An Enforcement-Coalton Model: Fshermen and Authortes formng Coaltons Lone Grønbæ Kronba Maro Lndroos December 003
All rghts reserved. No part of ths WORKING PAPER may be used or reproduced n any manner whatsoever wthout the wrtten permsson of IME except n the case of bref uotatons emboded n crtcal artcles and revews. Unversty of Southern Denmar, Esberg and the authors, 003 Edtor: Eva Roth Department of Envronmental and Busness Economcs IME WORKING PAPER 50/03 ISSN 399-34 Lone Grønbæ Kronba Department of Envronmental and Busness Economcs Unversty of Southern Denmar, Esberg Nels Bohrs Ve 9-0 DK-6700 Esberg Tel.: 45 6550 48 Fax: 45 6550 09 E-mal: lg@sam.sdu.d Maro Lndroos Department of Economcs and Management P.O. Box 7 Unversty of Helsn 0004 Fnland Tel: 358 9 9 58068 Fax: 358 9 9 58096 E-mal: maro.lndroos@helsn.f
Abstract The paper sets up a four-stage enforcement model of fsh uotas. The purpose of the paper s to show how the level of enforcement set by the authortes affects the way fshermen form coaltons. We show that a hgh level of control effort yelds less cooperaton among fshermen, whle n the case of low control effort, coaltons are somewhat self-enforcng. The paper further dscusses how the optmal enforcement level changes when the coalton formaton among authortes changes: centralsed, partly centralsed and decentralsed authortes. We show that decentralsed authortes set a lower level of control effort compared to the centralsed authortes. The theoretcal results are llustrated by smulatons of the Baltc Sea cod fshery. The authors acnowledge valuable comments and suggestons from Fran Jensen and Nels Vestergaard. Key words Coalton formaton, Fsheres management, Quota enforcement, Self-enforcng polcy JEL Codes C70, Q, Q8
Table of contents. Introducton... 7. The Basc Model... 3 3. A Centralsed Authorty... 7 3.. Three Sngletons among Fshermen... 7 3.. Coaltons among Fshermen... 9 3.3. Comparatve Statcs on the Level of Control Effort... 4. A Decentralsed Authorty... 4.. Three Sngletons among Fshermen... 3 4.. Two-Player Coalton among Fshermen... 5 4.3. Grand Coalton among Fshermen... 6 5. A Two-Player Coalton Authorty... 6 6. Stablty of Coalton Structures among Fshermen... 7 6.. Smulaton... 9 7. Dscusson, lmtatons and Concluson... 36 8. References... 40 9. Appendx... 4
. Introducton It s a general problem that management measures n fsheres decded at the regonal level often have to be mplemented on the natonal level; hence, a centrally determned polcy s enforced on a decentralsed level. Ths s termed by Holden (994), the Achlles heal of the Common Fsheres Polcy n EU. It s also nown from earler studes (e.g. Jensen 00), that the enforcement of regulatons at the natonal level may dffer tremendously among countres, f there s any enforcement at all. The essence of the problem s that the ndvdual states onng the agreement have no ncentve to employ costs for montorng and enforcement. The problem s also present n the Baltc Sea. The Internatonal Baltc Sea Fshery Commsson (IBSFC) was establshed pursuant to the Gdans Conventon (IBSFC 003). On sgnng ths Conventon, the Contractng Partes undertoo to "co-operate closely wth a vew to preservng and ncreasng the lvng resources of the Baltc Sea and the Belts and obtanng the optmum yeld, and, n partcular to expandng and co-ordnatng studes towards these ends,..." To comply wth the Conventon, the IBSFC ntroduced the frst total allowable catch (TAC) on cod n the Baltc Sea n 977. Untl that tme the fshery was subect to access based on blateral agreement, where countres agreed to share terrtores n return for satsfyng some techncal conservaton measures. In 977 the exclusve economc zones (EE) were also ncreased to 00 nautcal mles, dvdng the sea accordng to the centre lne, whch created some dsputes over the slands of Bornholm and Gotland. In partcular, the dspute between Sweden and the Sovet Unon over Gotland Island gave rse to an area freuently called the Whte one, n whch there exsted open access untl 987 when Sweden and the Sovet Unon fnally came to an agreement. Comparng the TAC wth actual harvests ndcates that the TAC has often been exceeded, see table I. Source: Artcle of the Gdans Conventon, IBSFC (003), www.bsfc.org. 7
Table I. TAC for Cod n the Baltc Sea and the actual Catches Year TAC Catch Excess Catch Excess catch Tonnes Tonnes Tonnes % of TAC 977 85. 6. 4.% 978 74 94.6 0.6.85% 979 75 7.7 97.7 55.85% 980 35 389.6 54.6 65.78% 98 7 384.4 57.4 69.33% 98 No TAC 363.6 983 No TAC 380.8 984 No TAC 44.4 985 No TAC 355. 986 No TAC 79.3 987 No TAC 35.6 988 No TAC 3.9 989 0 97.7 -.3-0.4% 990 7.3-39.7-8.80% 99 7 39. -3.8-8.59% 99 00 7.9-7. -7.% 993 40 66.4 6.4 66.03% 994 60 4.0 64.0 06.75% 995 0 4.6.6 8.0% 996 65 7.7 7.7 4.69% 997 80 3. -47.8-6.54% 998 45 0.5-43.5-9.97% Source: ACFM (000) and own calculatons. 8
Nether before the establshment of the IBSFC, nor after has there been any effectve enforcement and the fshery s consdered to be de facto open access. Furthermore, t s ponted out n Kronba (00) that the cod fshery, from 98-999, seems to ft a dynamc open access model rather well. Ths, agan, s an example of the general enforcement problem. Coaltons among fshermen do exst n some real world settngs, for nstance n the form of producer organzatons (POs). Producer organsatons are, however, not very common n the Baltc Sea, partcularly not n the Eastern European countres. Ths paper sets up a model to dscuss the effects of fshermen formng a coalton and the effect of havng a decentralsed versus a centralsed enforcement polcy. The model s nspred by the actual stuaton n the Baltc Sea, but t s a general model wth relevance to all regulated fsheres where management measures are decded centrally but mplemented on the decentralsed level. In the exstng lterature there are models where part of the control s at the centralsed level and part s at the decentralsed level (Caplan & Slva 999). Our model contrbutes to the lterature by modellng coaltons on the enforcement level tang nto account coaltons at the regulated level. In addton, t opens up for dscussng the ueston of how centralsed, decentralsed or partly centralsed enforcement can affect the way fshermen form coaltons. Prevous fsheres enforcement studes nclude Sutnen & Andersen (985) who examned the enforcement of fsh uotas n a sngle-player model, Jensen & Lndroos (00) who studed enforcement of fsh uotas n a two-player model and Jensen & Vestergaard (00a) who nvestgated the moral hazard problem when ndvdual catches are unobservable to socety. These studes have not consdered the possblty of formng coaltons. There exst studes that have addressed coalton formaton, manly on the nternatonal level, such as Lndroos (00), Duarte et al. (000) and Pntasslgo (003). However, these studes do not consder the enforcement problem. The present study ntegrates these In Denmar there are 3 POs; the Dansh Fshermen s Producer Organsaton, Denmar s Pelagc Producer Organsaton, and Sagen Fshermen s Producer s Organsaton. 9
