the theory s mplcaton that work ncentves would be weak wthout a resdual-clamng central montor, most evdence on worker-owned and proft-sharng frms, as well as that on self-managng teams, suggests that they acheve hgher-than-average effort levels wth less-than-average numbers of supervsors (Estrn, Jones, and vejnar (987); Wetzman and Kruse (990); Crag and Pencavel (995)). Incentves appear to be a strength rather than a weakness of proft-sharng, wth a frequently mentoned theme beng ts encouragement of mutual montorng. ee also the references to Alchan and Demsetz s hypothess n many of the papers cted n the prevous paragraph. 5

7 In a recent expermental study of work organzaton and ncentves Potters, efton, and van der Hejden (005) compare laboratory manager-less teams that play a standard publc goods game wth teams havng managers who can decde how much to pay the other members. They fnd that managers are able to elct hgher effort from team members than s forthcomng n the PGG, by lnkng pay to effort somewhat n the manner suggested by Alchan and Demsetz. Whle the performance of ther manageral frms s remarkable, ther manager-less frms may be a poor representaton of selfmanagng teams, snce lnkage of pay to effort s ruled out n such teams under ther expermental desgn. Another attempt to expermentally compare self-managed teams and centrally managed teams has been undertaken by Frohlch, Godard, Oppenhemer, and tarke (998). They desgned a real-effort experment wheren they observed hgher productvty, greater perceved farness n pay and lower need of supervsory efforts for employee owned frms compared to the conventonally owned frms. Another expermental study ncorporatng dfferent group ncentve mechansms s albantan and chotter (997). They compared revenue sharng, forcng contracts, competton between teams, proft sharng and montorng. Montorng n ther context was a probablty of beng observed and gettng fred when one s effort s too low. Ths knd of montorng was successful but only f the probablty s hgh enough; thus, successful montorng s expensve A model of team producton wth montorng We model a team consstng of members who play a fntely repeated game for T perods. In each perod, a team member receves an endowment e, whch we ll assume to be dentcal for all members. Team member chooses an amount c wth contrbute to a team producton process, leavng 0 c e to e c for prvate producton. The sum 3 The numerous socal dlemma experments begnnng wth Fehr and Gächter (000) or Carpenter, Bowles, and Gnts (006), n whch subjects can punsh those who contrbute too lttle to a publc good, can also be vewed as studyng alternatve ncentve mechansms for group producton. In these experments, the publc good always remans publc, whereas we allow ts publc character to be elmnated by montorng. 6

8 of the team members contrbutons (denoted by C c ) generates a team proft of R C wth < R <. The dvson of the team proft among the team members depends on the montorng technology appled to dentfy the ndvdual team contrbutons, whch s a result of a smultaneous nvestment process pror to the contrbuton decson. Each team member nvests m [0,...,] nto the montorng technology at a lnear cost κ m (wth the margnal montorng cost κ ). The total nvestment n montorng M m determnes the accuracy of the montorng technology and thus the proporton of the team proft whch s dvded accordng to the ndvdual contrbuton. M 0 allows no dentfcaton of the ndvdual contrbutons and hence the team proft s dvded equally among the team members. The hgher M s the hgher s the proporton of the team proft whch s allocated accordng to the ndvdual contrbutons. M allows a perfect dentfcaton of the team members contrbutons and hence the team proft s allocated accordng to the ndvdual contrbutons. The general rule for team member s proft s: π e κ m c + M R C + M R c () The montorng technology changes the nature of the team problem. Wthout any montorng (M 0) team producton s a classcal lnear publc good provson problem wth free-rder ncentves due to π e c + R C /. However, f each team member fully nvests n the montorng technology (M ), team producton s a prvate nvestment task wth π e κ c + R c. The postve nterest rate R - provdes ncentves for full contrbutons. Intermedate values of M lead to lnear combnatons of the publc and the prvate good provson. If, for example, half of all team members fully nvest n montorng,.e. M /, then half of the team output s allocated accordng to the prvate contrbuton and the other half s dstrbuted equally among the team members,.e. π e κ m c + R C + R c. Thus, the model reflects Alchan and Demsetz s dea that wthout montorng team producton s a pure publc good 7

