Unilateral Emissions Abatement: An Experiment

Transcription

1 Unlateral Emssons Abatement: An Experment Bodo Sturm and Joachm Wemann Abstract: Accordng to the model of Hoel (99), a unlateral emssons abatement of a global pollutant leads to lower aggregated emssons n a game wth a smultaneous decson protocol. Our experment tests the Hoel model and examnes the queston of whether a leader can nduce addtonal abatement of followers n a game wth a mxed sequental-smultaneous decson protocol. Usng an envronment wth a unque nteror equlbrum, our experments confrm the stylzed outcomes of prevous publc good experments. Changes n abatement and profts for the smultaneous decson protocol are n lne wth the theoretcal predctons of the Hoel model, albet not sgnfcantly n every case. In the treatments wth a mxed sequental-smultaneous decson protocol, the leader takes the opportunty to abate more than s predcted by theory. However, n most cases the leader faled to nduce cooperaton,.e. there are only few followers who react cooperatvely to the leader s sgnal. Hgh efforts by the leader and the cooperatve followers are exploted by the maorty of defectve followers. Support by the Deutsche Forschungsgemenschaft (DFG) and the CESfo, Munch, s gratefully acknowledged. The authors thank Jeannette Brosg, Hartmut Klemt, Manfred Köngsten, Thomas Rechmann, Martn Weber and an anonymous referee for ther helpful comments. Contact address of Bodo Sturm: Centre for European Economc Research (ZEW), Postfach 03443, Mannhem, Germany. E-mal: sturm@zew.de, phone: , fax: Contact address of Joachm Wemann: Otto von Guercke Unversty Magdeburg, Faculty of Economcs and Management, Postfach 420, 3906 Magdeburg, Germany. E-mal: oachm.wemann@ww.un-magdeburg.de, phone: , fax:

2 Unlateral Emssons Abatement: An Experment. Introducton Some of the most serous envronmental problems can be characterzed as nternatonal publc good problems. The damage each country suffers depends on the aggregated emsson of harmful materal and not (only) on local emssons. The most promnent example s the clmate change expected from global CO 2 emssons. It s not n the self nterest of each ndvdual country to abate the Pareto effcent amount of emssons, because parts of the total beneft generated by abatement cannot be nternalzed. Gven ths stuaton, envronmental pressure groups often demand that local poltcans take on a leadng role and abate more emssons than s n the narrow self nterest of the country. Obvously, they expect that a good example may encourage other countres to on the coalton of abatng countres n order to overcome the socal dlemma stuaton all countres are confronted wth. Furthermore, there s the hope that the leader hmself can proft from the leadng poston. As an example we can quote the German Federal Mnster for the Envronment (BMU, 2002): We are the leader n nternatonal clmate protecton and we want to mantan our leadng poston because clmate protecton creates new obs and opportuntes to export clmate protecton polcy generates not only envronmental benefts but also economc profts. The leadng poston of German clmate protecton polcy s proftable. There are numerous examples for stuatons n whch leadershp of one country may have the potental to nduce cooperaton of other countres. The polluton of the Baltc Sea or the acd ran problem between Fnland and the former USSR are hstorc examples for the European regon. It s not qute clear why countres should follow the good example of a leader even f t s not n ther mmedate self nterest. However, one may speculate that cooperatve solutons are only accessble f players (countres) manage to coordnate on the effcent outcome. 2 Therefore, leadershp may serve as a coordnaton devce. Alternatvely, one may hope that the good example creates some knd of a socal norm. If followers gnore ths norm, ths may cause emotonal costs. Thus there are several ways n whch leadershp possbly s able to nduce cooperatve behavor of the followers. In a semnal paper, Hoel (99) nvestgated the consequences of unlateral emssons abatement n a global publc good game,.e. abatement of a sngle country (say country ) above the equlbrum level, under the assumpton that all countres decde smultaneously and that all other countres behave fully ratonally and selfshly. It turns out that unlateral emssons abatement leads to a lower abatement of the other countres, but to a greater total abatement. Total welfare ncreases f country has the lowest margnal beneft from abate- See Katala et al. (992). 2 Brosg et al. (2003) was able to show n a standard publc good experment wth communcaton that successful cooperaton only occurs f subects had the opportunty to coordnate ther behavor by face to face communcaton. Thus coordnaton seems to be a necessary condton for cooperaton.

3 Unlateral Emssons Abatement: An Experment 2 ment. 3 However, the assumpton of selfsh behavor of all countres except rules out that the good example gven by country can nfect other countres. 4 Thus t remans an open queston whether leadershp matters. In ths paper, we try to answer ths queston by testng the Hoel model expermentally. The ssue of whether abatement on the part of the leader has an nfluence on the behavor of the followers s analyzed n an experment by van der Heden/Moxnes (2000). However, there are some mportant dfferences between our desgn and the desgn chosen by van der Heden and Moxnes. In ther experment, subects played a standard publc bad game 5 where both the Pareto effcent outcome and the equlbrum soluton for the smultaneous decson protocol and mxed sequental-smultaneous decson protocol had a boundary soluton. Therefore, they dd not really test the Hoel model, whch has nteror solutons and allows devatons from the equlbrum n two drectons. In van der Heden/Moxnes (2000), the leader had a sgnfcant nfluence on the other subects (followers). However, the nfluence of the leader on the followers was not strong enough to make leadershp proftable for the leader. Renner/Gächter (2003) confrm that despte the sgnfcant correlaton between the leader s and followers contrbutons, for the leader leadershp does not pay. In ther experment, the presence of a leader n a repeated standard publc good game dd not enhance the overall level of cooperaton relatve to a stuaton wthout a leader. In a smlar experment by Güth et al. (2004), leadershp had a postve but only weakly sgnfcant effect on the aggregated contrbutons to the publc good. However, as before, for the leader leadershp does not pay. In order to test the Hoel model expermentally, two methodologcal questons have to be answered. Frst, one has to decde how the experment should be framed. Ether subects are confronted wth the game as t s wthout any reference to envronmental problems, or they are told the cover story whch fts the story the Hoel model tells us. We decded on the latter because we wanted to test f unlateral abatement of harmful materal nduces further actvtes. A far test of the model should take nto account that t s desgned to deal wth envronmental problems. Second, one has to decde how to nform subects. Once agan, we decded to desgn the experment analogously to the model. Ths means that we gave subects all the nformaton the agents n the model are assumed to have. Game theoretc models mplctly make very strong assumptons about what people know. Normally, not only the rules of the game but also the equlbrum soluton and the consequences of all knds of devatons from ratonal behavor are assumed to be common knowledge. To test the model farly, we had to ensure that these knowledge pre-condtons were fulflled. Because the game has complcated nteror equlbrum solutons, we could not assume that subects would be able to compute the predcton of 3 Hoel also shows that ths postve result no longer holds f the unlateral abatement s followed by nternatonal negotatons on emsson reductons. Unlateral reductons weaken the poston of the leadng country. Therefore, total emsson reducton after nternatonal negotatons may be lower n the case of ex ante reductons of the leadng country compared to the case wthout unlateral abatement. We do not deal wth negotatons on emsson reducton n ths paper but only look at decentralzed decsons about abatement. 4 Hoel explctly ponts out that I do not take up the queston of whether such acton from one country mght lead to smlar behavor from other countres (p. 56). 5 See Andreon (995) for a publc bad game.