two types of models by ntroducng coalton formaton to both the authortes (nternatonal) and the fshermen. The purpose of the paper s to show the effects of fshermen formng coaltons and authortes formng coaltons gven the authorty undertaes a certan level of uota enforcement. The paper dscusses the effects of authortes beng centralsed, partly centralsed or decentralsed. The paper sets up a four stage statc model. The four stages of the model are llustrated n fgure. Fgure. The four stages of the model Stage Authortes choose coalton structure: Centralsed, Partly Centralsed, Decentralsed Stage Authortes choose control effort level. (Choose ) Stage 3 Fshermen choose coalton structure: Grand Coalton, Two-player coalton and a sngleton, 3 Sngletons Stage 4 Fshermen choose optmal effort level. (Choose e) The frst two stages of the model belong to the authortes. In stage one; the authortes decde ther level of coalton formaton. There are three defned levels of centralsaton among authortes; centralsed (a grand coalton among au- 0
thortes), decentralsed (no coalton among authortes) or partly centralsed (a two-player coalton and a sngleton). Gven the level of centralsaton decded by authortes, they then decde ther level of enforcement n stage two. The last two stages belong to the three groups of fshermen. They also start out by decdng whch coalton to belong to n stage three. The fshermen also have three possble coalton structures, namely, three sngletons playng Nash aganst each other, a two-player coalton and a sngleton or a grand coalton. In stage four they maxmse the expected profts by decdng the employed effort level. As wth the authortes, the fshermen also have the choce of onng three dfferent coalton formatons. Ths yelds nne dfferent scenaros to analyse. 3 These nne scenaros are llustrated n fgure. 3 We gnore that there are three possble two-player coaltons among authortes snce we later assume that the authortes are dentcal. We also gnore that there are three possble two-player coaltons among fshermen, n ths case we smply choose the most effcent coalton.
Fgure. Illustraton of nne dfferent scenaros Centralsed authorty decdes control effort level Non cooperatve behavour among groups of fshermen Two-player coalton among groups of fshermen Grand coalton among groups of fshermen Sngle country authorty decdes control effort level Two-player coalton authorty decdes control effort level Non cooperatve behavour among groups of fshermen Two-player coalton among groups of fshermen Grand coalton among groups of fshermen Sngle country authorty decdes control effort level Sngle country authorty decdes control effort level Sngle country authorty decdes control effort level Non cooperatve behavour among groups of fshermen Two-player coalton among groups of fshermen Grand coalton among groups of fshermen
In our paper we analyse analytcally sx of the nne scenaros; those where authortes are ether completely centralsed or completely decentralsed, leavng the three scenaros n-between, where authortes are partly centralsed for dscusson only. At present, there are sx contractng partes n the Baltc Sea: Estona, the European Communty, Latva, Lthuana, Poland and the Russan Federaton. We can ft the sx partes nto our coalton model by groupng the contractng partes nto 3 authortes. These 3 authortes are represented by; the European Communty, whch s the largest agent, catchng between 50-70% of the total catch of cod, Poland, whch s the second largest agent, catchng some 0-30% of the total catch of cod and the former Sovet Unon (now Russa) and the three Baltc countres (Estona, Latva and Lthuana) catchng some 0-0% of the total catch of cod. We can also group the fshermen explotng the cod stoc nto three groups represented by the technology they apply. The three man technologes for harvestng cod are demersal trawls, hgh openng trawls and gllnets, where gllnets catch up to 50% of the total catch, all three technologes are represented n each country group. Currently, there s no formalzed cooperaton among the authortes and there s only lttle cooperaton among the fshermen n the Baltc Sea n the form of POs. Ths model sees to explan the gans from cooperaton on both the authortes and the fshermen levels. The paper s organsed as follows. Frst a basc theoretcal model s set up. The model s dscussed theoretcally for centralsed and decentralsed authortes. Then how enforcement can affect the way fshermen form coaltons s dscussed. Smulatons follow the theoretcal model. Fnally, the man results are dscussed together wth the scope for future research.. The Basc Model The model follows the basc two-stage structure used by Ruses (998) and Lndroos (00). However, our model does dffer, snce we allow the players n each stage to mae two decsons; frst, whch coalton to belong to and sec- 3