9 problem n whch the team output s shared equally, however f a suffcent nvestment s made n montorng ndvduals contrbutons, then they can be pad accordng to ther contrbutons as a result of whch there wll be an ncentve to contrbute and not to free rde. For the analyss of the subgame perfect equlbra of the game t s convenent to restructure () as: π e κ m c + β c + γ C () where C c j j j denotes the sum of the others contrbutons, the weght R β ( M + M ) denotes the team member s margnal return from hs/her own R nvestment and the weght γ ( M ) denotes the team member s margnal return from the nvestment of the others. Wth no montorng β γ R, meanng that all team members proft equally from each unt of contrbuton, whle wth perfect montorng β R and γ 0, meanng that only the contrbutor profts from hs or her own contrbuton. Obvously, t s ndvdually ratonal to contrbute the entre endowment when β, because each token nvested has an ndvdual return of at least. β s satsfed f and only f M ~ : M. R Equlbrum nvestment n montorng and contrbutons to the team project The game conssts of two stages. In the frst stage players smultaneously nvest n montorng. After havng learned the total nvestment M the players decde on ther contrbuton to the team project. We analyze the game by backward nducton dentfyng the subgame perfect equlbra under the assumpton that the team member s solely motvated by the maxmzaton of her monetary payoff. Consder the subgames of the 8

10 contrbuton to the team project (after the amount M was made publc). It suffces to dstngush three classes of subgames: those wth β <, those wth β >, and those wth β. For β < the ndvdual return from the ndvdual contrbuton s lower than the cost of contrbutng and hence n the equlbra of these subgames all team members choose c 0. If, however, β > each team member ndvdually gans from contrbutng and hence wll choose c e n equlbrum. For β players are ndfferent between contrbutng and keepng the entre endowment or parts of t and hence each contrbuton 0 c e may be part of a subgame perfect equlbrum. ow turn to the nvestment n montorng. The subgame has multple equlbra. There are two symmetrc ash equlbra n pure strateges: one n whch each player does not nvest n montorng (m 0) and the other one n whch each player nvests the -th part of the amount necessary to make full contrbuton to the publc good ndvdually ratonal ~ M ( m ). In addton, there s an nfnte number of asymmetrc pure strategy equlbra of the subgame whch are all characterzed by nvestments m satsfyng M M ~. Hence the publc good dlemma of team producton may be resolved n the montorng phase pror to t. However, the nvestment n montorng s a coordnaton problem wth multple equlbra, thus vulnerable to severe coordnaton falures. 4 If decson maker beleves that other group members wll nvest lttle n montorng such that her nvestment m does not suffce to acheve M ~, her best reply s not to nvest. mlarly, f beleves that other group members wll nvest enough n montorng to acheve M ~, then her best reply s to abstan from montorng a stuaton resemblng the ncentve to free rde on montorng that Alchan and Demsetz appear to have had n mnd. Only f beleves that her nvestment s needed to exactly meet M ~ s t ratonal for her to nvest n montorng. pecalst montorng 4 Marx and Matthews (000) 9

11 To overcome the coordnaton problem n the montorng phase, team members may hre a specalst to take the montorng decson. The substtuton of peer montorng by specalst montorng has the advantage that the specalst s a sngle decson maker who (n equlbrum) chooses an ncentve compatble level of montorng wthout any coordnaton problems. The drawback s that she has to be pad a share of the team output n order to have the proper ncentves. 5 Let the specalst be enttled to a share of the team proft R C. uppose that the specalst has an endowment e whch enables her to nvest at least M ~ unts of montorng. Thus, the payoff functons under specalst montorng are as follows: π e κ m + C R for the specalst (3) π e c + β c + γ C for the team member (4) wth the adjusted weght β ( ) β denotng a team members margnal return from hs/her nvestment after deducton of the specalst s share and the adjusted weght γ ( ) γ denotng a team member s margnal return from the nvestment of the others after deducton of the specalst s share. Full contrbuton of the team members s ndvdually ratonal f and only f ~ M : ( ) R β M. 5 Alchan and Demsetz never spell out where the resdual earnngs of the central montor come from, smply assertng that the montor pays team members the estmated value of ther margnal products and keeps the resdual. Our model assgns to the montor a fracton of the output because wth average and margnal product equal, there s no resdual above the sum of margnal products. We mplement the model wth suffcently large R so that both montor and team members can proft from centrally montored team producton. 0

