Skip to main content
SpringerLink
Log in

Sharing a Fish Stock When Distribution and Harvest Costs are Density Dependent

  • Published:
Environmental and Resource Economics Aims and scope Submit manuscript

Abstract

We studied cooperative and competitive solutions for managing a trans-boundary fish stock that has a stock-size dependent distribution and harvesting costs, using Norwegian spring-spawning (NSS) herring (Clupea harengus) as a case study. This is among the first studies to investigate the effect of a dynamic distribution in a partition function game framework, i.e., including externalities. The special feature of NSS herring is that it comes under the sole ownership of Norway when the stock size is sufficiently low. The three players in our game are differentiated by stock ownership, cost per unit effort and stock elasticity of harvest. We find that cost asymmetry improves the likelihood of forming a stable grand coalition as harvesting load can be assigned to each fishing zone according to a player’s relative cost level and the density of fish. A dynamic distribution increases the bargaining power of Norway because of her ability to control both the total stock and the stock shares in different zones, especially during the stock transition years. However, the bargaining power of Norway may disappear if her cost of harvesting exceeds that of the other players. This loss of bargaining power can take on two forms: first, a dynamic distribution may encourage a minor player to free ride because Norway, needing a coalition partner to improve her cost-effectiveness, would be less inclined to retaliate as retaliation hurts her ally as much as the free-rider; second, in a stable grand coalition, Norway is not guaranteed to receive an allocation of benefit shares in proportion to (not to say in excess of) her stock ownership. At the current stock condition, the strategy where Norway reduces stock abundance below the level where the stock becomes non-migratory is found attractive only if the discounting rate is sufficiently high.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Notes

  1. Shares of the herring quotas allocated to Norway, EU, Faroes, Island and Russia are 61, 6, 5, 15, and 13 %, respectively.

  2. We allow fishermen to fish until the last fish of the fishable stock is taken. In Steinshamn’s model (2011), fishermen stop fishing when the first age class in the fishable stock becomes exhausted, even if other age classes are still present.

  3. The fishable stock abundance, \(N_{j,t}^{tot}\), is the total stock abundance summing over all age classes with positive selectivity, i.e., \(s_i>0\).

  4. This treatment is different from Steinshamn (2011) where he assumed \(\tau _{j,t}^e=\min _{i}(\tau _{i,j,t})\); i.e., the seasonal fishing length is determined by the age class that is exhausted first.

  5. This classic definition has been challenged for being ‘myopic’ (de Zeeuw 2008), because it assumes that the rest of the coalition stays intact after one player deviates. Solving far-sighted equilibrium requires a different set-up, e.g., in a repeated game. For our one-shot game, the classic definition of the stability still suits the best.

  6. We set \(c_1=2\), but its exact value is not important, the value is calibrated to a level under which fishing is generally profitable.

  7. The boundary where fishing ceases under this circumstance is not drawn in the figure.

  8. This would not be possible when \(c_2/c_1>1\), under which Norway becomes a dominant exploiter (see Example b in Table 2 for a proof).

  9. The total biomass during the transition years can sometimes go below \(B_{low}\), the low biomass threshold defined in Eq. 1.

References

  • Arnason R, Magnusson G, Agnarsson S (2000) The Norwegian spring-spawning herring fishery: a stylized game model. Mar Resour Econ 15:293–319

    Article  Google Scholar 

  • Bailey M, Sumaila UR, Lindroos M (2010) Application of game theory to fisheries over three decades. Fish Res 102:1–8

    Article  Google Scholar 

  • Bjørndal T (1987) Production economics and optimal stock size in a North Atlantic fishery. Scand J Econ 89(2):145–164

    Article  Google Scholar 

  • Bjørndal T (1988) The optimal management of North Sea herring. J Environ Econ Manag 15:9–29

    Article  Google Scholar 

  • Bjørndal T, Gordon DV, Kaitala V, Lindroos M (2004) International management strategies for a straddling fish stock: a bio-economic simulation model of the Norwegian spring-spawning herring fishery. Environ Resour Econ 29:435–457

    Article  Google Scholar 

  • Brown JS, Vincent TL (1987) Coevolution as an evolutionary game. Evolution 41:66–79

    Article  Google Scholar 

  • Clark CW (1990) Mathematical bioeconomics: the optimal management of renewable resources, 2nd edn. Wiley, New York

    Google Scholar 

  • D’Aspremont C, Jacquemin A, Gabszewicz JJ, Weymark JA (1983) On the stability of collusive price leadship. Can J Econ 16(1):17–25

    Article  Google Scholar 

  • De Clippel G, Serrano R (2008) Marginal contributions and externalities in the value. Econometrica 76(6):1413–1436

    Article  Google Scholar 

  • de Zeeuw A (2008) Dynamic effects on the stability of international environmental agreements. J Environ Econ Manag 55:163–174