ond, whch effort level to decde on. Ths explans the four stages of our oneshot model. The Gordon-Schaefer model sets out the bologcal and producton related characterstcs of the fshery consdered n the paper. Wth three players, or groups of asymmetrc fshermen, {,,3}, the dynamc euaton loos as follows: dx dt = G 3 h = ( x), () where x s a sngle fsh stoc and h s the harvest of the sngle group of fshermen. In ths one shot model the dscount rate s eual to zero for all groups of fshermen. It s assumed throughout that the fsh stoc s a common property of the fshermen and there are no potental new entrants. The natural growth of the fsh stoc s gven by the logstc growth functon: x = K G( x) rx, () where r s the ntrnsc rate of growth of fsh and K s the carryng capacty of the fshng ground. The harvest functon for a group of fshermen followng technology s assumed to be lnear, followng the Gordon-Schaefer type: h = e x, (3) where the term s the catchablty coeffcent for technology, and e s the effort employed by the group of fshermen applyng technology. We assume that the fshermen are asymmetrc snce they can dffer n ther catchablty coeffcents, s. A hgher catchablty coeffcent can be nterpreted as a technologcal advantage. Wthout loss of generalty we assume s the most effcent technology and s the least effcent technology, e.g. > >. 4
The steady state stoc can be derved, usng the euatons () to (3), where harvestng euals growth: 3 K = e r r = x, x > 0. (4) Hence, for each level of fshng effort, gven the catchablty coeffcents, there s a sustanable steady state stoc level. The authortes are able to act as Stacelberg leaders aganst the groups of fshermen. Therefore, the problem s solved bacwards. In the fourth stage, fshermen choose the effort that maxmses the ndvdual expected steady-state rents gven ther choosen coalton structure and the enforcement level. The ndvdual group of fshermen further taes the effort level by rval group(s) as gven. The fshermen, or coaltons, are playng a Nash game aganst each other. In the thrd stage the fshermen decde coalton formaton. In the second stage, each authorty unlaterally chooses the level of control effort n ts regon, tang nto account full nowledge of how control effort nfluences the thrd and fourth stage eulbrum and tang the foregn control effort level as gven, n the case of decentralsed control authortes. In the frst stage the authortes decde whch coalton structure to belong too. Each authorty plays a Stacelberg game n the effort level aganst the fshermen and a Nash game n control effort polces aganst the foregn authorty. The authortes problem s to set a level of enforcement, gven that control s costly. Ths type of authorty problem s dscussed n Jensen and Lndroos (00). We contrbute to the lterature by allowng for asymmetry among fshermen and also by allowng fshermen to form coaltons. Ths s relevant for the socety snce coaltons on both levels mght result n more complance wth TACs even though less effort s employed for control. The fshery s managed by a total allowable catch (TAC) and t s assumed that the TAC s set at a suffcently low level, restrctng the effort of the fshermen. Snce control s costly t s not optmal for the authortes to choose perfect con- 5
trol. The authortes are assumed to maxmse the economc surplus gven by the dfference between fshermen s profts and the control costs. Only fshermen havng homeport n own country group are consdered. The decson varable for the authortes s the level of control effort,. The maxmsaton problem for a sngle authorty s as follows: ( Ψ) s. t. 0 < 3 Maxπ = P = γ, (5) where P (Ψ) descrbes the fshermen s proft facng probablty Ψ of beng detected applyng technology. γ s the unt cost of control effort. The second term on the RHS descrbes the total costs of control; we see that f the control effort s extensve, approaches one, then the costs of control go to nfnty. On the other hand, f control effort approaches zero, there are stll some fxed management costs. The fshermen choose ther level of fshng effort based on expected proft maxmsaton accordng to the followng formula: Max E e ( P ) Max e = Max e ( Ψ) ph ce ΨΩ h > TAC ). (6) ( ph ce h TAC ) Assumng the TAC s set at a suffcently low level then there s noncomplance. 4 The proft when not complyng wth the TAC s determned by the ordnary proft mnus an expected lump-sum fne (ΨΩ) and an expected penalty dependng on the value of the harvest (Ψph ). Ψ s the probablty of beng caught. We assume there s a one-to-one lnear relatonshp between the control effort and the probablty of beng caught, hence =Ψ. 4 Non-complance s, of course, only true for some levels of control effort, but ether by assumng an extremely low TAC or by assumng fshermen face some hgh fxed costs, we can force the fshermen to non-complance. 6
The remander of the paper s organsed as follows; Frst, we analyse the three scenaros resultng from the authortes agreeng on beng completely centralsed, second we analyse the three scenaros resultng from the authortes beng completely decentralsed. Thrd, we dscuss what happens f the authortes are partly centralsed. Fnally, we dscuss the stablty of the coalton structures and llustrate some of the results usng a smulaton model. 3. A Centralsed Authorty Ths secton analyses the three scenaros resultng from the control authortes formng a grand coalton and actng as a sngle centralsed authorty. The fshermen can on three dfferent coaltons; act as three sngletons playng Nash aganst each other, a two-player coalton playng Nash aganst a sngleton or a grand coalton. The fshermen maxmse ther profts after decdng whch coalton structure to belong to. The fshermen s behavour and the optmal control effort n three dfferent coalton structures are evaluated. 3.. Three Sngletons among Fshermen The non-cooperatve eulbrum s determned where the groups of fshermen act as sngletons playng Nash aganst each other. Snce the control authorty acts as a Stacelberg leader, the problem s solved by bacwards nducton. Insertng the steady state stoc (euaton (4)) and the harvest functon (euaton (3)) nto the proft functon for the fshermen (euaton (6)) and maxmsng the expected proft for the groups of fshermen yelds the followng reacton functons for group : e b r e =, e, (7) 7
