Strategic Behavior and the Environment, 2013, 3: 97–120

Stability of International FisheriesAgreements Using PrecautionaryBioeconomic Harvesting Strategies∗Mika Rahikainen1,2,3,†, Marko Lindroos1,4 and Veijo Kaitala2

1Department of Economics and Management, University of Helsinki,P.O. Box 27, FI-00014, Finland; mika.rahikainen@helsinki.fi2Department of Biosciences, University of Helsinki, P.O. Box 65,FI-00014, Finland3Department of Environmental Sciences, University of Helsinki,P.O. Box 65, FI-00014, Finland4Nordic Centre for Research on Marine Ecosystems and Resources underClimate Change (NorMER), Oslo, Norway

ABSTRACT

International agreements are necessary for exclusion of non-cooperativebehavior. We parameterized an age-structured model for the North Seaherring fishery. The reference points of the current harvest control ruleoperationalize the precautionary approach. Applying the precautionaryapproach by the grand coalition adds the net present value of the fishery

∗ This study was funded by the Finnish Academy Project #121695. The research leadingto these results also received funding from the European Union’s Seventh FrameworkProgramme (FP7/2007–2013) under grant agreement no. 244706/ECOKNOWS project.However, the paper does not necessarily reflect the views of the European Commission(EC), and in no way anticipates the Commission’s future policy in the area. We acknowl-edge the input of the two anonymous referees whose comments improved the quality ofthe paper.

† Corresponding author. Fisheries and Environmental Management Group, Departmentof Environmental Sciences, University of Helsinki, Viikinkaari 2, P.O. Box 65, FI-00014,Finland; mika.rahikainen@helsinki.fi.

ISSN 1944-012X; DOI 10.1561/102.00000025c© 2013 M. Rahikainen, M. Lindroos and V. Kaitala

98 Rahikainen et al.

compared to another management approach, a fixed fishing mortalityrate strategy. The fishing strategy and costs have a strong impact on thestability of the coalitions. Adopting a precautionary harvest control rulehas potential to stabilize multilateral fishing agreements provided thatfishing costs are not identical among countries. If they are identical,there will always be incentive for free riding.

Keywords: Risk management; harvest control rule; precautionaryapproach; game theory; fisheries agreement; north seaherring.

JEL Codes: K32; Q22; Q57

Introduction

Herring stocks have contributed economic wealth in the past as well in thepresent days. Since the 1950s herring fisheries have expanded to a level atwhich they have a major impact on the harvested stocks revealing thatclupeoid populations have a general tendency to collapse under heavy fishingpressure (Murphy, 1977; Saville, 1980; Hay et al., 2001). Obviously, stockcollapse creates social, political, and ecological problems and dissipates largeamounts of economic rent (Garcia and de Leiva Moreno, 2003). Excessivefishing pressure on any stock may result from the practice of ignoring orunderestimating uncertainty in stock assessment and fisheries management(Hilborn and Walters, 1992; Walters and Maguire, 1996; Hilden, 1997) orfrom lack of national or international regulations (Bjørndal et al., 2000).

Exclusion of open access may help in preventing economic overfishing(Feeny et al., 1990) and international agreements have been establishedto reduce the undesirable effects due to common property exploitation.Since the sovereignty of states precludes external enforcement, internationalenvironmental agreements must be self-enforcing. The UN has provided aplatform to develop and agree upon international treaty laws such as theExtended Fisheries Jurisdiction (EFJ) with introduction of 200-mile exclu-sive economic zones (EEZs) in 1977 (UN, 1982). The EEZ do not completelyresolve the problem of open access to harvesting of the resources becausemany fish resources migrate or are spread across national boundaries and

Stability of International Fisheries Agreements 99

international waters (Kaitala and Munro, 1997). Cooperation in the frame-work of bi- and multilateral agreements is therefore necessary to solve man-agement problems by assigning property rights to international fish stocksor by regulating fisheries by other means such as national quotas, technicalrestrictions, spatial or temporal closures. Game theoretical models explainwhy full cooperation may fail as environmental externalities impact negoti-ations in international politics (Wagner, 2001). Coalition game theory hasbeen applied in real world fisheries to analyze the expected benefits of coop-eration among the fishing countries and to predict the possibilities of reach-ing stable agreements among them (Arnason et al., 2001; Brasao et al., 2000;Lindroos and Kaitala, 2000; Pintassilgo, 2003; Lindroos, 2004).