    Article  Google Scholar 

  • Dieckmann U, Law R (1996) The dynamical theory of coevolution: a derivation from stochastic ecological processes. J Math Biol 34:579–612

    Article  Google Scholar 

  • Dragesund O, Johannessen A, Ulltang Ø (1997) Variation in migration and abundance of Norwegian spring spawning herring (Clupea harengus L.). Sarsia 82:97–105

    Google Scholar 

  • Ekerhovd NA (2010) The stability and resilience of management agreements on climate-sensitive straddling fishery resources: the blue whiting (Micromesistius poutassou) coastal state agreement. Can J Fish Aquat Sci 67:534–552

    Article  Google Scholar 

  • Eyckmans J, Finus M (2004) An almost ideal sharing scheme for coalition games with externalities. Working paper no. 155.2004, Fondazione Eni Enrico Mattei, Italy. Version presented at the 7th meeting on game theory and practice dedicated to energy, environment and natural resources, May 2007, Montreal, Canada

  • Fuentes-Albero C, Rubio SJ (2010) Can international environmental cooperation be bought? Eur J Oper Res 202:255–264

    Article  Google Scholar 

  • Greenberg J (1994) Coalition structures. In: Aumann R, Hart S (eds) Handbook of game theory with applications, vol 2. North Holland, Amsterdam, pp 1305–1337

    Chapter  Google Scholar 

  • Hannesson R (2006) Sharing the herring: fish migrations, strategic advantage and climate change. In: Hannesson R (ed) Climate change and the economics of the world’s fisheries: examples of small pelagic stocks. Edward Elgar Publishing, Northampton, pp 66–99

    Chapter  Google Scholar 

  • Hannesson R (2007) Global warming and fish migrations. Nat Res Model 20:301–319

    Article  Google Scholar 

  • Hannesson R (2011) Game theory and fisheries. Annu Rev Resour Econ 3:181–202

    Article  Google Scholar 

  • Hannesson R (2013) Sharing the Northeast Atlantic mackerel. ICES J Mar Sci 70:259–269

    Article  Google Scholar 

  • Harley SJ, Myers RA, Dunn A (2001) Is catch-per-unit-effort proportional to abundance? Can J Fish Aquat Sci 58:1760–1772

    Article  Google Scholar 

  • Hilborn R, Walters CJ (1992) Quantitative fisheries stock assessment: choice, dynamics and uncertainty. Chapman and Hall, New York

    Book  Google Scholar 

  • Holst JC, Røttingen I, Melle W (2004) The herring. In: Skjoldal HR (ed) The Norwegian sea ecosystem. Tapir Academic Press, Trondheim, pp 203–226

    Google Scholar 

  • ICES (2010) Report of the working group on widely distributed stocks (WGWIDE), 28 August–3 September 2010, Vigo, Spain. ICES CM 2010/ACOM:15, ICES, Copenhagen

  • ICES (2013) Report of the working group on widely distributed stocks (WGWIDE). 27 Aug–2 Sept 2013. ICES Headquarters, Copenhagen, Denmark. ICES CM 2013/ACCOM: 15

  • Johnson JE, Welch DJ (2010) Marine fisheries management in a changing climate: a review of vulnerability and future options. Rev Fish Sci 18:106–124

    Article  Google Scholar 

  • Kaitala V, Lindroos M (2004) When to ratify an environmental agreement: the case of high seas fisheries. Int Game Theory Rev 6:55–68

    Article  Google Scholar 

  • Kronbak LG, Lindroos M (2007) Sharing rules and stability in coalition games with externalities. Mar Resour Econ 22:137–154

    Article  Google Scholar 

  • Lindroos M (2004) Sharing the benefits of cooperation in the Norwegian spring-spawning herring fishery. Int Game Theory Rev 6:35–53

    Article  Google Scholar 

  • Lindroos M, Kaitala V (2000) Nash equilibria in a coalition game of the Norwegian spring-spawning herring fishery. Mar Resour Econ 15:321–339

    Article  Google Scholar 

  • Liu X, Heino M (2013) Comparing proactive and reactive management: managing a transboundary fish stock under changing environment. Nat Res Model 26:480–504

    Article  Google Scholar 

  • Liu X, Heino M (2014) Overlooked biological and economic implications of within-season fishery dynamics. Can J Fish Aquat Sci 71:181–188

    Article  Google Scholar 

  • Macho-Stadler I, Perez-Castrillo D, Wettstein D (2007) Sharing the surplus: an extension of the Shapley value for environments with externalities. J Econ Theory 135:339–356

    Article  Google Scholar 

  • Mantua NJ, Hare SR, Zhang Y et al (1997) A pacific interdecadal climate oscillation with impacts on Salmon production. Bull Am Meteorol Soc 78(6):1069–1079

    Article  Google Scholar 

  • McGinty M (2007) International environmental agreements among asymmetric nations. Oxf Econ Pap 59:45–62