4 Unlateral Emssons Abatement: An Experment 3 game theory and the Pareto effcent soluton n the lab durng the experment. We therefore decded to teach the subects before the experment and to demonstrate the predcton of game theory as well as the Pareto soluton. One may argue that ths can nfluence subects. But f ths s the case, agents n the Hoel model should be nfluenced n the same way because they possess the same nformaton we gave our subects. Not nformng subects fully would mean not testng the model but testng the ablty of students to fnd ratonal strateges n complcated games. We would lke to emphasze that ths does not mean that the experment s a recommended play game n the sense of Brands/McLeod (995). Recommendaton of a partcular strategy combnaton served n ther experment as an equlbrum selecton devce. In our experment, the Nash equlbrum s unque. Our am was not to recommend one partcular equlbrum among dfferent exstng equlbra but to make sure that the subects perfectly understand that they are n a dlemma stuaton n whch ndvdual ratonalty leads to neffcent solutons. The paper s organzed as follows. In secton 2 the model s outlned and the parameters and functons used n the experment are ntroduced. 6 Secton 3 descrbes the expermental desgn. The results are presented n secton 4 and dscussed n secton 5. Secton 6 concludes. 2. The laboratory verson of the Hoel model ( ) X In the N-country verson of the Hoel model, each country emts a global pollutant. Every country, =,..., N, chooses abatement X and possesses beneft and cost functons B ( X ) and ' '' ' '' C, respectvely, wth B > 0, B < 0, C > 0, and C > 0. The sum of ndvdual abatements s X = = X N. In the Nash equlbrum (NE) of the game wth a smultaneous decson protocol, country abates to the amount at whch prvate margnal beneft equals margnal costs,.e. B ' ' ( X ) C ( X ) = (). In the Pareto optmum (PO), aggregated abatement s chosen such that socal margnal beneft equals margnal costs,.e. B ' ' ' N ( X ) = C ( X ) wth B ( X ) = = B ' (2). Because socal margnal beneft s above prvate margnal beneft, the NE abatement s smaller PO NE than the PO abatement,.e. X > X. In order to model unlateral abatement of country, Hoel assumes that ths country derves some knd of extra margnal beneft from total abatements, measured by a parameter h. It s not mportant where ths beneft comes from. It may be the case that the nhabtants of ths country 6 A more complete verson of the model can be found n appendx.

5 Unlateral Emssons Abatement: An Experment 4 have altrustc preferences or ust love to see a cleaner world. For country, the total beneft from abatement then s ( X ) hx B + wth h > 0 (3). Gven (3), n the new NE for the smultaneous decson protocol t holds that ' ( X ) h C ( ) B = ' ' + and B ( X ) C ( X ) ' X = wth = 2,..., N (4). The standard case () s contaned n ths formulaton wth h = 0. Hoel shows that n the equlbrum descrbed by (4) country abates more and countres 2,, N abate less than n the equlbrum gven by () and that total abatements are greater n the case of unlateral abatement. He also shows that under unlateral abatement B B for all = 2,, N s a ' ' suffcent condton for an ncrease n total welfare. We are seekng an answer to the queston of whether leadershp,.e. the pure tmng of acton, matters. Therefore, t s necessary for us to analyze the mplcatons of a change n the tmng of acton from a smultaneous decson protocol to a mxed sequental-smultaneous (n the followng sequental ) decson protocol,.e. country decdes frst, the other countres are nformed of ths decson, and then decde smultaneously on ther emsson reducton. Although the cost and beneft functons reman unchanged, the shft from the smultaneous decson protocol to the sequental decson protocol alters the game theoretcal predcton of ndvdual behavor. Country, the leader, now has a strategc advantage because t may choose the pont on the best response functon of the followers whch maxmzes ts own proft. In the subgame perfect equlbrum (SPE) of the sequental game, country abates less and country abates more than n the NE of the smultaneous game. 7 Aggregated abatement n the SPE s lower than n the NE,.e. leadershp generates a negatve envronmental effect. In order to test the model expermentally, the cost and beneft functons have to be specfed. Table shows the specfcaton of the model, and n appendx we derve the approprate NE, SPE, and PO soluton. Table : Cost and beneft functons 2 Cost functon of country, =,, N C ( X ) = cx T + 2 Beneft functon of country B ( X ) = b( AX 0. X ) + hx 5 B X = AX 0.5X Beneft functon of country = 2,, N ( ) 2 To test the Hoel model and the nfluence of leadershp, we use a 2x2 factoral desgn varyng the sequence of moves and parameter h. In the smultaneous treatments (sm), all the countres smultaneously decde on ther abatement. In the sequental treatments (seq), country decdes frst, the other countres are nformed of ths decson, and then smultaneously decde on ther 7 See appendx.

