Stability of International Fisheries Agreements Using Precautionary Bioeconomic Harvesting Strategies^*

Herring stocks have contributed economic wealth in the past as well in the present days. Since the 1950s herring fisheries have expanded to a level at which they have a major impact on the harvested stocks revealing that clupeoid populations have a general tendency to collapse under heavy fishing pressure (Murphy, 1977; Saville, 1980; Hay et al., 2001). Obviously, stock collapse creates social, political, and ecological problems and dissipates large amounts of economic rent (Garcia and de Leiva Moreno, 2003). Excessive fishing pressure on any stock may result from the practice of ignoring or underestimating uncertainty in stock assessment and fisheries management (Hilborn and Walters, 1992; Walters and Maguire, 1996; Hildén, 1997) or from 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 established to reduce the undesirable effects due to common property exploitation. Since the sovereignty of states precludes external enforcement, international environmental agreements must be self-enforcing. The UN has provided a platform to develop and agree upon international treaty laws such as the Extended Fisheries Jurisdiction (EFJ) with introduction of 200-mile exclusive economic zones (EEZs) in 1977 (UN, 1982). The EEZ do not completely resolve the problem of open access to harvesting of the resources because many fish resources migrate or are spread across national boundaries and international waters (Kaitala and Munro, 1997). Cooperation in the framework of bi- and multilateral agreements is therefore necessary to solve management problems by assigning property rights to international fish stocks or by regulating fisheries by other means such as national quotas, technical restrictions, spatial or temporal closures. Game theoretical models explain why full cooperation may fail as environmental externalities impact negotiations in international politics (Wagner, 2001). Coalition game theory has been applied in real world fisheries to analyze the expected benefits of cooperation among the fishing countries and to predict the possibilities of reaching stable agreements among them (Arnason et al., 2001; Brasão et al., 2000; Lindroos and Kaitala, 2000; Pintassilgo, 2003; Lindroos, 2004).

In addition to the lack of jurisdiction and property rights, assessment and management failures have also contributed to the inefficient use of marine resources globally. The apparent decline of fisheries has catalyzed more risk averse harvesting policies and management goals (FAO, 1995). Consequently, a concept of precautionary approach (PA) has been launched to promote prudent management and to decrease probability of recruitment overfishing and subsequent stock collapse (FAO, 1995, 1996, 1997). Biological reference points (BRPs) are used as signposts in implementing the precautionary approach and pragmatic fisheries management has been based on a variety of them. The rules to calculate biological reference points are typically based on the perception of risk of stock collapse or of "safe" harvest level (ICES, 2001). Biological reference points are usually expressed as fishing mortality rates (e.g., $Fmed ,Fx%SPR,F0.1,Fmsy$ ) or as critical levels of spawning or recruited biomass (e.g., $Bloss ,Bmbal ,B20% b− virg$ ) (Maguire and Mace, 1993; ICES 1997, 2001). The precautionary levels of mortality and spawning biomass ( $Fpa,Bpa$ ) are usually developed from the estimated overfishing thresholds ( $Flim ,Blim$ ).

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

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

We consider autumn-spawning North Sea herring stock in the ICES subarea IV, division VIId, and division IIIa (autumn spawners). The stock has undergone two major declines in the 1970s and the 1990s (Bjørndal, 1988; Bjørndal and Lindroos, 2004; Simmonds, 2007). The second period of decline resulted in an EU/Norway agreement on management actions. Subsequently, due to stricter regulations, the stock increased to an estimated level of 3.6 million tonnes in 2001 (Bjørndal and Lindroos, 2004). Since the second collapse in the mid-1990s the spawning stock biomass (SSB) has increased from 0.5 million tonnes to 1.8 million tonnes. The lowest estimated SSB was only 0.05 million tonnes in 1977. Catch has varied within the range $0.25−0.70$ million 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 proportional threshold strategy using a limit and a trigger reference point (ICES Advice, 2006). According to the EU-Norway agreement on management of North Sea "Every effort shall be made to maintain a level of spawning stock biomass (SSB) greater than the 0.8 million tonnes ( $Blim$ )." If the SSB is estimated to be below 0.8 million tonnes, the quotas are set to reflect a fishing mortality rate of less than 0.10 for 2 ringers (read: age group) and older and less than 0.04 for $0−1$ ringers. Consequently, the HCR does not impose a moratorium if SSB falls below the $Blim$⁠. When spawning stock biomass is estimated 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 a fishing mortality rate equal to:

which defines the proportional threshold strategy and subscripts refer to age groups.