c where b = > 0.The Nash eulbrum effort s derved by the ntersectons of the reacton functons for the groups of fshermen, whch yelds the best ( Ψ) pk response for all fshermen gven others best response. The optmal effort employed by a sngle group of fshermen where fshermen are playng a Nash game follows the followng formula: e N 3b b 4 =,. (8) b r 3b b b It must be assumed that <, to ensure that effort employed s postve. The Nash eulbrum effort depends on the rs of beng caught, Ψ, snce t s a part of b. If the rs of beng caught ncreases, that s f b ncreases, then the Nash effort level decreases f t s assumed that 3 > for all,,,. Snce the resource s a shared stoc among the three groups of fshermen, the effort employed by one group of fshermen has a negatve effect on the level of effort employed by others. If, for nstance, fshermen wth technology become more effectve, that s the catchablty coeffcent,, ncreases, then the effort of fshermen wth technology and decreases. The change n the effort for fshermen applyng technology s, however, ambguous. On the one hand there s an ncrease n the effort resultng from beng more effcent, but on the other hand wth a hgher catchablty, less effort s reured to retan the same harvest level. Solvng bacwards now allows us to solve the problem of the centralsed authortes. The beneft functon for the authortes s defned by (5), where the fshermen s proft functon (6), the steady state stoc (4) and the harvest functon (3) are nserted. The authortes maxmse ther beneft functon of harvestng mnus the control costs wrtten as follows: 8
Max 3 = γ π 0 = pe K ce. (9) = r K s.t. 0 < 3 e Penaltes pad by fshermen from exceedng the TAC are exactly offset by the ncome receved by the authorty. 5 Insertng the optmal effort level employed by fshermen (7) and determnng the frst order condton for the centralsed authorty (CA) when fshermen are playng Nash (N) yelds the optmal enforcement level, gven that enforcement s costly: N CA rc =, (0) 8rc rc Kprc 8Kp γ where =. It s observed, that a hgher level of control costs decreases the optmal control effort. The ntuton behnd ths s that more expensve enforcement s less approprate to apply (Becer 968). Hence, f enforcement control s extremely expensve, t mght mply less effort employed and thus more non-complance. If complance s the goal n such a case, t mght be wse to consder subsdsng the control polcy. The effects of changes n other parameters are ncluded n comparatve statcs later. 3.. Coaltons among Fshermen Ths secton dscusses the mplcatons of fshermen formng ether a two-player coalton or a grand coalton. 5 We assume no double dvdend exts; that s, tax revenues cannot be used to reduce other dstortng taxes Jensen & Vestergaard (00b). 9
Assume two groups of fshermen form a two-player coalton we assume and form a coalton, {,}. The two-player coalton plays a Nash game aganst the sngleton. The coalton s assumed to apply the most effcent technology n the coalton, snce the margnal benefts from applyng the most effcent technology are always hgher than the margnal benefts from applyng a less effcent technology. 6,7 It s ntutvely clear, that fshermen wth the hghest effcency have to employ the lowest level of effort to reach a certan level of harvest. Ths mples that the benefts are hghest from formng a coalton of heterogeneous fshermen compared to a coalton of homogeneous fshermen. Thus POs are most sutable across heterogeneous technologes. It s beyond the scope of ths paper to deal wth the ueston of how the benefts are dstrbuted among the groups n a coalton. The grand coalton s defned as full cooperaton among all groups of fshermen. The grand coalton s also assumed to apply the most effcent technology n the coalton. The optmal fshng effort and the optmal level of control effort when fshermen form coaltons are summarsed n the appendx, table A.I and table A.II. From the optmal level of control effort we can conclude, that n the scenaro wth a grand coalton among fshermen, self-regulaton wors and there s no need for government nterventon. Ths concluson s drawn from the fact, that only a corner soluton, where = 0, satsfes 0 <. 8 The ntuton behnd ths result s that fshermen formng a grand coalton maxmse an obectve functon comparable to the obectve functon of the socety except for the costs 6 We are analysng only the two-player coalton among and. Ths coalton s the most effcent coalton (together wth the coalton between and ) snce the technology of the least effcent group of fshermen () s hdden n a coalton and therefore not appled. 7 The reason that we do not have a reallocaton of effort n the coalton but a corner soluton, where the effort employed by the least effcent technology s zero, s that we assume margnal costs are constant. 8 We consder that the cases of havng a zero bologcal growth rate (r=0) or zero harvestng costs (c=0) are too unrealstc. 0
of control. Thus, f the socety observes that the fshermen are organsng n one large PO, then the crcumstances permt the control effort to be reduced to zero. Snce we are not able to mae further analytcal conclusons, we use comparatve statcs on the level of control effort. 3.3. Comparatve Statcs on the Level of Control Effort The effects of changes n economc parameters are determned by comparatve statcs analyss on the level of control effort n the case of fshermen playng Nash and n the two-player coalton. 9 The effects of changes n prce and costs are summarsed n table II and the effects of changes n the catchablty measure are summarsed n table III. Table II. Comparatve statcs on optmal control effort w.r.t. prce and cost parameters γ c p - - f f N CA c > r C CA - - f ( ) 8 γ c > r 6 γ ( ) c > r f ( ) 9 γ c > r 8 γ ( ) Note: - ndcates a negatve effect, ndcates a postve effect. From table II we can conclude that the optmal level of control effort unambguously decreases, f the costs of control ncrease. The result s, however, ambguous when analysng the effect of changes n prces and costs of harvestng. The ambguty s a result of control effort beng dependent on prces and costs n an advanced fashon. The authortes should, therefore, not react to changes n prces and costs, unless they have accurate nformaton about estmated pa- 9 Comparatve statcs n the scenaro of a grand coalton among fshermen are omtted snce t s a corner soluton. Only zero costs of harvestng can mae the corner soluton move from the no control to the full control effort level. Ths s, however, not a realstc scenaro.