12 If the specalst nvests less than M ~, team members n equlbrum contrbute a total of 0 unts of effort to team producton, so the specalst s earnngs from team producton wll be 0 0. If the specalst nvests at least M ~ n montorng, each team member n equlbrum contrbutes hs/her full endowment of e to team producton, so the specalst s earnngs from team producton wll be e R. Hence, for reasonable costs κ the specalst wll n equlbrum choose the lowest montorng level for whch t s ndvdually ratonal for the team members to fully contrbute ther endowment that s M ~ ~ - and gan a total proft ofπ e κ M + e R > 0. s To recap, we presented a formal model of team producton n the sprt of Alchan and Demsetz. The elegance of the model s that t allows a contnuous transformaton of the team problem wth free-rdng ncentves nto a proftable prvate nvestment problem through the actons of the team members and/or the decson of the specalst montor. Because of the coordnaton problem, t s dffcult though not mpossble that team members manage the transformaton on ther own. In contrast, the specalst s unambguously predcted to carry out the transformaton f parameters are consstent wth π > 0 when M M ~, snce she can accomplsh ths by a sngle ndvdual decson. s The drawback to the team members of hrng s ts cost, albet t s n equlbrum more than compensated compared to full free-rdng. A dscrete verson of the model For the expermental mplementaton of the game we chose a dscrete verson of the payoff functon and a bnary choce n the nvestment n peer montorng { 0,} m to facltate comprehenson by subjects. We exogenously ntroduce two dfferent thresholds of montorng T and T wth T < T. If M < T all team members equally proft from all contrbutons, for T M < T half of the team proft s allocated equally and the other half accordng to ndvdual contrbutons, and fnally, for T M each team member solely profts from hs/her own contrbuton. Hence, the payoff functon under peer montorng s:

13 + < + + < + M T c R c m e T M T c R C R c m e T M C R c m e,, 0, κ κ κ π (5) In terms of β and γ ths means: < + < M T R T M T R R T M R R 0,, ) ( 0 /, / γ β γ β γ β Example: The followng example llustrates the model and uses functonal forms and parameters that wll also be used n our experment. Let 5 be the number of team members wth an endowment e 0, a multpler R 3, the specalst s endowment e 5 and the specalst s share 0.5. Then < < M T T M T T M 0 3.0,.5.8, , γ β γ β γ β < < M T T M T T M 0.5,.5.35, , γ β γ β γ β Hence for T M full contrbuton to the team project s ndvdually ratonal, because the ndvdual return from nvestment β s greater than. In the subgame perfect equlbrum wthout peer montorng ( 0 * m ), contrbutons to the team project are 0

14 ( c * 0 ), leadng to team members payoffs of 0. However, there are also equlbra n whch montorng takes place. The smplfcaton of the model by choosng dscrete values of montorng and thresholds restrcts the number of these equlbra. everthe- less, there are stll subgame perfect pure strategy equlbra, characterzed by exactly T team members nvestng n T montorng. In the experment we used two treatments n whch T and three n whch T 4. Because team members are restrcted to nteger nvestments, a symmetrc equlbrum wth montorng s not achevable. Ths means that the only symmetrc equlbrum prescrbes no nvestment n peer montorng. All the equlbra wth montorng are asymmetrc and hence very vulnerable to coordnaton falure. In case of 5 and T, the game has 0 pure strategy equlbra n whch exactly out of the 5 players have to nvest n montorng and n case of 5 and T 4, the game has 5 pure strategy equlbra n whch exactly 4 out of the 5 players have to nvest n montorng. If team members are able to self-organze (.e. acheve M T ) each team member earns 30 mnus the nvestment n montorng (f ndvdually applcable). 6 In the equlbrum of specalst montorng the specalst nvests T n montorng and the team members contrbute ther entre endowment. Hence, the team members earn and the observer earns her endowment (of 5) mnus the montorng nvestment plus Obvously, t would be most proftable for the team members to play one of the equlbra wth postve peer-montorng. Then each member earns 9 or 30, dependent on whether he/she nvested n montorng or not. However, there s a hgh rsk of coordnaton falure. Falng to reach the suffcent level of montorng leads to drastcally lower ndvdual payoffs of 9 and 0, dependent on whether the ndvdual nvested n montorng or not. 7 Facng ths rsk, team members may decde to hre a specalst to make 6 otce that the montorng cost s pad out of end-of-round earnngs; thus, contrbutng to montorng doesn t prevent a subject from stll contrbutng a full 0 unts to team producton. 7 The other form of coordnaton falure n the form of over-provson of montorng s less dsastrous because t just leads to more players earnng 9 nstead of 30, than n equlbrum. 3