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 situation where the SSB is above 1.3 million tonnes. Moreover, the current agreement has 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 reduction in TAC if necessary (ICES, 2009). The current harvest control rule is limiting fishing mortality of 0-1 ringers to about $50%$ of fishing mortality of 2-ringers and older. It is enforced by a by-catch ceiling of the industrial fishery. The catch of the industrial fishery has been about $50%$ of that allowed for the last 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 $29%$ to Norway and $71%$ to the Community. Bjørndal and Lindroos (2004) have analyzed the optimal sharing rule of the North Sea herring quota and concluded that according to the Nash bargaining solution, the current sharing allocates 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 harvesting for human consumption and typically containing refrigerated sea water tanks.

3. The Norwegian fleet being a mixture of trawlers and purse seiners catching 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 fishing costs among segments. Those attributes are partly clustered according to national ownership of the vessels. Therefore, identical fishing cost among the countries participating in the North Sea herring fishery should not be anticipated.

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

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

where $R$ is recruitment to the stock and SSB is spawning stock biomass in year $y$⁠, and $α$ and $β$ are parameters having values 60.89 (unit: numbers $10∧9$ ) and 0.456 (unit: million tonnes), respectively.

All parameter values for life history are adopted from the ICES working group report (ICES, 2006). The number of fish of each age class is assumed to be known in the beginning of 2006 (Table 1), which is the initialization year for the analysis. The age-classes are then subject to natural and fishing 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 $a$⁠. Selectivity $Sa$ is estimated using the average fishing mortality profile at age during 1996-2005. Herring are partially recruited at ages 0-3 and are assumed fully recruited at ages 4+.

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

where $waS$ 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 the population abundance at the beginning of the year, total mortality between the beginning of the year and the spawning period, and by the maturation schedule mo:

where $waSSB$ 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 partially mature, and older component is fully mature (Table 1). Population dynamics are simulated for 20 years period in 2006-2025.

We apply a constant unit price of herring/kg and a linear cost function for exercised fishing mortality. Data of the Norwegian purse seine herring fishery is applied to derive the cost function. The variable costs associated with the North Sea herring fishery are estimates built on the assumption that the vessels spend 60 days a year harvesting NS herring (Nøstbakken, 2006 , pers. comm.). The purse seiners typically account for approximately $85%$ of the Norwegian landings of North Sea herring. The annual variable costs of the Norwegian purse seine fleet targeting on herring (Nøstbakken, 2006) were related with fishing mortality rate contrived by the Norwegian fleet annually in 1996-2000. The fishing mortality rate of the Norwegian fleet ( $FyN$ ) in year $y$ was estimated by:

where $Fy$ denotes the overall fishing mortality rate, $Yy$ total catch, and $YyN$ Norwegian catch in year $y$ (ICES, 2006). Effectively, this implies that the estimated Norwegian fleet's fishing mortality rate ( $FyN$ ) is that of the fishing mortality rate of the entire Norwegian fleet, which we assume are solely purse seiners.

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

where $φi$ is a scaling term, and $θ$ is a parameter (Table 2). Fishing costs likely differ among countries though published information is lacking. The differences are expected due to varying vessel attributes, crew shares, and dissimilar distances to the fishing grounds. We apply a scaling term, $φi$⁠, to characterize differences in the fishing costs among countries (Table 3). The actual values of the scaling term are arbitrary but describe two possible scenarios, minor and substantial cost asymmetry in the fishery. The cost per unit of instantaneous fishing mortality is applied instead of the conventional

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

The actual number of vessels in each country is unknown and is excluded from the analysis framework. It is implicitly assumed that vessels are identical with respect to variable fishing costs within a national fleet. The impact of relaxing the assumption of identical costs among countries is tested by scaling the costs by the term $φ$⁠. It is thus assumed that all economic differences 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 harvesting the North Sea herring stock form countries 2 and 3. These countries are United Kingdom, the Netherlands, Denmark, Germany, Sweden, Belgium, and France. Because of lacking data of the national fleet sizes and fishing cost, it is neither necessary nor helpful to assign any particular EU nation as country 2 or country 3 .