6 Unlateral Emssons Abatement: An Experment 5 emsson reducton. The varaton of h n the smultaneous case s a drect test of the model. Table 2 summarzes the treatments. varable Table 2: Expermental treatments sm sequence seq parameter h h = 0 treatment T I (h = 0, sm) treatment T III (h = 0, seq) h > 0 treatment T II (h > 0, sm) treatment T IV (h > 0, seq) To mplement the four treatments, we had to specfy the parameters of the functons n table n a way that ensures that the payoff functons are suffcently steep. Table 3 summarzes the parameter values for T I - T IV and the abatements and payoffs subects realze n the NE, SPE, and PO. The parameters were chosen so that the NE has a soluton n ntegers; numbers had to be rounded for the SPE and PO solutons. 8 Table 3: Summary of parameters, abatements, profts, and payments T I and T III: b = 30/47, h = 0, A = 500, c = 3, T = 40,000, N = 5 Nash equlbrum 2 Subgame perfect equlbrum 3 Pareto optmum Country 2,, 5 all 2,, 5 all 2,, 5 all Abatement Profts (LD),707 38,6 66,5 2,23 36,22 56,97 7,488 60, ,606 Payments (EUR) T II and T IV: b = 30/47, h =3000/47, A = 500, c = 3, T = 40,000, N = 5 Nash equlbrum 2 Subgame perfect equlbrum 3 Pareto optmum Country 2,, 5 all 2,, 5 all 2,, 5 all Abatement Profts (LD) 24,974 40,564 87,230 25,73 37,69 76,88 43,200 60, ,32 Payments (EUR) ,000 Labdollars (LD) = EUR; payments nclude 2 EUR show-up fee 2 smultaneous decson protocol 3 mxed sequental-smultaneous decson protocol The effcency loss n the NE and the SPE s consderable n all treatments. For h = 0, the proft for country n the PO s 49% (44%) above the proft n NE (SPE). The proft for country n the PO s 57% (68%) above the proft n NE (SPE). For h > 0, the proft for country n the PO s 73% (68%) above the proft n NE (SPE). The proft for country n the PO s 50% (62%) above the proft n NE (SPE). Free rder ncentves are also consderable. If all the other countres choose the PO abatement n T I, country () can ncrease ts proft by 72% (6%) compared to the PO proft provdng t chooses ts best response. In T II and the same stuaton, country () can ncrease ts proft by 24% (6%). If all other countres choose ther PO abate- 8 Subects had to enter ntegers n the smultaneous treatments. We allowed for one decmal place n the sequental treatments.

7 Unlateral Emssons Abatement: An Experment 6 ment, country can ncrease ts proft n T III (T IV) by 6% (9%) compared to the PO proft provdng t chooses ts best response. 9 Gven ths verson of the Hoel model, we can now formulate the two central hypotheses whch follow from standard game theory and whch wll be checked expermentally. Hypothess : The parameter h has a sgnfcant nfluence on the abatement and proft of country, =,, T 5, both n the smultaneous and sequental treatments. If we defne X as abatement of country n treatment T { h = 0, h > 0} for a gven sequence of moves, we can formulate hypothess for country and, = 2,, 5, as follows X X, h = 0 < h> 0 = 5 5 h 0 h>0 h= 0 X > X and = < = = X X. 0 h> 0 = T If we assume the same noton for proft π we get π π. h > 0 =0 > h Hypothess 2: The varable sequence has an nfluence on the abatement both at the ndvdual and the aggregate level. If we defne T sm, seq X as abatement of country, =,, 5, n treatment { } T for a gven choce of the parameter h, we can formulate hypothess 2 for country and, = 2,, 5, as follows sm seq X X >, 5 5 sm seq sm X < X and > = = X X. seq T If we assume the same noton for proft π we have to dstngush between country and.we get sm seq sm seq sm seq π < π, π > π and π > π = = The most nterestng pont of hypothess 2 s that the game theoretcal predcton, that leadershp results n less abatement for country and a world wth less aggregated abatement, s n 9 We assume that country has no free rder opton n the sequental treatments. 0 However, the hypothess for country s questonable due to the very small dfference n the NE and SPE abatement of country between treatments wth h = 0 and h > 0 (see table 3). At ths pont, we have to dscrmnate between the ncrease n profts n our experment and the postve welfare effect whch Hoel descrbes n hs model for the smultaneous game. The ncrease n profts s caused by a change n preferences due to parameter h, whch s an element of the real payoff functon of country. The postve welfare effect assumes that country voluntarly abates more than n the equlbrum and the resultng welfare loss s compensated for by the gan of all other countres. 2 Here the same problem as n footnote 0 appears. The dfference n NE and SPE profts of country between the smultaneous and sequental treatments s too small to get sgnfcant results (see table 3).

8 Unlateral Emssons Abatement: An Experment 7 drect contrast to the above-mentoned dea that leadershp may be a soluton to the socal dlemma stuaton countres are confronted wth. 3. Expermental desgn Each of the four treatments was orgnally played wth sx groups of fve subects. After a prelmnary analyss of the data, we decded to conduct 2 addtonal ndependent observatons n the sequental treatments,.e. we have sx ndependent observatons for the smultaneous treatments T I and T II and 8 ndependent observatons for the sequental treatments T III and T IV. All n all, 240 subects partcpated n the experment. There were 6 sessons wth three groups (5 subects) playng the game n parallel. Each sesson lasted about one hour. The sessons were conducted between December 2003 and May 2005 at the Magdeburg Expermental Laboratory (MaXLab). All subects were undergraduate economcs students famlar wth fundamental game theoretc concepts,.e. the dea of best response functons, the Nash equlbrum and ts applcaton to fntely repeated games. Each of the, n total, 48 groups played the game 0 tmes and subects were nformed about the number of repettons. The experment was fully computerzed and anonymous. 3 The subects were seated n soundproof booths and had no contact before, durng, and after the experment. The nformaton to the subects was organzed as follows. Durng the experment, subects were nformed about ther ndvdual and aggregated abatement, the aggregated abatement of all the other countres, the ndvdual profts of all countres, and the aggregated proft for all expred perods. The subects receved wrtten nstructons about the rules of the game, ther role (country or country 2,, 5), the parameters, and the functonal forms. 4 Furthermore, ther computers were equpped wth a payoff smulator whch had two elements. 5 The frst was the proft maxmzng functon. 6 In the smultaneous treatments, each country could put n the expected abatement of the other countres, and then ts proft maxmzng response was computed. In the sequental treatments, country used the same program as n the smultaneous treatment but country, the leader, could put n ts own abatement and then the proft maxmzng response of the other countres was computed. Addtonally, the expected proft and total abatement were computed for both cases. The second element was the smulator, whch subects could use to evaluate the consequences of non-proft-maxmzng actons. Here the subects could put n the expected abatement of the others and ther own arbtrary abatement. 7 The payoff smulator was dentcal for all subects n a treatment and was vsble both on the nput and the output screen. Before the experment started, questons were answered and all subects 3 We used Z-tree for programmng. See Fschbacher (999). 4 See appendx 3 for the nstructons. 5 See appendx 2 for a screenshot of the payoff smulator. 6 Instead of the term best response we use the term proft maxmzng response because the latter s more neutral n our vew. 7 Subects who tred to maxmze the collectve proft gven the expected abatement of the others could compute ther best response wth the help of the smulator.