15 the montorng decson and acheve a payoff 7.5 lower than the hghest equlbrum payoff, but 3.5 hgher than the worst payoff n case of coordnaton falure wthout suffcent montorng. 4. Expermental Desgn We conducted an experment consstng of fve treatments correspondng closely to the model above. In each sesson of the experment, subjects were randomly and anonymously assgned to groups of sx, wth one subject randomly assgned the role dubbed observer and the other fve the role team member. We mplemented the dscrete verson of the game descrbed above wth the parameters of the example above. ubjects were told at the outset that they would engage n thrty rounds of decsons n the same roles and wth the same anonymous group members. The two step structures -5 ( T and T 5) and 4-5 ( T 4 and T 5) specfy two sets of parameters for the thresholds T and T, whch n turn generate three possble ncentve regmes for team producton henceforth referred to as EQUAL, HALF/HALF, and ATIC ( accordng to ndvdual contrbuton ) (see Table ). Table tep tructures Dvson rule tep tructure -5 tep tructure 4-5 equal dvson ( EQUAL ) 0 M < 0 M < 4 half dvded equally, half accordng to contrbutons ( HALF/HALF ) dvson accordng to ndvdual contrbutons ( ATIC ) M < 5 4 M < 5 M 5 M 5 In step structure -5 at least two unts have to be nvested n montorng to make contrbutons to the team project ndvdually ratonal, whle n step structure 4-5 at least 4 unts have to be nvested. Each group of subjects was assgned to ether one structure or the other throughout ther sesson, wth no knowledge of the other structure. 4

16 The 30 rounds of a sesson were dvded nto sx phases, wth 5 rounds each. In every sesson, Phase I conssted of 5 rounds wth no montorng.e., a standard 5 round VCM condton. Phases II and III conssted of 5 rounds wth montorng (f any) by the observer and 5 rounds of montorng (f any) by peers, wth the order n whch observer and peer montorng occurred varyng among sessons (see Table ). In OP sessons, the observer made the montorng decsons n Phase II and the team members made the montorng decsons n Phase III; n PO sessons, the order was reversed. To avod boredom and unnecessary nequaltes and to motvate the observer to learn about ncentves n team producton, we assgned the observer a task to perform n those perods n whch he or she was not permtted to montor and earn a 5 percent share of team project revenue. The observer s task was to estmate the perod s sum of contrbutons C n hs/her group. As an ncentve for accuracy, the observer earned more the closer was hs/her guess to the actual C, whch was revealed to hm/her at the end of the perod. 8 ote that the observer mght learn somethng about how team members contrbutons respond to montorng by observng peer montorng phases, and accordngly sessons usng the PO orderng mght be expected to be more conducve than those wth orderng OP to successful decson-makng by the observer when n the montorng role. In each sesson, each of the last three phases could have ether observer or peer montorng, dependng on how the members of the team n queston voted. Before rounds 6,, and 6, each team member was asked to vote for ether observer or peer montorng. The group was nformed of the majorty vote (wthout a breakdown of the number of votes) and began to play fve rounds accordng to the chosen nsttuton. A schematc representaton of the course of the nteracton n the PO orderng s gven n Fgure. Phases I to III form the frst half of the experment, and phases IV to VI the second half. 8 The formula for the observers proft durng phases n whch he dd not play a montorng role, such as 30 Phase I, was: π C Guess of C 5

17 Fgure chematc representaton of the course of the nteracton for PO The alternatves of the PO or OP orderng and of the -5 or 4-5 montorng structure gve rse to a x desgn wth four treatments: PO5, OP5, PO45, OP45. Due to the unexpected nature of the results of those treatments, whch are dscussed n the next secton, we conducted sessons wth an addtonal treatment that s otherwse lke the OP45 treatment but n whch the cost of a unt of montorng was made three tmes hgher for a team member than n the other four treatments, whle the cost of montorng for the observer was left unchanged. We dstngush the two treatments by referrng to them as OP45MC and OP45MC3, wth the other three treatments also sharng the MC desgnaton. Table provdes an overvew of the fve treatments. 6

18 Table Treatment descrpton Treatment Phase equence tep structure Cost per unt of montorng Phase II Phase III Peer κ Observer κ PO5MC Peer Observer tep tructure -5 OP5MC Observer Peer PO45MC Peer Observer OP45MC Observer Peer tep tructure 4-5 PO45MC3 Peer Observer 3 In each treatment we have 6 groups (from two sessons of three groups each) each contanng 6 subjects (5 team members and observer). Hence we had 80 subjects n the experment. Each subject sat n a separate compartment n the experment lab at the Unversty of Erfurt, dd not know whch other subjects were n hs/her group, and had no communcaton wth others apart from nformaton about choces that was transmtted by computer. ubjects were frst read aloud and followed on ther screens nstructons explanng the structure of the entre sesson, worked through examples, and asked the expermenter questons, f any. All subjects were students who were recruted at the Unversty of Erfurt usng the Orsee ystem 9. The experment was conducted wth the z-tree oftware package (Fschbacher, 007). ubjects earned on average EUR. 5. Results Evaluaton of the data shows that there are no sgnfcant effects assocated wth whether the OP or the PO order s used n phases II and III, n partcular the nvestments n montorng and the contrbuton levels are not sgnfcantly dfferent. 0 Therefore, we The dfference n average contrbutons and montorng between OP and PO are not dfferent at 0 % level (exact Mann-Whtney-U-Test) wth one excepton (OP5MC vs. PO5MC n the observer montorng phase) 7