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

where $WaC$ is mean weight in catch at age $a$⁠.

The total annual harvest is the sum of national harvest:

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

s.t. (1-9) and s.t. $Fy≥0.1$⁠. Here, $p$ is the unit price per $kg,r$ is discount rate, $ρy=(1+r)y−y1$ is the discount factor, $Fˆ$ is the upper limit of the fishing mortality, and $Bpa$ is precautionary spawning stock biomass. Term $y$ denotes the index for year with $y1$ being the base year. According to the current harvest control rule coalitions engage in harvesting activities every year, even if it was not profitable for them. The rationale is that even if there were losses in some years, the exit from the fishery is a slow process which will not occur due to losses in one year. Year-to-year change in a TAC is not limited to $15%$ of the TAC in the previous year.

We specify three games to allow comparisons between the two management approaches, a fixed fishing mortality rate and a harvest control rule strategies. In the first version of the game the decision variable of the players is simply the players' fishing mortality, $Fi$⁠. The values of the coalitions in the game can be defined as follows

GAME 1

s.t. (1-9) for singletons

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

s.t. (1-9) for the grand coalition (GM).

In the second version, we assume that the grand coalition applies a harvest control rule while two player coalitions and singletons only adjust their fishing mortality rate. It this case the revenue of the grand coalition is given as

GAME 2

s.t. (1-9), where $Fˆ$ is the maximum fishing mortality and $Bpa$ is precautionary spawning biomass.

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

GAME 3

s.t. (1-9), where $Wi$ is the value of a single-player coalition as in game 1 , and $Wi,j$ is the value of a two-player coalition. The value of grand coalition $WM$ contains all cooperatively acting players as in game 2. Singletons cannot gain by adopting a conservative strategy (Pintassilgo, 2001), and the characteristic functions imply singletons optimizing a fixed fishing mortality rate without implementing a harvest control rule. The grand coalition can either 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 to each player until the decision variables converged. Three to four iterations were enough to find the solution.

The Shapley (1953) value measures the marginal contributions (averaged sums) of countries to each coalition. It is a single point solution with intuitive interpretations: each player is treated equally, and all benefits are shared among players. The Shapley value expresses the sum of dividends that each coalition pays to its members. The most effective country would harvest as a sole owner and give away the rest to the two other players. The Shapley values are:

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

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

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

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

where $Wi$ is the free-rider value for country $i$⁠. The stability conditions state that there should be enough cooperative benefits to be shared in order to make staying in the full cooperative mode optimal. If the sum of free-rider values $Wi$ of the countries is smaller than the value of the grand coalition $M$ then the grand coalition is stable.

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

The results identify that the grand coalition is always more profitable than any partial coalition or singletons (Table 4). If the grand coalition applies a harvest control rule, it adds about $2%$ to the net present value when a fixed fishing mortality rate strategy is the benchmark case. Importantly, applying the precautionary approach through the biomass trigger point and the fishing mortality rate ceiling adds NPV, at least when the reference points are optimal.

The range of the total cooperative benefits is $714−850$ million $€$ depending on the fishing cost scenario and the harvesting strategy (Table 4). The identical and high fishing cost scenarios yield equal total cooperative benefits because only the most effective country of the coalition would harvest as a 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

larger total benefits. The Shapley values indicate a justified share of the total cooperative benefits for all members of the grand coalition (Table 5). Each country will naturally receive an equal share of the benefits if fishing costs are identical among countries, regardless of whether the partial coalitions apply or not a harvest control rule. The shares change when costs are not identical and are impacted also by the applied management strategy. Applying a harvest control rule has a slight tendency to equalise the Shapley values 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 management approaches. Full cooperation is stable in 4 cases out of total 12 instances (Table 6). This means that only in these cases no single country would benefit from free-riding, that is, by leaving the grand coalition. Stability prevails when all the coalitions apply a harvest control rule and the costs are not identical (Table 6, upper right quarter). On the other hand, rejecting a harvest control rule by all coalition structures pre-empts full cooperation and a multinational fishing agreement is never stable (Table 6, lower left quarter). If fishing costs are identical among countries, there will always be incentive for free riding regardless of the management approach. Under the identical cost scenario, partial coalitions are stable provided that coalitions reject the harvest control rule (Table 4). Full cooperation is stable also in case fishing costs are low and either the grand coalition or a partial coalition applies a harvest control rule (Table 6, upper left quarter and lower right quarter, respectively).