9 Unlateral Emssons Abatement: An Experment 8 played two test rounds aganst the computer. The subects knew that n the test perods they were playng aganst four automated systems whose behavor would not change. As already mentoned n the ntroducton, we decded to use the frame also employed n the Hoel model and to nform subects comprehensvely about the decson stuaton. For ths purpose, we nvted the subects to attend a separate lesson held before the experment on the same day or a day before the experment was carred out. We conducted 5 lessons wth 2 or 24 subects, wth the anonymty wthn the groups beng guaranteed by the procedure. At the begnnng of the lessons, subects were told that they should magne that they were the head of a delegaton from ther country at an nternatonal conference on emssons abatement of a global pollutant. 8 Gven all necessary nformaton for ther country (costs and benefts), they had to decde on the level of domestc abatement. Then the most mportant features of the decson stuaton were explaned. Frstly, we demonstrated the Nash equlbrum for the smultaneous game and the subgame perfect equlbrum for the sequental game graphcally by means of best response functons. We showed that everybody was better off n the Pareto effcent soluton but that there were strong ncentves to devate from the effcent soluton. Secondly, the dea of the underlyng socal dlemma was llustrated by an example wth three countres. The abatement decsons n the equlbrum and the Pareto effcent solutons as well as the correspondng payoff mplcatons were depcted. At the end of the lecture, the nput screen, the output screen, and the payoff smulator were shown and explaned usng the above-mentoned example. The lesson lasted about one hour. Subects were nformed that n the experment countres would have dfferent roles (country and the other countres). However, the nformaton on whch role each subect would play and the tmng of acton was frst gven n the experment. At the begnnng of the experment, subects receved a show-up fee of 2 EUR and were told that possble negatve payoffs had to be settled usng ths fee. 4. Results 4. Abatement The payoffs per subect range from 4.40 EUR to EUR ncludng the show-up fee. The average payoff of all subects s 2.70 EUR. Fgure dsplays the average abatement over all ten rounds for country, the other countres, and all countres. The PO, NE, and SPE values are marked. 8 From the vewpont of game theory, the frame of the decson problem s rrelevant for ndvdual behavor. On the other hand, f we assume that people have green preferences,.e. that they behave more cooperatvely n a socal dlemma wth an envronmental frame, our frame provdes a worst case scenaro for game theory.

10 Unlateral Emssons Abatement: An Experment 9 abatement per perod NE---- country ----NE SPE Fgure : Abatement per perod ---SPE--- T I (h=0,sm) T II (h>0,sm) T III (h=0,seq) T IV (h>0,seq) abatement per perod NE---- country ----NE SPE SPE T I (h=0,sm) T II (h>0,sm) T III (h=0,seq) T IV (h>0,seq) abatement per perod total ----NE NE SPE SPE T I (h=0,sm) T II (h>0,sm) T III (h=0,seq) T IV (h>0,seq) We summarze our fndngs wth respect to the mean abatement (for country,, and total) as follows: Observaton : a. The mean abatement of country s ceters parbus hgher n the h > 0 treatments than n the h = 0 treatments. Abatement s hgher n the sequental than n the smultaneous treatments. However, none of these dfferences between treatments s sgnfcant (exact two-sded MW-U test, 5% level). 9 b. There s no sgnfcant dfference between the treatments for the mean abatement of country (MW-U test, 5% level). c. The dfference between the mean abatement and the SPE value n the sequental treatments s hghly sgnfcant for country (Wlcoxon sgned-rank test, % level). However, there s no sgnfcant dfference for country (5% level). d. Total abatement s hgher n the sequental treatments than n the smultaneous treatments but the dfference s not sgnfcant. However, the dfference between total abatement and the SPE value n the sequental treatments s sgnfcant (Wlcoxon sgned-rank test, 5% level). The most strkng observaton s that country does not reduce ts abatement n the change from a smultaneous to a sequental decson protocol as theory predcts but rases ts 9 If not otherwse stated all the followng tests are exact and two-sded.

11 Unlateral Emssons Abatement: An Experment 0 abatement. Due to the hgh varance of ndvdual behavor, the dfference between treatments s not sgnfcant. However, we must stll reect the hypothess that country abates at the level of the SPE values n the sequental treatments. In other words, the theoretcal predcton for country s supported by our data n the smultaneous treatments, but ths s not the case n the sequental treatments. On the other hand, the behavor of country does not vary much between the treatments and the correspondng theoretcal predcton s supported for all treatments. Although we have only a relatvely small number of ndependent observatons per cell n table 2, t s nterestng to look at the correlaton of the mean abatement of countres and. Whereas the Spearman rank correlaton yelds r S =.200 (p =.704) and.429 (p =.397) for the smultaneous treatments T I and II respectvely, values of r S =.78 (p =.000) and.546 (p =.029) are obtaned for the sequental treatments T III and IV respectvely,.e. there s a strong postve correlaton of leader s abatement wth followers abatements n both sequental treatments. Fgure 2: Scatterplots for seq-treatments T III (h=0, seq) T IV (h>0, seq) Abatement A A= A Ad R-squared=0.687 Abatement A A= A Ad R-squared= Abatement A Abatement A Table 4: Regresson analyss Model a = β 0 + β a b 0 p(b 0 ) b p(b ) ad. R 2 T I (h = 0, sm) T II (h > 0, sm) T III (h = 0, seq) T IV (h > 0, seq) a (a ) mean abatement of country () over rounds, N = 6/8 nd. obs. The smple lnear regresson n table 4 supports ths result and yelds a sgnfcantly postve coeffcent for the sequental treatments. The scatterplots for the sequental treatments n fgure 2 make ths concluson more clearly vsble. The SPE and the PO abatements are ndcated to