rameter values, but nstead accept a second best soluton. If the unt cost of harvestng s suffcently hgh, we can conclude that the optmal control effort ncreases f p s ncreased and decreases f harvestng costs are ncreased. Table III. Comparatve statcs on optmal control effort w.r.t. catchablty parameters N CA f { }, f CA cr ( 6c 6c Kp ) ( ) crkp ( ) Kp γ > for,, = {,,3}, 6c r 6 8c cr ( 8c Kp ) r crkp > for,, = {,,3 }, 8Kp γ Note: ndcates a postve effect. From table III we can conclude that f the catchablty coeffcent n ueston s suffcently hgh, then a further ncrease n the catchablty coeffcent mples an ncrease n the control effort level. Ths s true for the control effort level n both the Nash game among fshermen and the two-player coalton among fshermen. The ntuton behnd ths s that one player, who s already effcent, becomes even more effcent and t s thus easer to not comply. An ncrease n control effort has the opposte effect. In the two-player coalton case there s an effect of an ncrease n only when exceeds, otherwse the effect s zero. If the catchablty for group s ncreased such that >, then group becomes the most effcent n the coalton, and a swtch between technology and wll tae place. 4. A Decentralsed Authorty Consder the authortes to be completely decentralsed; e.g. there are three ndvdual authortes each settng ther own level of control effort based on a Nash game aganst other authortes and a Stacelberg game aganst the fsher-
men. The control effort n one country only affects fshermen from ths country. In each country there are fshermen representng all three dfferent technologes. Therefore, control effort levels set by all three authortes affect each group of fshermen. To smplfy, t s assumed that the groups of fshermen consst of one-thrd from each country; hence the control polcy from the countres has eual weght on each group of fshermen. 0 Ths assumpton mples that we can maxmse the proft of the groups of fshermen only consderng the level of control effort correspondng to the sum of s appled n the three countres. We also assume that countres are symmetrc, e.g. the lump-sum penalty for beng caught s the same n all three countres and so are the unt costs of control. We determne the optmal effort employed by fshermen and the optmal control effort by the authortes n the three scenaros resultng from fshermen formng coaltons. 4.. Three Sngletons among Fshermen Denote the three authortes by, and 3. The benefts for the fshermen applyng technology are now determned by the followng formula: P N = 3 N N N N = ( ) ph ( ) ph ( 3 ) ph ce Ω( 3 ) 3 3 3. () N N ( 3 ( )) ph ce Ω( ) 3 3 Euaton () s an extenson of euaton (5). It descrbes the fshermen s proft from applyng technology, but snce ths technology s represented n all three countres wth /3 n each of them, then /3 of them face control effort, /3 0 Ths assumpton does not change the general result snce the control effort wll always be nterpreted by the fshermen as the sum of control efforts. If the shares of dfferent technologes change, t only changes the weght the dfferent levels of control effort have n the sum of control efforts. Wthout symmetry among authortes the analyss becomes complcated, and t mght not be possble to acheve an analytcal soluton. 3
face control effort and /3 face control effort 3. The optmal effort employed n the fshery s determned and summarsed n the appendx, table A.III. The optmal effort employed by fshermen when the authortes are decentralsed s euvalent to the effort level employed n the centralsed authorty scenaro, except that the optmal control effort s now consdered as an average control effort. Snce the fshermen consder the control effort only as a sngle level, the way the authortes can affect the coalton structure s unchanged compared to the case wth a centralsed authorty. What dffers s, however, how to reach a certan level of control effort when the authortes play a Nash game aganst each other. The three authortes each maxmse ther net present values of harvest mnus the costs of control accordng to the followng formula: Max DA 3 = γ π = pe K ce. () = 3 r DA K 3 e Snce the optmal effort employed n the fshery depends on the optmal control effort set by other authortes there s an externalty n the control effort. The externalty n control effort arses from the fact that, f one country ncreases ts control effort, then t affects the optmal fshng effort and hereby nfluences the control effort level chosen by another country. Assumng the authortes play Nash aganst each other we can solve for optmal n each country (the results are summarzed n the appendx, table A.IV). We observe that the level of control effort for the centralsed authortes resembles the level of optmal control effort n the case of centralsed authortes (see table A.IV). The only dfference s the negatve factor n front of the control costs, γ, n the denomnator. In the centralsed case the factor s -8, n the decentralsed case the factor s three tmes smaller, namely -4. A man explanaton for ths 4
dfference can be found n the fact that the decentralsed authortes face three tmes the fxed costs faced by the centralsed authortes. We can conclude that when fshermen are playng a Nash game aganst each other and other thngs are eual, then the sngle authorty n the decentralsed scenaro has an optmal level of control effort that s lower than the optmal level of control for the centralsed authorty. The level of control effort s, however, dentcal for the centralsed authortes and the sngle decentralsed authorty f the costs of control, γ, are zero. An ncrease n the costs of control mples that the gap between the control efforts n the two scenaros ncreases. Snce we have assumed dentcal countres, the average control effort n the decentralsed scenaro s euvalent to the control effort set by a sngle authorty n the decentralsed case. Therefore, the fshermen face a lower level of control effort when the authortes are decentralsed compared to a centralsed authorty. The levels of control efforts are, however, euvalent f there are no control costs. The reason the control efforts are lower n the decentralsed scenaro s that the control costs are consdered to be an externalty wth hgh costs of control t s optmal for the sngle decentralsed authorty to choose a lower level of control effort snce t plays Nash aganst other authortes. The authortes are free rdng on each other. Holden (994) and Jensen (00) present some emprcal studes of the EU emphassng that the control effort s lower when authortes are decentralsed then when authortes are centralsed. These studes and our analytcal model suggest that, f socety wants complance, t mght be easer to reach f authortes are centralsed, gven that ths s a stable soluton. 4.. Two-Player Coalton among Fshermen The optmal effort level employed n the fshery and the optmal control effort s determned when the fshermen form a two-player coalton playng Nash aganst the sngleton. The optmal effort for group s summarsed n the appendx, table A.III. The optmal control effort n each country s found n the appendx, table A.IV. 5