Partial coalitions can be stable assuming that it is possible to switch the management approach between the harvest control rule and a fixed fishing mortality rate strategy. In addition, the cost level impacts stability of partial coalitions. 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 stability of the partial coalitions in this specific case. In this game, country 3 would choose country 1 or 2 and form a coalition, while the outside player would fish as a singleton. If the countries can switch between the two management approaches, the partial coalition will always abandon the harvest control rule and apply the fixed fishing mortality rate strategy. Clearly, it does not pay off for a partial coalition to apply a harvest control rule if the outside player does not adopt it, too. The loss as a net present value of the partial coalition is $82−97$ million $€$ if the unit costs are "identical" or "high". The range of economic losses of the partial coalitions increase if the fishing costs are "low", being 79-167 million $€$ (Table 4). Also the outside player will be negatively impacted if the partial coalition applies the harvest control rule.

The optimal parameter values of the decision variables ( $F,Fˆ,SSBpa$ ) are impacted by the fishing costs, coalition structure, and the management approach. The actual annual fishing mortality rate can have high variability when partial coalitions apply the harvest control rule and singletons apply a fixed $F$ strategy (Table 7). Optimal harvesting under a combination of low fishing costs and a harvest control rule based management approach will lead to very low $SSBpa$ and high $Fˆ$ for the partial coalitions (Table 7). The precautionary element of the harvest control rule will therefore vanish, and the actual spawning stock biomass will approach the minimum acceptable level, $Blim$ (Figure 1). In this particular game, the harvests of the partial coalition will fluctuate between the sporadic high and the dominating low yields. The harvests of the outside player will exhibit considerably less variability due to fixed $F$ strategy (Figure 2). This pattern is caused by the trigger points of the harvest control rule, which let the coalition to exercise high fishing mortality whenever the stock biomass exceeds $SSBpa$⁠. The biomass will, consequently, be harvested below $Blim$ during one time step (year), and fishing mortality rate generated by the partial coalition will stay at the minimum level until "recovery" takes place. The spawning stock biomass in general fluctuates around $Blim$ in case partial coalitions apply a harvest control rule and fishing costs are low. On the contrary, under the same management approach but high fishing cost scenario the spawning stock biomass reaches dynamic stability near the level of $SSBpa$⁠.

Most importantly, the optimal bioeconomic harvest control rule for the grand coalition maintains the precautionary element regarding stock abundance irrespective of the cost scenario. The biomass trigger point is, in fact, estimated to be considerably higher than the current $SSBpa$ while $Fˆ$ is reasonably close to the fishing mortality rate applied by the present harvest control rule (Table 8).

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

The simulations for the North Sea herring stock indicate that using precautionary bioeconomic harvesting strategies clearly promotes stability of international fishery agreements. Stability of agreements implies cooperation of all countries in the grand coalition which also increases profits of the fishery. Besides the management approach, the stability of agreements depends also on harvesting costs. The grand coalition is never stable - regardless of the management approach - if fishing costs are identical among countries (Table 6). In this case, there will be motivation for free riding as at least one of the countries will have incentives not to sign in the agreement or to sign out from the grand coalition. Heterogeneity in the fishing costs is therefore necessary for the stability of international agreements. The phenomenon was proved by Pintassilgo et al. (2010). We observed that a moderate $10−30%$ cost difference among countries is enough to induce the stability, provided that a precautionary harvest control rule is adapted. A harvest control rule is more likely to stabilize multilateral fishing agreements if fishing costs are low on the applied relative scale compared to high costs. Overall, acceptance of the precautionary approach as the baseline of management will induce stability of the grand coalition and 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 levels of fishing cost asymmetry was analyzed. They conclude that the success of coalition formation is positively correlated with the cost asymmetry among fishing states. The explanation suggests that the gains of cooperation increase in concert with the cost asymmetries (Weikart, 2005; Pintassilgo et al., 2010). These findings are supported by our study. Pintassilgo et al. (2010) conclude also that the higher the overall efficiency of the fishing states, the lower is the probability of success of coalition formation. We did not observe this tendency, but this deviance in the result is likely a product of chance alone as Pintassilgo et al. (2010) report probabilities. In addition, the set up of these two studies are not completely comparable. For example, the applied production functions (age-structured population model using Ricker stock-recruitment function versus classical Gordon-Schaefer model), and the treatment of fishing costs (multiplier $φ$ versus inverse efficiency parameter $b$ (Masterton, 1993)) are obvious differences. The different approaches (coalition game theory versus partition function approach) also may be the cause for deviations in the results.