12 Unlateral Emssons Abatement: An Experment provde a better orentaton and the lne of best ft s obtaned from the regresson analyss n table 4. Observaton 2 s summarzed as follows: a. There s a sgnfcant and postve correlaton between the abatement of the leader and the abatement of the followers. b. An ncrease n the leader s abatement by one unt ncreases the total abatement of countres by about 2 unts. Ths observaton s therefore an ndcaton that (at least some) followers follow the leader s example and that abatements of followers and leaders are postvely correlated. Fgure 3 shows the abatements n the four treatments round by round. abatement PO NE NE T I (h=0, sm) country country Perod Fgure 3: Abatement over perods abatement PO NE NE T III (h=0, seq) country country Perod abatement PO NE NE T II (h>0, sm) country country Perod abatement PO NE NE T IV (h>0, seq) country country Perod The round-by-round analyss of the abatements confrms the fndngs of observaton : Observaton 3: a. The hypothess that the abatement of country s equal to the NE/SPE values must be reected n each of the 20 rounds of the sequental treatments. The hypothess cannot be reected for any round of the smultaneous treatments (Wlcoxon sgned-rank test, 5% level).

13 Unlateral Emssons Abatement: An Experment 2 b. The same hypothess must be reected n only 2 of the 40 rounds of all treatments for country. Nne of these cases appear n the frst four rounds. Remarkably, country s abatement n the last round of both sequental treatments s sgnfcantly below the SPE value (Wlcoxon sgned-rank test, 5% level). c. The hypothess that abatements for country are equal to the PO level must be reected n all 40 rounds of the treatments. The same hypothess must be reected for country n 7 of the 20 rounds of the smultaneous treatments and n 7 of the 20 rounds of the sequental treatments (Wlcoxon sgned-rank test, 5% level). The downward pattern of abatement for both countres n fgure 3 suggests that subects presumably learn the equlbrum strategy despte the fact that they know the equlbrum soluton before the experment starts. Therefore we splt the mean abatement of both countres n two subsamples, a subsample whch contans the frst fve perods and a subsample wth the last fve perods. Observaton 4 summarzes our fndngs regardng both subsamples: a. The average abatement for the last fve perods s for both countres n all treatments lower than the average abatement for the frst fve perods. Ths dfference s sgnfcant except for country n the smultaneous treatments (Wlcoxon matched-pars sgnedrank test, 5% level). b. The average abatement for the last fve perods of country s sgnfcantly above the SPE abatement n the sequental treatments (Wlcoxon sgned-rank test, % level). There are no other sgnfcant dfferences between the subsamples of abatement and the NE or SPE values. Based on ths observaton we may conclude that there s some learnng of equlbrum behavor. Nevertheless the surprsng contradcton between the theoretcal predcton regardng the abatement of country and the correspondng behavor of ths country as a leader preserves over the course of the experment. 4.2 Convergence and ndvdual behavor The overall mpresson from fgure 3 s that subects show a clear tendency towards the equlbrum strategy durng the course of the game and that ths tendency s more pronounced n the smultaneous treatments than n the sequental treatments. In the sequental treatments, the downward trend to the SPE s nterrupted by phases of constant, and even ncreasng, abatement, especally for country. In order to gan more nsght nto the way subects adust ther behavor, we use the coeffcent N α = t N X = PO X t, t, X X Eq t, Eq t,

14 Unlateral Emssons Abatement: An Experment 3 as a smple measure of the devaton of ndvdual behavor from ndvdual ratonalty. X t, s Eq the ndvdual abatement of country n perod t, X t, s s ndvdual equlbrum (the NE or PO SPE) abatement n perod t and X t, s s ndvdual PO abatement n perod t. Coeffcent α t measures the mean absolute value of the devaton of ndvdual abatement from equlbrum abatement as a fracton of the dfference between the equlbrum and PO abatement,.e. α t summarzes the nformaton about ndvdual abatement behavor n fgure 3. We observe α t = 0 () for country () f all countres of ths type play ther equlbrum (PO) abatement. alpha country Perod Fgure 4: Alpha alpha country Perod As expected, the α t values n fgure 4 decrease, although not monotoncally. At frst glance, we observe that the α t values are hgher for the sequental treatments than for the smultaneous treatments for both countres over almost all rounds. 20 The smlarty between the α t values for the smultaneous treatments, on the one hand, and for the sequental treatments, on the other hand, s strkng. Furthermore, the decrease n the α t values seems to be sharper for country than for country. Because the NE and SPE are not at a boundary, α t measures departures from equlbrum behavor n both drectons. Abatements below the NE level or SPE level may therefore serve as a means of punshng subects who behave selfshly. In order to analyze the structure of the devatons from the NE behavor and the SPE behavor, we classfy the ndvdual decsons of countres and nto three groups: cooperatve behavor, best response or NE/SPE behavor, and abatements that are below the best response or NE/SPE. The correspondng ntervals are descrbed at the bottom of fgure 5, whch shows the fractons of the three behavoral patterns n the smultaneous and sequental treatments. 20 However, sgnfcant dfferences for the α t values can only be observed for few perods.