In addition to the lack of jurisdiction and property rights, assessment andmanagement failures have also contributed to the inefficient use of marineresources globally. The apparent decline of fisheries has catalyzed morerisk averse harvesting policies and management goals (FAO, 1995). Conse-quently, a concept of precautionary approach (PA) has been launched topromote prudent management and to decrease probability of recruitmentoverfishing and subsequent stock collapse (FAO, 1995, 1996, 1997). Biologi-cal reference points (BRPs) are used as signposts in implementing the pre-cautionary approach and pragmatic fisheries management has been basedon a variety of them. The rules to calculate biological reference points aretypically based on the perception of risk of stock collapse or of ‘‘safe’’ har-vest level (ICES, 2001). Biological reference points are usually expressed asfishing mortality rates (e.g., Fmed, Fx%SPR, F0.1, Fmsy) or as critical levelsof spawning or recruited biomass (e.g., Bloss, Bmbal, B20% b−virg) (Maguireand Mace, 1993; ICES 1997, 2001). The precautionary levels of mortalityand spawning biomass (Fpa, Bpa) are usually developed from the estimatedoverfishing thresholds (Flim, Blim).

Biological reference points, e.g., biomass and fishing mortality limits,targets and trigger points, are commonly applied to develop harvestingstrategies. They are intended as robust plans stating how the catch fromthe stock will be adjusted to the changes in the stock abundance and tounpredictable or uncontrolled biological, economic, and social fluctuations(Hilborn and Walters, 1992). Harvest control rules (HCRs) are explicitexpressions of harvesting strategies and include proportional and thresh-old strategies. Proportional harvesting removes a constant fraction of fisheach year. F0.1 strategy is an example of proportional harvesting strategy.

100 Rahikainen et al.

Since Beverton and Holt (1957), F0.1 strategy has attracted a paramountinterest in practical fisheries management applications (e.g., ICES, 2001).Additionally, a combination of these has been applied, namely proportionalthreshold strategies (Enberg, 2005). In proportional threshold harvesting,a fixed proportion of fish is harvested when the stock biomass is belowthe limit threshold or above the trigger threshold. When stock biomass isbetween these reference points, the harvested proportion is adjusted accord-ingly. Here, we analyse explicitly the economic consequences of proportionaland proportional threshold strategies and their influence on likely successof international fisheries agreements. We parameterize the analysis for theautumn-spawning North Sea herring fishery.

Fish Stock and the Current Management Scheme

We consider autumn-spawning North Sea herring stock in the ICES sub-area IV, division VIId, and division IIIa (autumn spawners). The stock hasundergone two major declines in the 1970s and the 1990s (Bjørndal, 1988;Bjørndal and Lindroos, 2004; Simmonds, 2007). The second period of declineresulted in an EU/Norway agreement on management actions. Subsequently,due to stricter regulations, the stock increased to an estimated level of 3.6million tonnes in 2001 (Bjørndal and Lindroos, 2004). Since the second col-lapse in the mid-1990s the spawning stock biomass (SSB) has increased from0.5 million tonnes to 1.8 million tonnes. The lowest estimated SSB was only0.05 million tonnes in 1977. Catch has varied within the range 0.25–0.70million tonnes since 1987 (ICES Advice, 2006).

Harvest control was agreed between the EU and Norway in 1997(Patterson et al., 1997). Currently, the harvest control rule applies propor-tional threshold strategy using a limit and a trigger reference point (ICESAdvice, 2006). According to the EU–Norway agreement on management ofNorth Sea ‘‘Every effort shall be made to maintain a level of spawning stockbiomass (SSB) greater than the 0.8 million tonnes (Blim).’’ If the SSB isestimated to be below 0.8 million tonnes, the quotas are set to reflect a fish-ing mortality rate of less than 0.10 for 2 ringers (read: age group) and olderand less than 0.04 for 0–1 ringers. Consequently, the HCR does not imposea moratorium if SSB falls below the Blim. When spawning stock biomass isestimated to be below 1.3 million tonnes but above 0.8 million tonnes, i.e.,between the limit and the trigger reference points, quotas are set to reflect

Stability of International Fisheries Agreements 101

a fishing mortality rate equal to:

Fadults = 0.25 − 0.15((1.3 − SSB)/0.5), (1)

Fjuveniles = 0.12 − 0.08((1.3 − SSB)/0.5), (2)

which defines the proportional threshold strategy and subscripts refer to agegroups.

The rule also specifies fishing mortalities for juveniles (F0−1) and for adults(F2−6) not to be exceeded, at 0.12 and 0.25 respectively, for the situationwhere the SSB is above 1.3 million tonnes. Moreover, the current agreementhas a constraint on change in a TAC that is no more than 15% greater or 15%less than the TAC of the preceding year, but allows for a stronger reductionin TAC if necessary (ICES, 2009). The current harvest control rule is limitingfishing mortality of 0-1 ringers to about 50% of fishing mortality of 2-ringersand older. It is enforced by a by-catch ceiling of the industrial fishery. Thecatch of the industrial fishery has been about 50% of that allowed for thelast 10 years.

This HCR regulates fishing activities of Norway and seven EU countries.The allocation of TAC for the directed fishery for herring shall be 29% toNorway and 71% to the Community. Bjørndal and Lindroos (2004) haveanalyzed the optimal sharing rule of the North Sea herring quota and con-cluded that according to the Nash bargaining solution, the current sharingallocates a too large fraction to the EU.