Also the profits of the partial and grand coalitions are impacted by the management approach. Change in the profits of cooperation is the driving force of coalitional stability. As predicted by the theory (Pintassilgo, 2003), a grand coalition is always more profitable than any partial coalition or singletons. Applying the precautionary approach by the grand coalition through a harvest control rule adds net present value of the fishery compared to the fixed fishing mortality rate strategy. The fixed fishing mortality rate is inelastic by definition, while the harvest control rule allows annual changes in the fishing mortality rate - determined by trigger reference points - according to changes in biomass allowing more elasticity in the harvest rate.

The biological benefits of a precautionary threshold strategy have been confirmed earlier (Enberg, 2005) but our results support using these strategies also on economic grounds. This result is significant for two reasons. First, the fixed $F$ strategy has a reputation of performing reasonably well through large fluctuations in life history parameters and equilibrium abundance (Clark, 1991). A precautionary threshold strategy now seems to be an useful alternative to a fixed exploitation rate strategy. Secondly, fisheries industry often blames precautionary harvest strategies as causing severe negative economic impact on their business. Our result falsifies that argument and proves that a precautionary approach can be a profitable long term management strategy.

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

A partial coalition applying a precautionary harvest control rule will suffer a substantial economic loss, ranging 79-169 million $∈$ NPV during the simulation period, if the outside player applies a fixed exploitation rate strategy. The losses will be largest when costs are low. Therefore, a partial coalition would be better off by switching to a fixed $F$ strategy as well. Also the outside player will be negatively impacted if the partial coalition applies a harvest control rule, but losses are considerably smaller. The total loss of such 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 partial coalition applies fixed $F$ strategy.

The North Sea herring fishery has served as a case study to compile a biological production model, and as a source of fishing cost information to parameterize a bioeconomic game model. The major difference between the analysis and the actual North Sea herring fishery is the fact that the fishery is cooperatively managed by the EU and Norway. The agreed management strategy is based on proportional threshold strategy and the agreement has been in force since 1997 (Patterson et al., 1997). The fact that the agreement has been in force about 15 years indirectly supports the main finding of this study: a precautionary harvest control rule has potential to stabilize multilateral fishing agreements. Moreover, it suggests that fishing costs between Norway and the EU are not identical. Unfortunately, we failed to acquire information about the costs of the EU fleets.

The constraint on change in a TAC that is no more than $15%$ greater or $15%$ less than the TAC of the preceding year, which is included in the current harvest control rule for the North Sea herring, is omitted from the analysis because our primary aim is to evaluate the influence of precautionary (bioeconomic) reference points on stability of fishery agreements. When both the quota increase and decrease per year are severely limited, the optimum average quota is somewhat reduced. Optimally, the quota should be decreased or increased as rapidly as possible (Walters and Martell, 2004). The $15%$ constraint is instead closely linked to practical management procedure about how to adjust TAC according to the scientific advice (STECF, 2008) and avoiding abrupt changes in the catch quotas. However, the constraint of maximum change in the consecutive TACs obviously influences the optimal bioeconomic reference points. For instance, the pattern in catches of a partial coalition (Figure 2) would have been impossible.

Many of the biological reference points essentially rely on a reliable stock-recruitment function. For various fish stocks, including the North Sea herring (ICES, 2009), derived stock-recruitment scatterplots are uninformative (noisy). We apply deterministic stock-recruitment function which largely drives the stock dynamics in the simulations, especially the recovery of the stock. Currently there are hypotheses put forward about a regime shift in the recruitment, and uncertainty about recruitment process has not been considered in our analysis (ICES, 2006). In such cases, alternative criteria or information sources may be considered to determine threshold of sustainable harvesting. For instance, spawning per recruit (SPR) analysis has received some attention in establishing thresholds for recruitment overfishing (Sissenwine and Shepherd, 1987; Mace and Sissenwine, 1993; Caddy and Mahon, 1995).