19 analyze the pooled treatments PO5MC and OP5MC as 5MC and the pooled treatments PO45MC and OP45MC as 45MC. In each of the pooled treatments we now have ndependent observatons. Dscusson of treatment PO45MC3 s postponed to secton Votng Results and consequences One of our man research focuses s on the endogenous montorng choce after subjects ganed experence wth peer as well as wth observer montorng. Therefore, we start off wth the presentaton of the result of the second half of play. Dd the votng process exhbt a preference for observer montorng to avod the coordnaton problem n peer montorng? The answer s a surprsngly clear o! As Table 3 shows, the observer was never chosen by majorty vote n the 36 votng rounds of treatment 45MC and chosen only once n the same number of votes n treatment 5MC. Table 3 Choce of Observer or Peer Montorng n the second half umber of choces of Observer montorng Peer montorng 5 MC ( 3%) 35 ( 97%) 45 MC 0 ( 0%) 36 (00%) Result : In the four MC treatments, the observer s almost never chosen by the majorty vote of the team members. How dd the peer montorng teams perform? In the majorty of cases team members faled to reach an equlbrum level of montorng. In 5MC an nvestment n montorng of was reached n 37.7 percent of the cases, whle n 45MC the equlbrum level of 4 unts of montorng was only reached n 8.3 percent of all cases. Ths demonstrated the hgh vulnerablty of montorng to coordnaton falure. evertheless, n the two MC treatments the peer montored groups were very successful n mplementng a dvson rule n whch full contrbuton to the team project s ndvdually ratonal (see Fgure a). They mplemented HALF/HALF or ATIC n 93 percent of the cases. Fg- 8

20 ures b and c addtonally show that contrbutons as well as payoffs under both sharng rules are extremely hgh. Result : In the MC treatments, peer montorng performs extremely well: n 93 percent of the cases a rule capable of elctng full contrbutons s reached; contrbutons are near 00 percent of endowments and payoffs are hgh. However, we observe an nterestng dfference between HALF/HALF and ATIC. A payoff-maxmzng subject should contrbute her full endowment under both dvson rules, because n both cases one unt of contrbuton s repad by more than one, for all possble actons of the other team members. evertheless we observe that contrbutons under ATIC are on average 9.9, whereas contrbutons under HALF/HALF are on average 8.7. The dfference s sgnfcant (p < 0.00, two taled exact Wlcoxon test). The explanaton for ths phenomenon may be attrbuted to socal preferences. Under ATIC only the contrbutng team member profts from her contrbuton, whereas under HALF/HALF all other team members also proft (at least partly). Although t maxmzes the ndvdual payoff, a team member may (for example, due to farness concerns) wthhold contrbuton n order to reduce a potental free-rder s beneft from her contrbutons. However, role-of-thumb or boundedly ratonal reasonng could also explan some dfference. Fgure : a) Frequency of mplemented dvson rules; b) Contrbutons; c) Payoffs; dsplayed are averages over the observatons n the second half 9

21 An nterestng fndng s that the average payoffs n 45MC are sgnfcantly hgher than n 5MC (p0.043 one sded Mann-Whtney U), although 4 nstead of unts of montorng are requred to make full contrbuton ndvdually ratonal. The reason s the extremely hgh number of mplementatons of ATIC n 45MC accompaned by hgh contrbutons n ATIC (see above). A lkely reason s that by overnvestment n montorng, the rsk of coordnaton falure s reduced at a low cost. Gven the lack of verbal communcaton t seems practcally mpossble to agree on an alternaton rule n whch one of the fve team members wll refran from montorng each perod. Thus, most team members seem to have decded to montor every perod. ot only s the average cost of over-montorng to each subject only one unt every fve perods, but n practce that cost s not wasted, gven that subjects respond to ATIC wth more effort than to HALF/HALF. The hstograms of the total nvestment M n Fgure 3 show systematc overnvestment n montorng. Fgure 3: Hstogram of the sum of nvestments n peer montorng; dsplayed are averages over the observatons Phases IV IV. 5.. Causes What causes the clear results of the second half of the experment? To answer ths queston t s useful to analyze behavours n the frst half of the experment, wth ts exogenous phases of no montorng, peer montorng, and observer montorng. 0