Four fleet segments have been identified in the North Sea herring fishery(Dickey-Collas, M., pers. comm.):

(1) Globally operating freezer trawlers from the Netherlands, Germany,France, and England (under Dutch ownership).

(2) ‘‘Standard” trawlers from Scotland, Denmark, and Sweden harvestingfor human consumption and typically containing refrigerated sea watertanks.

(3) The Norwegian fleet being a mixture of trawlers and purse seiners catch-ing both adults and juveniles in the Norwegian Sea.

(4) Industrial fleet catching herring solely as a by-catch in the sprat fishery,vessels being Danish and deploying dominantly small-meshed gears.

The diversity in the fleet attributes manifests differences in the fishingcosts among segments. Those attributes are partly clustered according tonational ownership of the vessels. Therefore, identical fishing cost among

102 Rahikainen et al.

the countries participating in the North Sea herring fishery should not beanticipated.

The Model

We begin by presenting the biological model of the herring fishery. We thendescribe the economic model, which will then be used in the game-theoreticanalysis.

Biological Model

Population dynamics of herring are simulated using an age-structured modeldescribing recruitment, mortality, and life history attributes in discrete time.The mature component of the stock first spawns and produces new recruitsin the youngest age groups. Spawning stock biomass is adjusted to begin-ning of September when spawning mostly takes place. The Beverton–Holtstock-recruitment function is fitted in maximum likelihood using the stockand recruitment estimates by ICES (2006). The deterministic model is:

Ry =αSSBy−1

β + SSBy−1, (3)

where R is recruitment to the stock and SSB is spawning stock biomassin year y, and α and β are parameters having values 60.89 (unit: numbers10∧9) and 0.456 (unit: million tonnes), respectively.

All parameter values for life history are adopted from the ICES workinggroup report (ICES, 2006). The number of fish of each age class is assumedto be known in the beginning of 2006 (Table 1), which is the initializationyear for the analysis. The age-classes are then subject to natural and fish-ing mortality F , which reduces the number of fish when they grow older.Natural mortality Ma is constant over the years y but vary by age a. Selectiv-ity Sa is estimated using the average fishing mortality profile at age during1996–2005. Herring are partially recruited at ages 0–3 and are assumed fullyrecruited at ages 4+.

Population biomass at year y is given as the sum of the number of fishover all age classes multiplied by the stock weights as follows:

By =a=9∑

a=0

wSa Na,y, (4)

Stability of International Fisheries Agreements 103

Table 1. Age dependent parameter values for the North Sea herring stock(ICES, 2006).

Age Ma moa Sa wSSBa wS

a wCa N2006

0 1.0 0 11 — 0.006 0.013 26.981 1.0 0 25 — 0.043 0.040 7.572 0.3 73 53 0.129 0.123 0.107 2.573 0.2 95 83 0.170 0.166 0.149 1.374 0.1 100 100 0.200 0.200 0.173 1.495 0.1 100 100 0.223 0.226 0.198 2.776 0.1 100 100 0.242 0.247 0.214 0.827 0.1 100 100 0.258 0.265 0.231 0.938 0.1 100 100 0.278 0.283 0.251 0.269 0.1 100 100 0.290 0.281 0.264 0.21

Instantaneous NumbersUnit rate Percentage Percentage kg kg kg 109

Source Estimatedin ICES Table Table from Table Table Table Table Table(2006) 2.7.1 2.7.1 2.6.12.2 2.4.1.1 2.6.12.2 2.6.12.2 2.7.1

All weights at age are averages in 2001–2005.

where wSa is weight at age in the stock (Table 1) and Na,y is number of fish

at age a in the beginning of year y. Spawning stock biomass is given by thepopulation abundance at the beginning of the year, total mortality betweenthe beginning of the year and the spawning period, and by the maturationschedule mo:

SSBy =a=9∑

a=0

wSSBa moaNa,ye0.67(−(SaFy+Ma)), (5)

where wSSBa is weight at age in the spawning stock, moa is maturity at age.

It is assumed that age groups 0 and 1 are immature, ages 2 and 3 partiallymature, and older component is fully mature (Table 1). Population dynamicsare simulated for 20 years period in 2006–2025.

Economic Model

We apply a constant unit price of herring/kg and a linear cost functionfor exercised fishing mortality. Data of the Norwegian purse seine herring

104 Rahikainen et al.

fishery is applied to derive the cost function. The variable costs associatedwith the North Sea herring fishery are estimates built on the assumptionthat the vessels spend 60 days a year harvesting NS herring (Nøstbakken,2006, pers. comm.). The purse seiners typically account for approximately85% of the Norwegian landings of North Sea herring. The annual variablecosts of the Norwegian purse seine fleet targeting on herring (Nøstbakken,2006) were related with fishing mortality rate contrived by the Norwegianfleet annually in 1996–2000. The fishing mortality rate of the Norwegianfleet (FN

y ) in year y was estimated by:

FNy = Fy

Y Ny

Yy, (6)

where Fy denotes the overall fishing mortality rate, Yy total catch, and Y Ny

Norwegian catch in year y (ICES, 2006). Effectively, this implies that theestimated Norwegian fleet’s fishing mortality rate (FN

y ) is that of the fishingmortality rate of the entire Norwegian fleet, which we assume are solelypurse seiners.