When comparng the level of optmal control effort n the decentralsed and the centralsed scenaros (see table A.IV) the concluson s exactly the same as n the case where fshermen play a Nash game. Namely, that the control effort only dffers by the factor n front of the control effort costs. Hence, also n the two-player coalton among fshermen the level of control effort s also hgher when authortes are centralsed then when authortes are decentralsed. 4.3. Grand Coalton among Fshermen The optmal effort level for the grand coalton among fshermen and the correspondng level of optmal control are determned and the results are summarsed n the appendx, tables A.III and A.IV. The optmal control effort s, agan, a corner soluton wth =0. We can conclude that even f enforcement s decentralsed, a grand coalton among fshermen s self-enforcng. 5. A Two-Player Coalton Authorty Authortes formng a two-player coalton playng Nash aganst a sngleton complcates the analytcs snce the symmetry of the authortes dsappears. The two-player coalton among authortes contans twce as many of fshermen as the sngleton, but snce the case s non-lnear n, we cannot say anythng about the relaton between the optmal control effort for the coalton and the sngleton. The fshermen formng coaltons are, however, not very dfferent from the other scenaros. The fshermen stll vew the control effort as a sngle level and therefore the optmal effort employed for harvest n the three scenaros resembles the scenaros where the authortes are centralsed and decentralsed. We are not able to solve these three scenaros analytcally, but can conclude that the asymmetry mples results that are not drectly comparable to the other sx scenaros. Numercal smulatons do, however, suggest that there s only a corner soluton, where =0 for both rvals, satsfyng the constrants when fsh- 6
ermen form a grand coalton. Ths seems lely snce t underlnes the results acheved when authortes are centralsed or decentralsed. To sum up; so far we have shown that the effort employed n the fshery s dependent on the average control effort level, but s otherwse ndependent of the coalton formaton among authortes. Furthermore, we have shown that the control effort level s hgher when the authortes are decentralsed compared to the control effort level set by centralsed authortes, and ths holds no matter whch coalton formaton the fshermen choose. 6. Stablty of Coalton Structures among Fshermen Ths secton analyses the stablty of the dfferent coalton formatons among fshermen. For a coalton to be stable there must be no group of fshermen wth ncentves to leave the coalton. To determne the benefts for the group of fshermen t s assumed that fshermen are ratonal and apply the optmal effort level gven the control effort and the coalton structure. Snce we assume the TAC s set at a suffcently low level, the benefts for the sngle group or a coalton of fshermen are determned by the followng formula: P ( Ψ) = ( Ψ) p e x ce ΨΩ. (3) The total benefts for the groups of fshermen are derved when fshermen are sngletons, form a two-player coalton and form a grand coalton. The sum of benefts from free rdng s also derved to determne when the grand coalton s stable. The total benefts when the fshermen act as three sngletons are as follows: 3 = P N cr N ( ) = ( N ) 4 4 c pk 3 4 N N ( ) pk ( ) c c r 3 4 c N ( ) pk 7 pk 3 N Ω. (4)
The benefts n the case of a two-player coalton {,} are as follows: { } { } ( ) ( ) { } { } { } { } ( ) { } Ω = = C e e c b K e b K e p P,,,,,,,. (5) The total benefts n the scenaro of the grand coalton are as follows: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Ω = GC GC GC GC GC GC GC pk c r c pk c r pk c pk P / / /. (6) The sum of benefts from fshermen free rdng s determned as follows: { } ( ) { } ( ) { } { } { } { } { } { } ( ) { } Ω = = F e e e c b K e b K e b K e p P,,,,,,,, 3, 3 3 3 3 * (7) The grand coalton s stable f and only f no group of fshermen has the ncentve to leave the coalton. As dscussed n Pntasslgo (003), the benefts from the grand coalton must exceed the sum of benefts from free rdng, otherwse the cooperatve benefts cannot be dstrbuted n a way that satsfes each country. Furthermore, the benefts from the grand coalton must exceed the sum of benefts from a non-cooperatve game. The two-player coalton s stable f the sum of benefts from ths scenaro exceeds the benefts from a Nash game, whch are euvalent to the benefts from free rdng. Snce we are not able to conclude further from these euatons, we llustrate the stablty by a smula- 8 There are two other possbltes for two-player coaltons, namely {,} and {,}. The former mples that wll have no harvestng actvty and wll act as a sngleton, the latter does not change our results snce wll contnue to have no harvestng actvty.
ton. The smulaton model also dscusses whch soluton s preferred by the authortes. 6.. Smulaton A smulaton model s set up to determne when the grand coalton among fshermen s stable and whether the government s able to affect the fshermen s coalton formaton by ts choce of control effort. It further determnes whch eulbrum coalton structure s preferred by the authortes. Parameter values nspred by the Baltc Sea cod fshery are appled. The costs of harvestng are determned as the average daly costs over the perod 995-999 for a Dansh vessel harvestng cod n the Baltc Sea. The prce s determned as the average prce per logram of cod over the same perod. The cod stoc s assumed to follow an ntrnsc growth rate, r=0.4, whch s an approxmaton for the growth rate from an OLS regresson usng data from 966-999. The OLS regresson does, however, suggest an extremely hgh carryng capacty. Ths level of carryng capacty s, n our vew, unrealstcally hgh, snce the exploted stoc has not, even n extremely good years, been a thrd of the estmated carryng capacty. We therefore assume a more moderate carryng capacty level, and perform a senstvty analyss w.r.t. the carryng capacty. The catchablty coeffcents are assumed to le between 6 and 8, whch are beleved to be moderate values. 3 The parameter values are summarsed n table IV. Table IV. Parameter values appled n the smulaton model c K p r 649 30 8.07 8 6.5 6 0.4 The benefts of the dfferent coalton structures among fshermen are determned as functons of the control effort appled by the authortes and are plotted n fgure 3. The fshermen regard the level of control effort as an average 3 A senstvty analyss w.r.t. the catchablty coeffcents, s possble but to save space we have omtted ths. 9