22 The results of the frst phase of play, n whch subjects nteract n a classcal publc goods envronment, are well n lne wth the observatons from numerous prevous expermental studes of VCMs. Average contrbutons start off at about half of the endowment and decrease from there on. In all four treatments we observe a negatve trend n contrbutons over tme whch s n lne wth past experments and llustrates Alchan and Demsetz s ntuton about free rdng f montorng s absent, yet departs (as s typcal n VCMs) from the strct theoretcal predcton of zero contrbutons assumng payoff-maxmzng agents. 3 How dd subjects respond to the varous dvson rules? Durng the observer and peer montorng perods of Phases II and III, subjects responded to HALF/HALF and ATIC dvson rules wth consderable ncreases n contrbutons. There were, however, two mld surprses. Frst, as already noted for the endogenous rule phases, subjects contrbuted moderately but sgnfcantly more under ATIC than under HALF/HALF, even though a payoff-maxmzng agent s predcted to contrbute the full endowment under ether dvson rule. econd, subjects tended to contrbute somewhat less when the observer montored than when the team members dd. 4 otce that the prvate margnal return from contrbutng effort s smaller under HALF/HALF compared to ATIC and smaller under observer montorng than under montorng. It seems that subjects responded to dfferences n margnal returns 5, even though full contrbuton s prvately optmal (snce β and β > ) for both dvson rules and both assgnments of the montorng role. A lnear regresson shows a negatve tme trend n contrbutons for Phase I (The standard publc good phase). A regresson s performed wth the average (per group) contrbutons of Phase I as the dependent varable. The tme coeffcent s sgnfcantly negatve at % for all treatments but the PO 45 MC treatment. (robust, Huber Whte standard errors). ee agan Ledyard (995) as well as Davs and Holt (993) for a revew of the lterature on VCM experments. 3 There s by now an mmense lterature attemptng to explan ths anomaly. ome of the explanatons emphasze heterogenety of agent preferences, a matter to whch we return shortly. 4 For 5MC and 45MC, two sded exact Wlcoxon sgned-rank test: HALF/HALF p0.074, ATIC Whch s somewhat n lne for example wth Isaac and Walker (988b) although the MPCR there was below whle n our case the subjects respond on dfferent MPCR > as well.

23 Result 3: Responses to EQUAL dvson are consstent wth those n the expermental lterature on the voluntary contrbuton mechansm and wth presence of a free-rdng problem, though there s less free rdng than theory predcts. ubjects also respond to changes n margnal prvate return assocated wth the dfference between ATIC and HALF/HALF rules and wth that between observer and peer montorng, although theory predcts full contrbutons regardless of these dfferences. Peers managed to supply ncentve-mpartng montorng at least as often as dd specalst observers. The peers chose an ncentve compatble mechansm n 95 percent of the cases, the observers n 8.5 percent (n the frst half). Ths dfference s sgnfcant (p0.044, exact Wlcoxon sgned rank test). Yet, as Fgure 5a shows, observers faled to provde enough montorng to reach HALF/HALF dvson more often than dd peers n both 5MC and 45MC. Fgure 5: a) Frequency of mplemented dvson rules; dsplayed are averages over the observatons n the frst half n the 5MC and 45MC treatments. b) Average contrbutons over the observatons n the frst half n the 5MC and 45MC treatments. c) Average profts over the observatons n the frst half n the 5MC and 45MC treatments. Result 4: Falure to acheve a dvson rule provdng ncentves to contrbute the full endowment occurred less often n the exogenous peer than n the exogenous observer montorng phases. It comes as a surprse that despte ther coordnaton problem team members succeeded more often n achevng an ncentve compatble allocaton rule than observers. How

24 dd the teams manage the coordnaton problem? One explanaton could be that subjects followed an overprovson strategy 6 ( nvest n montorng regardless of others choces ) because the benefts from full provson over-compensated the excess n provson. Another explanaton s that subjects are guded by non-standard or socal preferences. uppose, for example, that some subjects are condtonal cooperators 7 for whom the (subjectve) payoffs n a VCM may resemble those of an assurance or stag hunt game more than those of a prsoners dlemma. Ther presence could help to explan the hgher-than-predcted contrbutons n Phase I, and lkewse would account for propenstes to contrbute to montorng even f coordnaton were mpossble or f no equlbrum strateges exsted, for payoff-maxmzers. 8 Evdence that subjects wth preference-based nclnatons to cooperate account both for some contrbutons and some montorng could take the form of a sgnfcant correlaton between contrbutons especally n the frst perod of Phase I, and average montorng durng a peer montorng phase. We checked the correlaton at ndvdual subject level between montorng nvestment durng the exogenous peer montorng phase and frst perod contrbuton n Phase I. Poolng the data for the two MC treatments, we found a sgnfcant postve correlaton, meanng that the subjects wth hgh contrbutons also tend to nvest n montorng (asymptotc pearman correlaton test, stratfed by treatment, p0.06). Takng together the lower rate of achevng ncentves to contrbute fully and the hgher costs under observer montorng, t comes as no surprse that team members earnngs were sgnfcantly lower under exogenous observer montorng than under exogenous peer montorng (p<0.0 percent Mann-U-test). Indeed, n the frst half n all 6 ote that n the settng of our experment a group could succeed n montorng even f only two members adhered to an overprovson strategy, n 5MC, or f four adhered to t n 45MC. 7 In the sense of Fehr and Gächter (000) and Fschbacher, Fehr, and Gächter (00) 8 Duffy, Ochs, and Vesterlund (007) fnd that subjects are not much more lkely to complete a publc project of fxed sze when a fnal payoff jump causes equlbrum strateges n postve contrbutons to exst than when absence of such a jump makes a postve gvng equlbrum theoretcally non-exstent, a result that mght also be explaned by the presence of some condtonal wllngness to cooperate. evertheless, the absence of a payoff jump may explan some of the dfference between behavors n the treatments dscussed thus far and those n our QUAD treatment (see ecton 5.4, below). 3