The variable costs Qi of harvesting by country i is defined by:

Qi = ϕiθFiy, (7)

where ϕi is a scaling term, and θ is a parameter (Table 2). Fishing costslikely differ among countries though published information is lacking. Thedifferences are expected due to varying vessel attributes, crew shares, anddissimilar distances to the fishing grounds. We apply a scaling term, ϕi, tocharacterize differences in the fishing costs among countries (Table 3). Theactual values of the scaling term are arbitrary but describe two possiblescenarios, minor and substantial cost asymmetry in the fishery. The cost perunit of instantaneous fishing mortality is applied instead of the conventional

Table 2. Harvesting and economic parameters.

Parameter Value Unit

θ 116.1 Mr 5 percentp (price) 0.184 /kg

Stability of International Fisheries Agreements 105

Table 3. Interpretation of the identical, high, and low unitcosts in terms of the scaling term ϕi.

Singletons Partial coalitionsGrand

coalition

Costs {1} {2} {3} {12} {13} {23} {123}Low 1 0.9 0.7 0.9 0.7 0.7 0.7Identical 1 1 1 1 1 1 1High 1 1.1 1.3 1 1 1.1 1

The realized scaling terms are determined by the most efficient countryof any coalition.

usage of the cost of fishing effort because there are no estimates availableabout effort or catchability for the North Sea herring fishery (ICES, 2006).

The actual number of vessels in each country is unknown and is excludedfrom the analysis framework. It is implicitly assumed that vessels are iden-tical with respect to variable fishing costs within a national fleet. Theimpact of relaxing the assumption of identical costs among countries is testedby scaling the costs by the term ϕ. It is thus assumed that all economicdifferences among countries are captured by the cost function differences(Table 3). Since the marginal revenue of the fishing is equal for all counties,only the one with the lowest unit cost will harvest.

Norway is designated as country 1, and the EU countries harvestingthe North Sea herring stock form countries 2 and 3. These countries areUnited Kingdom, the Netherlands, Denmark, Germany, Sweden, Belgium,and France. Because of lacking data of the national fleet sizes and fishingcost, it is neither necessary nor helpful to assign any particular EU nationas country 2 or country 3.

The catch (harvest) for country i is calculated in terms of the fleet specificfishing mortality and natural mortality rate of the stock:

Ciy =

a=9∑

a=0

WCa Na,y

SaFiy

Ma + SaF iy

(1 − e−Ma−SaF iy), (8)

where WCa is mean weight in catch at age a.

106 Rahikainen et al.

The total annual harvest is the sum of national harvest:

Cy =i=3∑

i=1

Ciy, (9)

Game Theory Framework

The coalition game under certainty is described by Nash equilibrium solu-tion. We apply an open loop model, where fishing strategy is determined inthe beginning of the simulation period. The net present values (NPV) indi-cate the obtained profits during a 20-year period. NPVs are functions of thecontrol variables, derived from the management strategy, and are given by:

J i(F, F , Bpa) =∑

y

πiy =

∑

y

pCiy − Qi

y

ρy, (10)

s.t. (1–9) and s.t. Fy ≥ 0.1. Here, p is the unit price per kg, r is discountrate, ρy = (1 + r)y−y1 is the discount factor, F is the upper limit of thefishing mortality, and Bpa is precautionary spawning stock biomass. Term y

denotes the index for year with y1 being the base year. According to thecurrent harvest control rule coalitions engage in harvesting activities everyyear, even if it was not profitable for them. The rationale is that even ifthere were losses in some years, the exit from the fishery is a slow processwhich will not occur due to losses in one year. Year-to-year change in a TACis not limited to 15% of the TAC in the previous year.

We specify three games to allow comparisons between the two manage-ment approaches, a fixed fishing mortality rate and a harvest control rulestrategies. In the first version of the game the decision variable of the playersis simply the players’ fishing mortality, Fi. The values of the coalitions inthe game can be defined as follows

GAME 1

W (i) = maxFi

J i(Fi, Fj , Fk), i = 1, 2, 3, i �= j, k, j �= k,

s.t. (1–9) for singletons

W (i, j) = maxFi,Fj

∑

s=i,j

J j(Fi, Fj , Fk), i = 1, 2, 3, i �= j, k, j �= k,

Stability of International Fisheries Agreements 107

s.t. (1–9) for two-player coalitions, and

W (M) = maxF1,F2,F3

3∑

i=1

J i(F1, F2, F3).

s.t. (1–9) for the grand coalition (GM).In the second version, we assume that the grand coalition applies a har-

vest control rule while two player coalitions and singletons only adjust theirfishing mortality rate . It this case the revenue of the grand coalition is givenas

GAME 2

W (M) = maxF1,F2,F3,F1+F2+F3≤F ,F ,Bpa,

3∑

i=1

J i(F1, F2, F3, F , Bpa).

s.t. (1–9), where F is the maximum fishing mortality and Bpa is precaution-ary spawning biomass.