and do not change ther behavour accordng to the authortes coalton formaton. Fgure 3. Benefts from the grand coalton, sum of benefts from free rdng, sum of benefts from three sngletons Total Proft 60 40 0 0. 0.4 0.6 0.8 Control Effort HL Hence, for 0 < 0.3 the grand coalton s stable. For 0.3 < 0.54 the scenaro wth the three sngletons yelds the hghest proft, and for 0.54 the sum of free rdng yelds the hghest proft. The scenaro of all fshermen free rdng s, however, not a possble soluton. We, therefore, have to determne the proft of the three possble two-player scenaros to determne whether ths proft exceeds the sum of profts for three sngletons. The benefts from a two-player coalton are determned and plotted n fgure 4 to determne when t s a stable scenaro. 4 4 We have only exploted the {,} coalton, but snce s the least effcent technology, hghest payoff results f ths technology s avoded by ncludng t n a coalton. Coalton {,}and coalton {,} do, however, yeld the same pay-offs snce both scenaros result n a Nash game amongst and. 30
Fgure 4. Benefts from a two-player soluton and benefts from a Nash game Total Proft 70 60 50 40 30 0 0 0. 0.4 0.6 0.8 Control Effort HL From fgure 4 we can conclude that the two-player coalton s stable only when the control effort level s suffcently low ( 0.4). Ths concluson s drawn from the fact that, here, the benefts of the two-player coalton exceed the benefts of the fshermen actng as three sngletons playng a Nash game. The twoplayer coalton s, however, not n the core snce the grand coalton s also stable for these values of, and the grand coalton yelds hgher benefts. Combnng the results from fgure 3 and fgure 4 we can conclude that for 0 < 0.3, the grand coalton s stable, 5 for 0 0.4 the two-player coalton s stable, but snce the grand coalton yelds hgher payoffs, we assume that the fshermen choose ths coalton formaton. For large only the scenaro wth three sngletons s stable. Thus, when control effort s low, t s optmal to form coaltons, hence coaltons are somewhat self-enforcng. Ths means that a hgh level of control effort yelds a Nash game among three sngletons snce the au- 5 The grand coalton among fshermen s only socally optmal for zero control effort. 3
thorty does the ob of controllng the fshermen. Ths result can be explaned by the effect of free rdng; the stoc s harvested down snce the punshment for exceedng the TAC s low, and a low stoc mples a lower proft than can be acheved by cooperaton. A hgher control effort ensures a hgher steady state stoc level when thus mang free rdng more proftable and hence, more lely. Ths s some sort of self-regulaton and mght explan that cooperaton s more lely when the control effort s low. Thus f socety sets a low level of control effort, then one would expect more POs, whch mght explan why we see POs n real world settngs. The uncertanty about carryng capacty emphasses that a dscusson of the effects of changes n K s necessary. We have determned how the stablty of the coalton formaton among fshermen changes f K s decreased by 5% or ncreased by 5%, 75% or 500%, respectvely. 6 The results are summarzed n table V. Table V. The effect of changes n K on the stablty of the coalton formaton among fshermen Low values of Low-Md values of Md-Hgh values of Hgh values of 5% decrease grand coalton 3 sngletons 3 sngletons Orgnal K grand coalton 3 sngletons 3 sngletons 5% ncrease -player coalton grand coalton 3 sngletons 3 sngletons 75% ncrease -player coalton grand coalton 3 sngletons 3 sngletons 500% ncrease -player coalton -player coalton grand coalton 3 sngletons 3 sngletons Note: An arrow ( ) ndcates that as ncreases we are movng towards another soluton. 6 We focus our dscusson manly on an ncrease n the carryng capacty snce we are aware of havng chosen K lower than suggested by regressons. 3
A decrease n the carryng capacty does not change the result. What does change our result s an ncrease n the carryng capacty. For low values of, the grand coalton s no longer stable snce the sum of free rdng yelds a hgher payoff and therefore benefts from the grand coalton cannot be dstrbuted such that t satsfes all fshermen. The hgher the carryng capacty becomes the broader becomes the area of where free rdng gves the most benefcal outcomes. All fshermen free rdng s, however, not an opton; therefore the sum of benefts of three sngletons and a two-player coalton playng Nash aganst a sngleton s compared. Even wth changes n the carryng capacty, the model llustrates a somewhat self-enforcng behavour for low values of control effort. For large ncreases n the carryng capacty the grand coalton among fshermen s now also possble for hgher levels of control effort, ths s, however, not a socally optmal soluton snce authortes would prefer zero control effort f fshermen form a grand coalton. The general concluson s that for low to md values of, a two-player coalton or a grand coalton s preferred among fshermen, whle for hgh values of, the non-cooperatve behavour wth three sngletons playng Nash aganst each other s preferred. The senstvty analyss suggests that f the stoc s low, whch t s now, then t s lely that the POs wll collapse, snce the area wth 3 sngletons domnates. Snce we now from the comparatve statcs that there s an unambguous negatve relatonshp between control effort and control costs, we can conclude that nexpensve control effort leads to less cooperaton, whle an expensve control effort leads to more cooperaton. When control costs are hgh and conseuently control effort low, the fshermen have no choce but to organse adeuate control themselves by onng together. In the opposte case the control effort of the authorty ensures enough profts for the fshermen n the non-cooperatve case. Hence, n our numercal example the authorty can, by ts desred level of control, affect the optmal coalton structure of the fshermen. The coalton formaton of the authortes ndcates that the level of control effort s, on average, lower f the authortes are decentralsed than f they are centralsed. 33