25 our ndependent observatons team members earned hgher profts under peer montorng than under observer montorng. Result 5: Team members earnngs were lower under exogenous observer than under exogenous peer montorng. Ths experence from the frst half may well explan why team members voted to mplement peer rather than observer montorng n the second half of ther sessons. Of course, f teams had then faled to acheve suffcent montorng to sustan contrbutons n later phases, they mght be expected to have swtched to votng for observer montorng (see ecton 6). But no team experenced more than one perod of ncentve falure durng phases IV and V, so ther contnued preference for peer montorng s ratonal Rasng the bar a further test As we have seen, n sectons 5. and 5. team members seem to reduce the rsk of coordnaton falure by overnvestment n montorng. Obvously, overnvestment n montorng s not n equlbrum, but t s a less costly way of achevng an ncentve compatble dvson rule than hrng the observer. In the lght of these results we extended our analyss by conductng a new treatment PO45MC3 whch s dentcal to PO45MC, wth the only excepton that for the peers the cost of one unt of montorng s rased to 3. Ths rases the bar for peer montorng: t ncreases the cost of mplementng the HALF/HALF rule from 4 to, trples the cost for mplementng ATIC from 5 to 5, and t also trples the cost to the ndvdual of adherng to an overnvestment strategy. 0 otce that the observer s cost remans at per unt of montorng. We col- 9 We can fnd no explanaton for the one nstance n whch three of fve team members voted for observer montorng after Phase IV, occurrng n OP5MC. Although the team n queston had acheved HALF/HALF montorng n four of fve perods of Phase II wth a bare two subjects montorng (achevng ATIC one tme), team members have no way to know whether, 3 or 4 montored, and ther earnngs were hgher under peer (Phase II) than observer (Phase III) montorng n every perod. on-parametrc tests for dfferences between the antecedents of that vote and others n the MC treatments are mpossble snce the case n queston s sngular. 0 As before, the montorng charge s stll pad out of end-of-round earnngs, so t s possble to pay 3 to montor, yet stll contrbute 0 to team producton. 4

26 lected sx ndependent observatons n ths treatment. Through ths change montorng by the observer should become more attractve because coordnaton and overnvestment n montorng s more costly and hence can be expected to be more dffcult to acheve. Votng Results and Consequences Indeed, we observe a sharp ncrease n votng results mplementng observer montorng. The observer was voted for by a majorty n 6 percent of the 8 votes. Fgure 6a shows that the observer mplements ATIC n the majorty of cases. In response to ths, team members make hgh contrbutons and receve payoffs whch are dluted by the observer s share of 5 percent. Interestngly, n those groups and phases n whch peer montorng was the votng choce, team members manage to acheve HALF/HALF or ATIC n almost 90 percent of perods. Hence, when peer montorng s voted by the majorty of the team, the team s qute successful n provdng enough unts of montorng to provde ncentves for makng full contrbutons ndvdually ratonal, despte the hgher costs and contnued, perhaps even exacerbated, coordnaton problem. What s t that makes the observer model more appealng to subjects n PO45MC3? Fgures 6 shows the dfferences n the frst half between those groups votng for the observer later on (vote O) and those who dd not (vote P). It s clear from Fgure 6a that there were more falures to acheve HALF/HALF or ATIC under exogenous peer (observer) montorng n groups that eventually voted for observer (peer) montorng. Those groups whch vote for peer montorng experenced hgher average contrbutons under peer montorng n the frst phase, whle those who vote for observer montorng experenced hgher contrbutons under observer montorng n the frst phase (see Fgure 6b). The same tendency s observed when lookng at profts (see Fgure 6c). Result 6: If the unt cost of peer montorng s rased to 3, the majorty of teams vote for observer montorng. However, almost 40 percent stll vote for peer montorng and perform well, out-earnng those who hre the observer. 5