In the third game version, we assume that also two-player coalitions applyHCR. Then, for the two-player coalitions we have,

GAME 3

W (i, j) = maxFi,Fj ,Fi+Fj≤F ,F ,Bpa,

∑

s=i,j

Js(F1, F2, F3, F , Bpa),

i = 1, 2, 3, i �= j, k, j �= k,

s.t. (1–9), where W (i) is the value of a single-player coalition as in game 1,and W (i, j) is the value of a two-player coalition. The value of grand coalitionW (M) contains all cooperatively acting players as in game 2. Singletonscannot gain by adopting a conservative strategy (Pintassilgo, 2001), and thecharacteristic functions imply singletons optimizing a fixed fishing mortalityrate without implementing a harvest control rule. The grand coalition caneither apply harvest control rule or adjust only the fishing mortality rate.The same alternatives apply also to partial coalitions.

The results were solved by calculating the best response successively toeach player until the decision variables converged. Three to four iterationswere enough to find the solution.

The Shapley (1953) value measures the marginal contributions (averagedsums) of countries to each coalition. It is a single point solution with intuitiveinterpretations: each player is treated equally, and all benefits are shared

108 Rahikainen et al.

among players. The Shapley value expresses the sum of dividends that eachcoalition pays to its members. The most effective country would harvest asa sole owner and give away the rest to the two other players. The Shapleyvalues are:

Zi =∑

K⊂M

[W (K) − W (K − {i})](k − 1)!(l − k)!

l!, (11)

where k denotes the number of elements in coalition K and l is the numberof players in the game (Shapley, 1953).

The core conditions ensure that cooperation does yield surplus benefitsthat can be shared among players. This verification is carried out by checkingthat Shapley value of each country is within the core for all coalitions K as(Mesterton-Gibbons, 2001):

∑

i∈K

Zi − W (K) ≥ 0. (12)

This core condition implies that all members of coalitions regard the impu-tation as fair because they could not do better outside the grand coalition(Kaitala and Lindroos, 1998). These conditions are also linked with coopera-tive stability stating that each country should be satisfied with their Shapleyvalues.

The stability conditions (non-cooperative stability) are given as:

W (M) −∑

i∈M

Wi ≥ 0, (13)

where Wi is the free-rider value for country i. The stability conditions statethat there should be enough cooperative benefits to be shared in order tomake staying in the full cooperative mode optimal. If the sum of free-ridervalues Wi of the countries is smaller than the value of the grand coalitionM then the grand coalition is stable.

Results

Stability of the Agreements

The core exists in all our games and the Shapley lies in the core implyingthat each coalition receives more than it would gain by harvesting as a

Stability of International Fisheries Agreements 109

Table 4. Profit by country or coalition (NPV in 10ˆ6) for three simulatedunit cost cases.

Singletons

Coalitions and thecorresponding free rider next

to the rightGrand

coalition

Costs {1} {2} {3} {12} {3} {13} {2} {23} {1} {123}The partial coalitions and the grand coalition applies a harvest control rule

Low 84 144 265 98 312 169 159 256 133 850Identical 142 142 142 187 272 187 272 187 272 732High 211 153 72 278 181 218 237 169 303 732

The partial coalitions and the grand coalition applies a fixed F strategy

Low 84 144 265 241 392 392 241 422 211 834Identical 142 142 142 285 285 285 285 285 285 714High 211 153 72 360 189 313 254 254 313 714

Partial coalitions and the grand coalition may or may not adopt harvest control rule.Singletons have only one strategy option, i.e., a fixed F strategy.

singleton or as two-player coalitions. Thus, the grand coalition is stable inthe cooperative stability sense. The result holds for all tested fishing costscenarios and harvesting strategy combinations.

The results identify that the grand coalition is always more profitable thanany partial coalition or singletons (Table 4). If the grand coalition appliesa harvest control rule, it adds about 2% to the net present value when afixed fishing mortality rate strategy is the benchmark case. Importantly,applying the precautionary approach through the biomass trigger point andthe fishing mortality rate ceiling adds NPV, at least when the referencepoints are optimal.

The range of the total cooperative benefits is 714–850 million dependingon the fishing cost scenario and the harvesting strategy (Table 4). The iden-tical and high fishing cost scenarios yield equal total cooperative benefitsbecause only the most effective country of the coalition would harvest asa sole owner. That is country 1 in both of these cost scenarios (Table 2).Country 3 is the most effective one in the ‘‘low cost’’ scenario resulting in

110 Rahikainen et al.

Table 5. Shapley values by country (NPV in 10∧6) for three unit costscenarios.