15 Unlateral Emssons Abatement: An Experment 4 fracton of behavor n % Fgure 5: Indvdual behavor of country and country : sm-treatments Perod fracton of behavor n % country : seq-treatments Perod fracton of behavor n % country : sm-treatments Perod fracton of behavor n % Cooperatve behavor,.e. abatement between max(br, Eq) and PO. country : seq-treatments Perod Abatement between mn(br, Eq) and max(br, Eq) wth br as ndvdual best response to the aggregated abatement of the others n the current perod and Eq as ndvdual abatement n NE or SPE (each wth +/- 20%). Abatement below mn(br, Eq). Although ths classfcaton serves only an llustratve purpose, several behavoral patterns are strkng. 2 Regardng country, fgure 5 confrms the observaton that cooperatve behavor s more frequent and rather stable n the case of leadershp,.e. leadershp matters from the vewpont of country. However, n the last rounds abatement above the ndvdual ratonal level becomes less frequent even n the sequental treatments. Ths ndcates that the efforts to nduce cooperaton through leadershp are, on average, not very successful. On the other hand, there s vrtually no abatement below the ndvdual ratonal level for country. Although the behavor of country dffers consderably between the smultaneous and sequental treatments, the behavor of country seems to be rather stable for both knds of sequence. Indvdual ratonal behavor prevals and becomes more frequent n the course of the experment. On average, one thrd of the decsons can be classfed as cooperatve behavor. However, ths knd of behavor clearly becomes less mportant over the perods. Remarkably, a sgnfcant fracton of abatement decsons of country s below the best response level. A reason for ths behavor may come from the exstence of some punshment behavor or negatve recprocty shown by the 2 We get a smlar pcture f we generate ths classfcaton based on myopc best response behavor,.e. the ndvdual best response to the aggregated abatement of the others n the prevous perod.

16 Unlateral Emssons Abatement: An Experment 5 subects n the role of country. The proporton of ths knd of devaton from ndvdual ratonal behavor seems to be hgher n the sequental treatments than n the smultaneous case. Ths may be a reacton of some subects to the frustratng experence made n the early rounds that the hgh abatement of country does not motvate the other countres,.e. country, to follow sut. 4.3 Profts and effcency Fgure 6 shows the average profts earned by the subects. These profts are not dentcal to the welfare measure used n the Hoel model because there the extra proft country derves from abatements above the Nash level (measured by h) s not part of the welfare of country. The postve aggregated welfare effect of over-abatng of country results because the welfare loss suffered by ths country s overcompensated for by the welfare gans of the other countres. Fgure 6: Proft per perod Proft n.000 LD per perod country ----NE SPE NE SPE T I (h=0,sm) T II (h>0,sm) T III (h=0,seq) T IV (h>0,seq) Proft n.000 LD per perod country ----NE NE SPE SPE T I (h=0,sm) T II (h>0,sm) T III (h=0,seq) T IV (h>0,seq) total Proft n.000 LD per perod NE NE SPE SPE T I (h=0,sm) T II (h>0,sm) T III (h=0,seq) T IV (h>0,seq) We summarze our fndngs concernng the profts n the followng. Observaton 5: a. Country earns a sgnfcantly hgher proft n the h > 0 treatments than n the h = 0 treatments (MW-U test, % level). The proft n T III s sgnfcantly below the proft n T I but there s no sgnfcant dfference between the profts n T IV and T II (MW-U test, 5% level). The hypothess that the proft of country s equal to the NE value or

17 Unlateral Emssons Abatement: An Experment 6 SPE value can only be reected for treatment T III where the proft s below the SPE predcton (Wlcoxon sgned-rank test, 5% level). b. Country s able to ncrease ts profts above the NE and SPE values n all treatments. The dfference s sgnfcant n T I and n both sequental treatments (Wlcoxon sgnedrank test, 5% level). c. Total proft s slghtly above the NE and SPE values n all treatments. The dfference s sgnfcant n T I and T IV (Wlcoxon sgned-rank test, 5% level). 22 The pcture we get based on ths observaton s qute clear. Although the abatement behavor of country wth leadershp dffers consderably from that wthout leadershp, t turns out that country s unable to ncrease ts profts by usng leadershp. On the other hand, the followers are able to ncrease ther proft above the equlbrum predcton. Due to the asymmetry of profts n the equlbrum and the PO soluton for both types of countres t s useful to normalze the realzed profts of all treatments. We use the effcency ndex Eff as an ndex to facltate the comparablty of results. The ndex Eff measures the dfference between the realzed proft ( π real Eq ) and the equlbrum proft ( π ) as a fracton of the PO dfference between the maxmal possble proft n the PO soluton ( π ) and the equlbrum proft for a country,.e. π π Eff =. π π real PO Eq Eq If a country realzes ts equlbrum proft the effcency s zero, f t s able to acheve the socal optmal proft the effcency s equal to one. Therefore the effcency ndex permts to compare the ablty of both countres to realze profts above the equlbrum. Table 5 depcts the results for country, and all countres. Table 5: Effcency ndex Treatment T I (h = 0, sm) T II (h > 0, sm) T III (h = 0, seq) T IV (h > 0, seq) Country Country Total We summarze our fndngs concernng the effcency ndex n the followng. Observaton 6: a. The overall effcency s qute low and cannot be sgnfcantly enhanced n the game wth leadershp (MW-U test, 5% level). 22 The dfference s weakly sgnfcant for T III (Wlcoxon sgned-rank test, 0% level).

18 Unlateral Emssons Abatement: An Experment 7 b. Country realzes n both sequental treatments a lower effcency than n the smultaneous treatments. However, only the dfference between the effcency of T I and T III s sgnfcant (MW-U test, 5% level). c. There s no sgnfcant dfference between the effcency values of the smultaneous and sequental treatments for country. d. In the smultaneous treatments both countres do not dffer n ther ablty to realze profts above the equlbrum. However, countres acheve effcency values whch are sgnfcantly hgher than those of country n the sequental treatments (Wlcoxon sgned-rank test, % level). The nterpretaton of observaton 6d s qute clear. In terms of effcency country performs worse relatve to country when t becomes a leader,.e. the rate of realzed supra-equlbrum profts to maxmal possble profts above the equlbrum are hgher for the followers compared to the leader. None of the countres, nether the leader nor the follower, are able to ncrease the effcency n a game wth leadershp Dscusson Our data support the Hoel model for the treatments wth a smultaneous decson protocol at least for the second half of the 0 rounds. Therefore, t seems far to state that the Hoel model descrbes actual behavor surprsngly well,.e. we cannot reect hypothess, n an envronment where subects act smultaneously. On the other hand, our fndngs for the smultaneous treatments are n lne wth the stylzed facts of many publc good experments: abatement starts between the NE level and the PO level, decays durng the course of the game, and then dsplays a fnal-round effect. Brosg et al. (2003) have shown that, n standard publc good games, subects try to coordnate ther behavor n order to realze the effcent outcome but that ths coordnaton s only successful f all subects stck to ther promse to cooperate. Normally, ths s not the case and cooperaton breaks down after a few perods. Ths lne of reasonng seems to be n lne wth our observatons. 23 However, we have to admt that the treatment T III seems to be an outler as country s not able to realze even the SPE proft.