27 Fgure 6: a) Frequency of mplemented dvson rules; dsplayed are averages over the observatons n the frst half of PO45MC3 comparng those groups votng for the observer (vote O) wth those who voted for peer montorng (vote P), the overall share of the rules n the frst half (st H) and the second half (nd H). b) and c) averages of the contrbutons resp. profts over the frst half of those groups votng later for the peer montorng (vote P) or observer montorng (vote O) plus the averages of the frst and second half wthout the votng decson dstncton. 5.4 Extendng the Model: The Zero Montorng Equlbrum Case Our model presented so far ncorporates a coordnaton problem n montorng. Thus, there exst equlbra wth a postve level of montorng, although coordnatng on them may be nearly mpossble. We wondered whether the tendency of team members to pay for montorng despte the temptaton to let others do the job would survve a stll harder challenge: a stuaton n whch the only equlbrum n montorng nvolves no montorng at all. To model peer montorng as a pure publc good problem, we need a specfcaton n whch the gans from montorng lack the dscrete jump that can make the margnal unt prvately proftable. We acheve ths by ntroducng a quadratc cost func- 6

28 ton n producton. pecfcally, we change the proft functon for a team member n the peer montorng phase to π c e κ m + β c + γ f C. (6) where f s a cost functon parameter. As a second change, we elmnate the step-lke relatonshp between payoffs and montorng, now allowng β and γ to ncrease and decrease, respectvely wth each unt by whch M rses or declnes. Durng the observer montorng regme the β and the γ n equaton (6) are replaced by ther by ( ) reduced counterparts β and γ. The ndvdual optmal contrbuton for the peer montorng mechansm wth the new model s f + M ( ) f c * R β (7) Proft-maxmzng peers wll never nvest n montorng as long as: fr ( ) κ + M + 4 (8) If (8) s fulflled, the team members have no ncentve to montor and thus M 0 leavng ndvdual optmal effort choce c fr smaller than the socally optmal fr. 3 Intutvely, the quadratc cost functon causes the margnal return to effort c so Quadratc cost functons n the context of publc good experments were used for example n Isaac and Walker (988a), Irlenbusch and Ruchala (008), Keser (996), efton and tenberg (996). R R The γ and the β are agan γ ( M ) and β ( M + M ) 3 ee Appendx for the dervaton. 7

29 to declne as montorng nduces more effort, renderng montorng ndvdually unproftable at the margn despte the fact that an outcome wth more montorng and hgher effort would be collectvely preferable a classc socal dlemma. Hence, our game conssts of the sequence of two socal dlemmas: frst the dlemma n montorng and secondly the dlemma n contrbutng. Overcomng the montorng-dlemma mght change the contrbuton stage nto an ncentve compatble nvestment problem. However, n an equlbrum of proft-maxmzng agents the players refran from montorng as well as from contrbutng. We conducted two expermental sessons of the new treatment we dub QUAD for ts quadratc cost functon, collectng eght new ndependent observatons (wth 40 new subjects), testng the model wth the parameters κ 3. 5, f and 0%. 4 (The other parameters reman as before.) Because (8) holds, peer montorng by proftmaxmzng ndvduals should lead to M 0. Wth the observer recevng 0% of the group producton durng those phases n whch he s exogenously assgned or chosen by vote as the montor, he s predcted to maxmze earnngs by selectng M 5. These montorng levels mply that team members maxmze ther ndvdual earnngs by each selectng effort levels c * under peer and c * 8 under observer montorng, for earnngs of 5.37 and 9.6 respectvely. The observer, n turn, earns a maxmum of.5 when choosng M 0 and 30 when choosng M 5, assumng that team members respond n prvately optmal fashon. nce we dd not fnd a sgnfcant effect of the order, all ndependent observatons were conducted usng frst the peer and second the observer montorng phase n the frst half, as before preceded by a 5 perod phase wth no montorng. Results Even though the new parameters and cost functon make montorng more costly, reduce the gans from team producton, and generate a pure free rder problem (as op- 4 The values assgned to κ and especally to f hnt at the dffculty of fndng parameters that yeld the desred equlbrum propertes. In fact, mportant features dsappear wth mnor perturbatons. The condtons of ths secton s equlbrum, and by extenson of Alchan and Demsetz s ntuton about the susceptblty of mutual montorng systems to free rdng, may therefore be somewhat specal. 8