Partial coalition rejects HCR Partial coalition applies HCR

unit costs unit costs

Z Identical High Low Identical High Low

Country 1 244 304 208 244 303 2022 244 246 253 244 250 2763 244 182 389 244 179 372

W (M) 732 732 850 732 732 850

The grand coalition applies a harvest control rule but the partial coalitions may (right-hand side of the table) or may not (left-hand side of the table) apply HCR.

Table 6. The non-cooperative stability of the grand coalition.

Partial coalitionrejects HCR

Partial coalitionapplies HCR

Unit costs Unit costs

Low Identical High Low Identical High

Grand coalition applies HCR Yes No No Yes No YesGrand coalition rejects HCR No No No Yes No No

larger total benefits. The Shapley values indicate a justified share of thetotal cooperative benefits for all members of the grand coalition (Table 5).Each country will naturally receive an equal share of the benefits if fishingcosts are identical among countries, regardless of whether the partial coali-tions apply or not a harvest control rule. The shares change when costs arenot identical and are impacted also by the applied management strategy.Applying a harvest control rule has a slight tendency to equalise the Shapleyvalues compared to a fixed fishing mortality rate strategy.

The impact of applying a harvest control rule versus adopting a fixed F

strategy was examined under the three cost scenarios and two managementapproaches. Full cooperation is stable in 4 cases out of total 12 instances(Table 6). This means that only in these cases no single country wouldbenefit from free-riding, that is, by leaving the grand coalition. Stability

Stability of International Fisheries Agreements 111

prevails when all the coalitions apply a harvest control rule and the costs arenot identical (Table 6, upper right quarter). On the other hand, rejectinga harvest control rule by all coalition structures pre-empts full cooperationand a multinational fishing agreement is never stable (Table 6, lower leftquarter). If fishing costs are identical among countries, there will always beincentive for free riding regardless of the management approach. Under theidentical cost scenario, partial coalitions are stable provided that coalitionsreject the harvest control rule (Table 4). Full cooperation is stable also incase fishing costs are low and either the grand coalition or a partial coalitionapplies a harvest control rule (Table 6, upper left quarter and lower rightquarter, respectively).

Partial coalitions can be stable assuming that it is possible to switch themanagement approach between the harvest control rule and a fixed fishingmortality rate strategy. In addition, the cost level impacts stability of partialcoalitions. Coalitions {1,3} and {2,3} are stable in case fishing costs are‘‘high’’ and a fixed F strategy is applied by the partial coalitions (Table 4).The strategy choice of the grand coalition has no impact on the stabilityof the partial coalitions in this specific case. In this game, country 3 wouldchoose country 1 or 2 and form a coalition, while the outside player wouldfish as a singleton. If the countries can switch between the two managementapproaches, the partial coalition will always abandon the harvest controlrule and apply the fixed fishing mortality rate strategy. Clearly, it does notpay off for a partial coalition to apply a harvest control rule if the outsideplayer does not adopt it, too. The loss as a net present value of the partialcoalition is 82–97 million if the unit costs are ‘‘identical’’ or ‘‘high’’. Therange of economic losses of the partial coalitions increase if the fishing costsare ‘‘low’’, being 79–167 million (Table 4). Also the outside player will benegatively impacted if the partial coalition applies the harvest control rule.

Fishing Mortality Rate Trajectories Under the Harvest Control Rule

The optimal parameter values of the decision variables (F , F , SSBpa) areimpacted by the fishing costs, coalition structure, and the managementapproach. The actual annual fishing mortality rate can have high variabilitywhen partial coalitions apply the harvest control rule and singletons apply afixed F strategy (Table 7). Optimal harvesting under a combination of lowfishing costs and a harvest control rule based management approach willlead to very low SSBpa and high F for the partial coalitions (Table 7). The

112 Rahikainen et al.

Table 7. Optimal fixed fishing mortality rate (F ) for singletons, and opti-mal harvest control rule reference points, F and SSBpa, for the coalitions.

Coalition structure/coalition Range inthe actual

{1,2,3} {1} {2} {3} {1,2} {1,3} {2,3} Fy

Grand Bpa 1.94 0.21–0.31coalition F 0.31{1},{2},{3} 0.13 0.18 0.24 0.55{1},{2,3} 0.34 Bpa 0.95 0.44–1.37

F 1.03{2},{1,3} 0.45 Bpa 0.81 0.55–1.42

F 0.97{3},{1,2} 0.47 Bpa 0.81 0.57–1.41

F 0.94

The units of the harvest control rule reference points are instantaneous rate and milliontonnes, respectively. The low fishing cost scenario is used, and the partial coalitions applyharvest control rule. The grand coalition is stable (while the partial coalitions are not).

precautionary element of the harvest control rule will therefore vanish, andthe actual spawning stock biomass will approach the minimum acceptablelevel, Blim (Figure 1). In this particular game, the harvests of the partialcoalition will fluctuate between the sporadic high and the dominating lowyields. The harvests of the outside player will exhibit considerably less vari-ability due to fixed F strategy (Figure 2). This pattern is caused by thetrigger points of the harvest control rule, which let the coalition to exer-cise high fishing mortality whenever the stock biomass exceeds SSBpa. Thebiomass will, consequently, be harvested below Blim during one time step(year), and fishing mortality rate generated by the partial coalition willstay at the minimum level until ‘‘recovery’’ takes place. The spawning stockbiomass in general fluctuates around Blim in case partial coalitions apply aharvest control rule and fishing costs are low. On the contrary, under thesame management approach but high fishing cost scenario the spawningstock biomass reaches dynamic stability near the level of SSBpa.