  • Miller KA, Munro GR (2004) Climate and cooperation: a new perspective on the management of shared fish stocks. Mar Resour Econ 19:367–393

    Article  Google Scholar 

  • Norwegian Ministry of Fisheries and Coastal Affairs (2013) Firepartsavtale om forvaltning av norsk vårgytende sild. Press release 3/2013: http://www.regjeringen.no

  • Patterson K (1998) Biological modelling of the Norwegian spring-spawning herring stock. Fisheries Research Services, Report 1/98, Aberdeen

  • Perry AL, Low PJ, Ellis JR, Reynolds JD (2005) Climate change and distribution shifts in marine fishes. Science 308:1912–1915

    Article  Google Scholar 

  • Pham Do KH, Norde H (2007) The Shapley value for partition function form games. Int Game Theory Rev 9(2):353–360

    Article  Google Scholar 

  • Pintassilgo P, Finus M, Lindroos M (2010) Stability and success of regional fisheries management organizations. Environ Resour Econ 46:377–402

    Article  Google Scholar 

  • Planque B, Loots C, Petitgas P, Lindstr øm U, Vaz S (2011) Understanding what controls the spatial distribution of fish populations using a multi-model approach. Fish Oceanogr 20:1–17

    Article  Google Scholar 

  • Sandberg MG, Olafsen T (2006) Kartlegging av kompetansebehov i norsk fiskeri-og havbruksnæring. SINTEF, Trondheim

    Google Scholar 

  • Shapley LS (1953) A value for \(n\)-person games. In: Roth A (ed) The Shapley value—essays in honor of Lloyd S. Shapley. Cambridge University Press, Cambridge, pp 31–40

    Google Scholar 

  • Sissener EH, Bjørndal T (2005) Climate change and the migratory pattern for Norwegian spring-spawning herring-implications for management. Mar Policy 29:299–309

    Article  Google Scholar 

  • Sønvisen SA (2013) Recruitment to the Norwegian fishing fleet: storylines, paradoxes, and pragmatism in Norwegian fisheries and recruitment policy. Marit Stud 12:8

    Article  Google Scholar 

  • Steinshamn SI (2011) A conceptional analysis of dynamics and production in bioeconomic models. Am J Agric Econ 93:803–812

    Article  Google Scholar 

  • Thrall R, Lucas W (1963) N-person games in partition function form. Nav Res Logist Quart 10:281–298

    Article  Google Scholar 

  • Toresen R, Østvedt OJ (2000) Variation in abundance of Norwegian spring-spawning herring (Clupea harengus, Clupeidae) throughout the 20th century and the influence of climatic fluctuations. Fish Fish 1:231–256

    Article  Google Scholar 

  • Touzeau S, Lindroos M, Kaitala V, Ylikarjula J (2000) Economic and biological risk analysis of the Norwegian spring-spawning herring fishery. Ann Oper Res 94:197–217

    Article  Google Scholar 

  • Varpe Ø, Fiksen Ø (2010) Seasonal plankton-fish interactions: light regime, prey phenology, and herring foraging. Ecology 91:311–318

    Article  Google Scholar 

  • Yi S-S, Shin H (2000) Endogenous formation of research coalitions with spillovers. Int J Ind Organ 18:229–256

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre for Applied Research, Norwegian School of Economics, Helleveien 30, 5045, Bergen, Norway

    Xiaozi Liu

  2. Department of Economics and Management, University of Helsinki, P.O. Box 27, 00014, Helsinki, Finland

    Marko Lindroos

  3. Department of Business and Management Science, Norwegian School of Economics, Helleveien 30, 5045, Bergen, Norway

    Leif Sandal

Authors
  1. Xiaozi Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marko Lindroos
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Leif Sandal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiaozi Liu.

Additional information

We would like to thank Mikko Heino, Stein Ivar Steinshamn, Rögnvaldur Hannesson, and Sturla F. Kvamsdal for their input and comments and Vivienne B. Knowles and Leslie Tse for language editing. We wish to thank all three anonymous referees for their constructive comments. Liu acknowledges the financial support from the Nordic network on ‘Climate impacts on fish, fishery industry and management in the Nordic seas’. Lindroos acknowledges funding from Academy of Finland AKVA programme’s project ‘Economics of Aquatic Foodwebs’.

Appendix

Appendix

See Tables 4, 5 and 6.

Table 4 Age-specific parameters
Full size table
Table 5 Notational summary
Full size table
Table 6 Age-unspecific parameters
Full size table

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, X., Lindroos, M. & Sandal, L. Sharing a Fish Stock When Distribution and Harvest Costs are Density Dependent. Environ Resource Econ 63, 665–686 (2016). https://doi.org/10.1007/s10640-014-9858-9

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10640-014-9858-9

Keywords

JEL Classification

Search

Navigation