19 Unlateral Emssons Abatement: An Experment 8 Fgure 7: Classfcaton of 36 groups n the sequental treatments number of groups successful leadershp leadershp wth defecton no leadershp Remark: successful leadershp : Country chooses the PO abatement (+/- 20%) and all countres follow wth the PO abatement (+/- 20%) n at least 8 of the 0 perods. leadershp wth defecton : Country chooses the PO abatement (+/- 20%) n one or more perods and at least one country does not follow wth the PO abatement n each of ths perods (+/- 20%). no leadershp : Country does not choose the PO abatement (+/- 20%) n any perod. The most mportant queston we sought to answer wth ths experment was whether or not leadershp matters. Havng a leader may open a way to solvng the coordnaton problem ust mentoned. If the leader starts each round wth the PO abatement, ths could serve as a knd of focal pont for the followers. The observatons from secton 4. show that, on average, the leaders take a chance gong ahead wth a good example. Country s abatement s sgnfcantly above the SPE abatement n the sequental treatments. However, followers, on average, react only a lttle to these efforts by the leader. On average, ther reacton to the leader s efforts s not suffcent to boost the proft of the leader above the equlbrum value. In ths context, the dentfcaton of dfferent types of behavor as an mportant result of expermental economcs s of partcular mportance,.e. average data may not be an approprate means to analyze ndvdual behavor. 24 A smple analyss of the group specfc data (see fgure 7) shows three nterestng behavoral patterns n ths context. In contradcton to the game theoretcal predcton, leaders try to lead and set a good example,.e. n 33 of 36 groups country s abatement s near the PO abatement at least once over the perods. 25 The reacton of the followers s qute mxed. There are some groups (5 of 33) whch succeed n abatng at the PO level n at least 8 of the 0 rounds. One of these groups even plays the PO abatement n all rounds, ncludng the last round. 26 However, n most cases (28 of 33) the leader fals to nduce cooperaton,.e. n these groups there are few followers who react cooperatvely to the leader s sgnal. Hgh efforts by the leader and the cooperatve followers are exploted by the maorty of defectve followers. Ths behavoral pattern s the explanaton for the fact that the mean proft of country does not exceed the SPE values n the sequental treatments although the mean abatement of country s sgnfcantly hgher than the SPE values. Moreover, t explans the fact that the mean proft of 24 See Wemann (994) and Fschbacher et al. (200). 25 In 3 of 36 groups we observe behavor near the SPE for both the leader and the followers. 26 Also see fgure 2 where these 5 groups can be easly dentfed.

20 Unlateral Emssons Abatement: An Experment 9 country exceeds the SPE values n the sequental treatments. The change of the effcency values regardng country and from a smultaneous to a sequental game serves as another llustraton of our man fndng: by assumng leadershp country loses ground n relaton to country. Furthermore, these observatons are n lne wth the related expermental research on leadershp whch was dscussed n the ntroducton. Based on these observatons, we must reect hypothess 2, but otherwse our data do not support the dea that leadershp s an effectve means to create stable cooperaton. 6. Concluson The prmary obectve of our experment was to test the Hoel model and to analyze the nfluence of leadershp. Snce the external valdty of results ganed n sngular laboratory experments s restrcted to the specfc laboratory envronment, we have to admt that we are not able to make any recommendatons for envronmental polcy purposes. 27 However, we may come to the concluson based on our results that, frstly, the Hoel model descrbes the ndvdual behavor surprsngly well n an envronment wth a smultaneous decson protocol and, secondly, leadershp matters a lot but s not able to ncrease the proft of the leader and to overcome the socal dlemma stuaton all countres are confronted wth. Only the followers who free rde at the expense of the leader and the cooperatve followers n cooperatve groups can ncrease ther profts. In partcular, the experments show that countres that want to ncrease ther own proft and the total proft of the group by showng leadershp should not put too much hope n the effectveness of ther good example. Even f some follow ths example, the probablty that other followers free rde and cooperaton breaks down very soon s hgh. All n all, leadershp by tself does not seem to be an approprate tool to overcome socal dlemma problems, even f leaders have a strong ncentve to nduce cooperatve behavor. 27 See Sturm/Wemann (forthc.) for a detaled methodologcal dscusson.

21 Unlateral Emssons Abatement: An Experment 20 References Andreon, J. (995): Warm Glow versus Cold-Prckle: The Effects of Postve and Negatve Framng on Cooperaton n Experments, The Quarterly Journal of Economcs, 0, p. -2. Barrett, S. (994): Self-Enforcng Internatonal Envronmental Agreements, Oxford Economc Papers, 46, p BMU (2002): Regerungserklärung von Bundesumweltmnster J. Trttn vor dem Deutschen Bundestag am Brandts, J./MacLeod, W. B. (995): Equlbrum Selecton n Expermental Games wth Recommended Play, Games and Economc Behavor,, p Brosg, J./Ockenfels, A./Wemann, J. (2003): The Effect of Communcaton Meda on Cooperaton, German Economc Revew, 4, p Fschbacher, U. (999): z-tree: A Toolbox for Readymade Economc Experments, Workng Paper No. 2, Unversty of Zurch, 999. Fschbacher, U./Gächter, S./Fehr, E. (200): Are People Condtonally Cooperatve? Evdence from a Publc Goods Experment, Economc Letters, 7, p Gächter, S. /Renner, E. (2003): Leadng by Example n the Presence of Free-Rder Incentves, Workng Paper, Unversty of St. Gallen. Güth, W./Levat, M. V./Setter, M./van der Heden, E. (2004): Leadershp and Cooperaton n Publc Goods Experments, Max Planck Insttute for Research nto Economc Systems, Dscusson Papers on Strategc Interacton, No Hoel, M. (99): Global Envronmental Problems: The Effects of Unlateral Actons Taken by One Country, Journal of Envronmental Economcs and Management, 20, p Katala, V./Pohola, M./Tahvonen O. (992): Transboundary Ar Polluton and Sol Acdfcaton: A Dynamc Analyss of an Acd Ran Game between Fnland and the USSR, Envronmental and Ressource Economcs, 2, p Sturm, B./Wemann, J. (forthc.): Experments n Envronmental Economcs and some Close Relatves, Journal of Economc Surveys. Van der Heden, E./Moxnes, E. (2000): Leadershp and Followng n a Publc Bad Experment, workng paper, SNF Report No. 3/00, Bergen. Wemann, J. (994): Indvdual Behavor n a Free Rdng Experment, Journal of Publc Economcs, 54, p