Most importantly, the optimal bioeconomic harvest control rule forthe grand coalition maintains the precautionary element regarding stock

Stability of International Fisheries Agreements 113

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.9

SSB (million tonnes)

Fis

hin

g m

ort

alit

y ra

te

current HCR

alternative HCR

Figure 1. The current harvest control rule (dashed line) and that of {1,3}with an assumption of the low variable fishing costs. The coalition appliesan optimal HRC (F 0.97, Bpa 0.81 million tonnes). The partial coalition{1,3} is not stable (Table 4).

2005 2010 2015 2020 20250

1

2

3

4

5

6

7

8

9x 108

Time (year)

Yie

ld (

kg)

Figure 2. Harvest of {1,3}{2} with an assumption of the low variable fishingcosts. The coalition (solid line) applies an optimal HRC (F 0.97, Bpa 0.81million tonnes) and the outside player (dashed line) uses an optimal fixedfishing mortality rate (F 0.45). The partial coalition {1,3} is not stable(Table 4).

114 Rahikainen et al.

Table 8. The trigger reference points for the optimal harvestcontrol rule under the three cost scenarios.

The relative fishing costs

Reference point identical high low Current HCR

F 0.27 0.27 0.31 0.25SSBpa 2.23 2.23 1.94 1.30

The GM is not stable if fishing costs are identical among countries.

abundance irrespective of the cost scenario. The biomass trigger point is, infact, estimated to be considerably higher than the current SSBpa while F isreasonably close to the fishing mortality rate applied by the present harvestcontrol rule (Table 8).

Discussion

We analysed consequences of a harvest control rule on the dynamics ofinternational fisheries negotiations. Indicating the key obstacles to stablemultinational arrangements is a key issue in international risk management.In some cases risks may increase cooperation and in some cases decreaseit. In fisheries economics, game theory is a common tool for analysing thestrategic interactions among countries. The main point is that all countriesshould be better off by cooperating, i.e., by complying with the agreement,than non-cooperating. The trigger points of a harvest control rule can beregarded as strategic bioeconomic reference points. Non-cooperative Nashequilibria were compared to the partial (subcoalition) and full cooperative(grand coalition) outcomes. The shares that each country will receive weredetermined by cooperative solution concept (Shapley value). We solved thereaction functions of the involved countries to find the optimal harvestingstrategy of a country as a function of the strategies of other countries fishingthe same stock.

The simulations for the North Sea herring stock indicate that usingprecautionary bioeconomic harvesting strategies clearly promotes stabil-ity of international fishery agreements. Stability of agreements implies

Stability of International Fisheries Agreements 115

cooperation of all countries in the grand coalition which also increasesprofits of the fishery. Besides the management approach, the stability ofagreements depends also on harvesting costs. The grand coalition is neverstable — regardless of the management approach — if fishing costs areidentical among countries (Table 6). In this case, there will be motivationfor free riding as at least one of the countries will have incentives not tosign in the agreement or to sign out from the grand coalition. Heterogeneityin the fishing costs is therefore necessary for the stability of internationalagreements. The phenomenon was proved by Pintassilgo et al. (2010). Weobserved that a moderate 10–30% cost difference among countries is enoughto induce the stability, provided that a precautionary harvest control ruleis adapted. A harvest control rule is more likely to stabilize multilateralfishing agreements if fishing costs are low on the applied relative scalecompared to high costs. Overall, acceptance of the precautionary approachas the baseline of management will induce stability of the grand coalitionand markedly increased profits as well (Tables 4 and 6).

These findings are in line with a recent article by Pintassilgo et al. (2010)where the stability and success of fisheries coalitions under different lev-els of fishing cost asymmetry was analyzed. They conclude that the suc-cess of coalition formation is positively correlated with the cost asymmetryamong fishing states. The explanation suggests that the gains of cooperationincrease in concert with the cost asymmetries (Weikart, 2005; Pintassilgoet al., 2010). These findings are supported by our study. Pintassilgo et al.(2010) conclude also that the higher the overall efficiency of the fishingstates, the lower is the probability of success of coalition formation. We didnot observe this tendency, but this deviance in the result is likely a productof chance alone as Pintassilgo et al. (2010) report probabilities. In addi-tion, the set up of these two studies are not completely comparable. Forexample, the applied production functions (age-structured population modelusing Ricker stock–recruitment function versus classical Gordon–Schaefermodel), and the treatment of fishing costs (multiplier ϕ versus inverse effi-ciency parameter b (Masterton, 1993)) are obvious differences. The differentapproaches (coalition game theory versus partition function approach) alsomay be the cause for deviations in the results.