Proectng our smulaton model to the Baltc Sea cod fshery, where enforcement s set at the natonal level, the probablty of beng caught s not very hgh, at least not n countres belongng to the EU (Holden 994). Ths supports the concluson that enforcement set at a decentralsed level mples a low level of control. The smulaton model then ndcates that fshermen should on together and form coaltons. Ths happens to some extent snce the fshermen n some countres on together n POs, but t s not as common as our model suggests, and there s no grand coalton. There mght be several explanatons for ths. One s that the fshermen mght not be aware of the benefts, another mght be, that our model s only a stylsed model, where the resource s exploted by three fshermen, n realty more fshermen are represented n the fshery, and even though they apply the same technology, they mght not on together as a group, perhaps because of cultural and language barrers. If the number of fshermen ncreases, t most lely becomes more dffcult, f not mpossble, to acheve a grand coalton soluton. Olson (965) dscusses ths as a general problem to collectve goods, and Hannesson (997) dscusses t as a problem n fshery models, where he defnes the crtcal number of fshermen for a full cooperatve soluton. However, there s some cooperaton among POs (at least n Denmar) and they plan to assst the Eastern European fshermen to organze POs when the EU s enlarged towards the east. Ths can be regarded as a step towards a coalton. Another pont of nterest s to determne whch soluton the authortes prefer. We are not able to solve ths problem analytcally, however we are able to gve an ndcaton of the preferred soluton by applyng our numercal example. We cannot determne the case of a partly centralsed authorty, but we determne the sum of the benefts for the authortes and we compare these to determne whch of the scenaros yelds the hghest sum of benefts. 7 The benefts from the three scenaros where the authortes are completely centralsed are plotted n fgure 5. 7 It should be noted, that ths smulaton only yelds an ndcaton of whch soluton s preferred by the authortes. We are not determnng the stablty of the solutons and we are not determnng the benefts from the two-player coalton among authortes. 34
GC π CA Fgure 5. Total benefts for authortes n the three scenaros where the authortes are centralsed Sum of Proft CA 60 55 50 45 40 35 30 GC π CA {, } N π CA 5 0 5 0 5 π CA Control Cost HγL Usng our numercal parameter values, fgure 5 shows that when the authortes are centralsed, they prefer a soluton where the fshermen form a grand coalton. The fgure s plotted assumng the authortes choose the corner soluton wth zero control effort when fshermen form a grand coalton. If there are control effort costs these, however, reman. The sum of benefts when the authortes are decentralsed yelds the same pcture, namely that the overall soluton s preferred when fshermen form a grand coalton. Comparng the two scenaros where fshermen form a grand coalton and the authortes have the choce between beng centralsed or decentralsed, the centralsed scenaro yelds a hgher payoff snce the centralsed authorty only has to pay the fxed cost of control once. 8 We can conclude that the authortes receve the hghest sum of payoffs when they are centralsed, settng a zero-level of control effort and then tang advantage of the self-enforcng mechansm where the fshermen form a grand coalton. 8 The sums of benefts for the authortes are, however, the same f the costs of control are zero. 35
In the Baltc Sea the authortes do not cooperate on enforcement, whch, accordng to our smulaton model s not the soluton wth the hghest benefts. We have, however, not determned the stablty of havng centralsed authortes and are therefore not able to comment on the actual behavour of authortes n the Baltc Sea. 7. Dscusson, lmtatons and Concluson Ths paper contrbutes to the lterature by settng up a model to dscuss coalton formaton both on the ntergovernmental level and on the fshermen level. The paper shows that the control polcy set by regonal, natonal or multnatonal authortes nfluences the cooperatve behavour of the fshermen. We show that centralsed authortes tend to set a level of enforcement that s hgher than the level set by the decentralsed authortes, and the gap between the effort levels ncreases as the unt costs of control ncrease. The man reason for ths concluson s that the control effort becomes an externalty when authortes play a Nash game aganst each other, and the more expensve the control becomes, the less control effort the sngle authorty s gong to apply. Therefore, f socety wants a hgh level of control effort, ths s easer to reach f the control effort s decded on a multnatonal level. The concluson underlnes the fact that the probablty of an offence beng detected n the EU, where enforcement s decentralsed, s very low (Holden 994). The paper also shows that the grand coalton among fshermen s stable and socally optmal f and only f the authortes set a zero control effort; ths s true no matter whether the authortes are centralsed or decentralsed. The ntuton s, that wthout any control effort, the grand coalton among fshermen faces the same obectve functon as the socety, and the soluton becomes socally optmal. The paper sets up a smulaton model applyng parameter values nspred by the Baltc Sea cod fshery. The smulaton model shows that for low values of control effort the fshermen wll organse adeuate control themselves by onng together. For hgh values of control effort fshermen wll act as sngletons. The ntuton s that the gan from cooperaton s much larger f there s no control. 36
There s, however, a great uncertanty about the level of the carryng capacty. Therefore the paper ncludes a senstvty analyss, to analyse the effects of changes n the carryng capacty. Ths analyss shows that the overall results do not change sgnfcantly. It s worth notng that the smulaton model shows that wthout any control effort, the fshermen are not powerless, but may well organze a control of ther own va formaton of a grand coalton or a two-player coalton. For hgh values of control effort the fshermen let the government do the controllng and they play a non-cooperatve Nash game aganst each other. What does change when the carryng capacty ncreases s that t becomes more attractve to form coaltons, also for md-hgh values of the level of control effort. For example a 500% ncrease n the carryng capacty mples that for mdhgh values of the level of control effort the grand coalton s stable for the fshermen. It s, however, not a socally optmal soluton snce we showed that only zero control effort would be socally optmal f fshermen form a grand coalton. The reason that t becomes more optmal for fshermen to on together when the carryng capacty ncreases s that externaltes n the fshery become more sgnfcant, whch mples that the benefts from coaltons ncrease. The model could not determne the stablty of the coaltons among authortes or tae nto what happens f the countres are no longer symmetrc. However, t s not possble to analyse these scenaros wth the set up we have chosen for the model. The model suggests a socally optmal soluton, where authortes may or may not form coaltons, but where no control effort should be appled and fshermen should form coaltons. We suggest an alternatve way of thnng, namely, how to reach a cooperatve soluton among fshermen. One (perhaps naïve) way to reach such a soluton mght be for government to drop the exstng system wth TACs, uotas and enforcement and nstead encourage cooperaton among fshermen. The cooperaton can be encouraged for nstance by subsdsng or nformng about ownershp across boarders or by encouragng exstng POs to help organze POs n the eastern European countres when the EU s enlarged 37