Acta Biotheoretica

, Volume 62, Issue 3, pp 325–338 | Cite as

Fishermen’s Profits Maximization: Case of Generalized Nash Equilibrium of a Non-symmetrical Game

Regular Article

Abstract

In the present paper, we consider a bio-economic equilibrium model which describes the dynamics of a fish population fished by several fishermen seeking to maximize their profits. Each fisherman tries to find the fishing effort which maximizes his profit at biological equilibrium without any consultation with others, but all of them have to respect two constraints: (1) the sustainable management of the resources ; and (2) the preservation of the biodiversity. With all these considerations, our problem leads to a generalized Nash equilibrium problem. The objective is to show that even when a fisherman \(i\) provides a fishing effort equal to twice the fishing effort of a fisherman \(j\), then the profit of fisherman \(i\) is not necessarily double that of fisherman \(j\).

Keywords

Population dynamics Bio-economic equilibrium model Generalized nash equilibrium Sustainable management of the resources Preservation of the biodiversity Fisherman’s profit maximization 

References

  1. Bulte EH (2003) Open access harvesting of wildlife: the poaching pit and conservation of endangered species. Agric Econ 28:27–37CrossRefGoogle Scholar
  2. Clark WC (1990) Mathematical bioeconomics: the optimal management of renewable resources, 2nd edn. A Wiley-Interscience, New YorkGoogle Scholar
  3. Cottle RW, Dantzig GB (2006) A life in mathematical programming. Math Program 105:1–8CrossRefGoogle Scholar
  4. Cottle RW, Pang JS, Stone RE (1992) The linear complementarity problem. Academic Press, New YorkGoogle Scholar
  5. El Foutayeni Y, Khaladi M (2010) A new interior point method for linear complementarity problem. Appl Math Sci 4:3289–3306Google Scholar
  6. El Foutayeni Y, Khaladi M (2012a) Using vector divisions in solving the linear complementarity problem. J Comput Appl Math 236:1919–1925CrossRefGoogle Scholar
  7. El Foutayeni Y, Khaladi M, Zegzouti A (2012b) A generalized Nash equilibrium for a bioeconomic problem of fishing. Stud Inform Univ HERMANN 10:186–204Google Scholar
  8. El Foutayeni Y, Khaladi M (2012c) A generalized bio-economic model for competing multiple-fish populations where prices depend on harvest. J Adv Model Optim 14:531–542Google Scholar
  9. El Foutayeni Y, Khaladi M (2013) General characterization of a linear complementarity problem. Am J Mod Optim 1:1–5Google Scholar
  10. Lemke CE (1965) Bimatrix equilibrium points and mathematical programming. Manage Sci 11:681–689Google Scholar
  11. Merinoa G, Maynou F, García-Olivares A (2007) A new bioeconomic simulation tool for small scale fisheries based on game theory: GAMEFISTO model. Aquat Living Resour 20:223–230CrossRefGoogle Scholar
  12. Murty KG (1971) On a characterization of P-matrices. SIAM J Appl Math 20:378–383CrossRefGoogle Scholar
  13. Purohit D, Chaudhuri KS (2007) Nonselective harvesting of two competing fish species: a dynamic reaction model. Int J Comput Appl Math 2:191–208Google Scholar
  14. Smith VL (1969) On models of commercial fishing. J Polit Econ 77:181–198CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Analysis, Modeling and Simulation Laboratory LAMSHassan II UniversityCasablancaMorocco
  2. 2.Mathematical Populations Dynamics Laboratory LMDPCadi Ayyad UniversityMarrakechMorocco
  3. 3.UMI UMMISCO, IRD - UPMCParisFrance

Personalised recommendations