Also the profits of the partial and grand coalitions are impacted by themanagement approach. Change in the profits of cooperation is the driv-ing force of coalitional stability. As predicted by the theory (Pintassilgo,2003), a grand coalition is always more profitable than any partial coalition

116 Rahikainen et al.

or singletons. Applying the precautionary approach by the grand coalitionthrough a harvest control rule adds net present value of the fishery com-pared to the fixed fishing mortality rate strategy. The fixed fishing mortalityrate is inelastic by definition, while the harvest control rule allows annualchanges in the fishing mortality rate — determined by trigger referencepoints — according to changes in biomass allowing more elasticity in theharvest rate.

The biological benefits of a precautionary threshold strategy have beenconfirmed earlier (Enberg, 2005) but our results support using these strate-gies also on economic grounds. This result is significant for two reasons.First, the fixed F strategy has a reputation of performing reasonably wellthrough large fluctuations in life history parameters and equilibrium abun-dance (Clark, 1991). A precautionary threshold strategy now seems to bean useful alternative to a fixed exploitation rate strategy. Secondly, fisheriesindustry often blames precautionary harvest strategies as causing severe neg-ative economic impact on their business. Our result falsifies that argumentand proves that a precautionary approach can be a profitable long termmanagement strategy.

An earlier study (Kaitala et al., 2003), considering a sole owner case,suggests that an increase in the threshold value (Bpa) in the proportionalthreshold strategy will increase the variability in the yield. This patternreverses when competition is present. Now, the lower the threshold, thehigher is variability in the catches (Figure 2).

A partial coalition applying a precautionary harvest control rule will suffera substantial economic loss, ranging 79–169 million NPV during the simu-lation period, if the outside player applies a fixed exploitation rate strategy.The losses will be largest when costs are low. Therefore, a partial coalitionwould be better off by switching to a fixed F strategy as well. Also theoutside player will be negatively impacted if the partial coalition applies aharvest control rule, but losses are considerably smaller. The total loss ofsuch behavior ranges between 89 and 244 million . In the relative terms,the total profits are 16–43% lower compared to a case where also the partialcoalition applies fixed F strategy.

The North Sea herring fishery has served as a case study to compile abiological production model, and as a source of fishing cost information toparameterize a bioeconomic game model. The major difference between the

Stability of International Fisheries Agreements 117

analysis and the actual North Sea herring fishery is the fact that the fisheryis cooperatively managed by the EU and Norway. The agreed managementstrategy is based on proportional threshold strategy and the agreement hasbeen in force since 1997 (Patterson et al., 1997). The fact that the agreementhas been in force about 15 years indirectly supports the main finding of thisstudy: a precautionary harvest control rule has potential to stabilize multi-lateral fishing agreements. Moreover, it suggests that fishing costs betweenNorway and the EU are not identical. Unfortunately, we failed to acquireinformation about the costs of the EU fleets.

The constraint on change in a TAC that is no more than 15% greateror 15% less than the TAC of the preceding year, which is included in thecurrent harvest control rule for the North Sea herring, is omitted from theanalysis because our primary aim is to evaluate the influence of precaution-ary (bioeconomic) reference points on stability of fishery agreements. Whenboth the quota increase and decrease per year are severely limited, the opti-mum average quota is somewhat reduced. Optimally, the quota should bedecreased or increased as rapidly as possible (Walters and Martell, 2004).The 15% constraint is instead closely linked to practical management pro-cedure about how to adjust TAC according to the scientific advice (STECF,2008) and avoiding abrupt changes in the catch quotas. However, the con-straint of maximum change in the consecutive TACs obviously influences theoptimal bioeconomic reference points. For instance, the pattern in catchesof a partial coalition (Figure 2) would have been impossible.

Many of the biological reference points essentially rely on a reliablestock–recruitment function. For various fish stocks, including the North Seaherring (ICES, 2009), derived stock–recruitment scatterplots are uninfor-mative (noisy). We apply deterministic stock-recruitment function whichlargely drives the stock dynamics in the simulations, especially the recoveryof the stock. Currently there are hypotheses put forward about a regimeshift in the recruitment, and uncertainty about recruitment process has notbeen considered in our analysis (ICES, 2006). In such cases, alternative cri-teria or information sources may be considered to determine threshold ofsustainable harvesting. For instance, spawning per recruit (SPR) analysishas received some attention in establishing thresholds for recruitment over-fishing (Sissenwine and Shepherd, 1987; Mace and Sissenwine, 1993; Caddyand Mahon, 1995).

118 Rahikainen et al.

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