22 Unlateral Emssons Abatement: An Experment 2 Appendx In ths appendx we derve the solutons for the Nash equlbrum for the smultaneous decson protocol, the subgame perfect equlbrum for the mxed sequental-smultaneous decson protocol, and the Pareto optmal soluton based on the specfcaton used n the experment. Nash equlbrum (NE) for the smultaneous decson protocol Country maxmzes the dfference between beneft and costs of abatement gven the abatement of all other countres,.e. 2 2 [ A( X + X ) 0. ( X + X ) ] + h( X + X ) ( cx + T ) maxπ = b 5 X wth X = X 2 (A). = N The reacton functon of country s R ( X ) = ( ba + h bx ) (A2). 2c + b Snce all other countres ( = 2,..., N ) are dentcal n ther beneft and cost functons, we can substtute abatement X = N X. The reacton functon X wth ( ) ( X ) ( ba + h ( N ) ) R = bx (A3) 2c + b descrbes the best response of country to the abatement chosen by country, X. Country, = 2,..., N, maxmzes the dfference between beneft and costs of abatement gven the abatement of all other countres,.e. 2 2 ( X + X ) 0.5( X + X ) ( cx T ) maxπ = A wth X = X (A4). X + The reacton functon of s R ( X ) = ( A X ) 2c + N (A5). Snce country and all other N 2 countres k, k k, have dentcal beneft and cost functons, we can substtute abatement X = N 2 X X. The reacton functon of, R ( X ) ( A X ) X wth ( ) + = N + 2c (A6),

23 Unlateral Emssons Abatement: An Experment 22 descrbes the best response of country to the abatement of country, X. The NE for the smultaneous decson protocol results as the ntersecton of the reacton functons (A3) and (A6), and the nteror soluton for the NE s h( N + 2c) 2 ( N ) c 4c 2cbA + =, X NE 2cb NE NE and X = X + ( N ), we have the perfectly symmetrc NE 28 for the smultaneous decson pro- For b = and h = 0 tocol wth X NE ( b + N ) 2cA h =, 2cb ( N ) c + 4c NE A + h X = (A7). N + 2c + b NE NE A X = X = and N + 2c X NA NE = N + 2 (A8). c NE NE For b < and a suffcently small h, we have X < X,.e. the country wth the smaller margnal beneft from abatement (here country ) abates less than all other countres n NE. We are nterested n analyzng the effects of a margnal ncrease n h. It s easy to show that the results of the general model hold for our specfcaton,.e. X NE h 0, X NE h < 0, and > X NE NE NE NE h > 0. For profts, we can show that π h 0, π h > 0, and π h > 0, >.e. payoffs ncrease wth a margnal ncrease n h, whch s an element of the real payoff functon of country here. Ths effect s ndependent of the relatve sze of the margnal beneft of country. Subgame perfect equlbrum (SPE) for the mxed sequental-smultaneous decson protocol Country maxmzes the dfference between beneft and costs of abatement gven the knowledge that the N- other countres wll behave accordng to ther best response functon (A6) 2 [ A( X + ( N ) R ( X )) 0.5( X + ( N ) R ( X )) ] + h X + ( N ) R ( X ) maxπ = b X 2 [ ] ( cx + T ) (A9),.e. country can use ts frst mover advantage by choosng a pont on the follower s best response functon whch maxmzes ts proft by backward nducton. The soluton for the subgame perfect equlbrum s h( N + 2c) ( N c) 2 2cbA + X SPE = 2cb + + 2, SPE SPE and X X + ( N ) X SPE A( N + 2c) h 2cb + ( N + 2c) 2 ( N )( N + 2c) + + ( N + c) 2 =, SPE 2cbA + A 2ch = X = 2cb 2 (A0). 28 See Barrett (994).

24 Unlateral Emssons Abatement: An Experment 23 We can show that SPE NE X X <, X > X, and SPE NE SPE NE X < X,.e. the change from the smultaneous decson protocol to the mxed sequental-smultaneous decson protocol leads to a lower aggregated abatement. Regardng profts, the change from the smultaneous decson protocol to the mxed sequental-smultaneous decson protocol leads to a hgher proft for country, a lower proft for country, and (for the chosen parameters) a lower aggregated proft. The nfluence of parameter h on abatements and profts s the same as n the smultaneous case. Pareto optmum (PO) In the Pareto optmal allocaton, total proft from abatement s maxmzed,.e. the global planner has the followng optmzaton problem: 2 c 2 maxπ = π + ( N ) π = ( b + N )( AX 0. 5X ) + hx X + NT (A). X N In the PO, all countres adust ther margnal abatement costs to the margnal socal beneft ' from abatement. Snce all countres have the same margnal abatement costs, C = 2cX, n the PO all countres choose an equal abatement, ndependent of the protocol of play, gven by ( + N ) A b + h = and c N b N N X PO X PO ( + N ) A b + h = c b N N (A2). PO NE It s easy to show that X > X holds. For abatement, t follows that X PO h > 0 and X PO PO PO h > 0. For profts, we can show that π h 0, π h > 0, and therefore PO π h > 0. >

25 Unlateral Emssons Abatement: An Experment 24 Appendx 2 Screenshot: Payoff smulator (T I and II)