Grazing Games: Sharing Common Property Resources with Complex Dynamics

Environmental and Resource Economics volume 44, pages 29–46 (2009)Cite this article

Abstract

Grasslands used for domestic livestock are often the common property of several owners and are typically characterized by complex ecosystem dynamics. We account for both these aspects by modeling the problem as a differential game where each farmer maximizes profits, given the dynamics of livestock and grass interaction. We compare the first best outcome obtained when farmers cooperate with that for non-cooperative farmers. By accounting for grassland dynamics, we challenge conventional results from the common pool literature. Although we do identify situations where the standard result holds—a tragedy of the commons unless farmers cooperate—we also find examples where a tragedy is exacerbated due to ecosystem dynamics as well as cases where a non-cooperative regime under-exploits the grassland compared to the first best outcome.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

US$ 39.95

Tax calculation will be finalised during checkout.

References

  1. Akiyama T, Kawamura K (2007) Grassland degradation in China: methods of monitoring, management and restoration. Grassl Sci 53: 1–17

    Article  Google Scholar 

  2. Baland J-M, Platteau J-P (1996) Halting degradation of natural resources—is there a role for rural communities. Food and Agriculture Organization of the United Nations, Italy

    Google Scholar 

  3. Bement R (1969) A stocking-rate guide for beef production on blue-gamma range. J Range Manag 22: 83–86

    Article  Google Scholar 

  4. Birkhoff GD (1927) Dynamical systems, volume 9 of Colloquium Publications (1966 edn). American Mathematical Society, USA

    Google Scholar 

  5. Brock WA, Starrett D (2003) Managing systems with non-convex positive feedback. Environ Resour Econ 26(4): 575–602

    Article  Google Scholar 

  6. Brock W, Xepapapdeas A (2003) Regulating nonlinear environmental systems under Knightian uncertainty. In: Arnott R, Greenwald B, Kanbur R, Nalebuff B (eds) Economics for an imperfect world: essays in honor of Joseph Stiglitz. MIT Press, Cambridge

    Google Scholar 

  7. Crépin A-S (2002) Tackling the economics of ecosystems. PhD thesis, Stockholm University, Department of Economics. Dissertations in economics 2002:6

  8. Crépin A-S (2003) Multiple species boreal forests—what Faustmann missed. Environ Resour Econ 26(4): 625–646

    Article  Google Scholar 

  9. Crépin A-S (2007) Using fast and slow processes to manage resources with thresholds. Environ Resour Econ 36(2): 191–213

    Article  Google Scholar 

  10. Dutta PK, Sundaram RK (1993) The tragedy of the commons?. Econ Theory 3: 413–426

    Article  Google Scholar 

  11. Feichtinger G (2004) Multiple equilibria in optimal control models—a research program. Cent Eur J Oper Res 12(2):157–169

    Google Scholar 

  12. Hardin G (1968) The tragedy of the commons. Science 162: 1243–1248

    Article  Google Scholar 

  13. Hart RH, Samuel MJ, Test PJ, Smith MA (1988) Cattle, vegetation, and economic responses to grazing systems and grazing pressure. J Range Manag 41(4): 282–286

    Article  Google Scholar 

  14. Holling C (1959) Some characteristics of simple type of predation and parasitism. Can Entomol 91: 385–389

    Article  Google Scholar 

  15. Janssen MA, Anderies JM, Walker BH (2004) Robust strategies for managing rangelands with multiple stable attractors. J Environ Econ Manag 47: 140–162

    Article  Google Scholar 

  16. Kossioris G, Plexousakis M, Xepapadeas A, de Zeeuw A, Mäler K-G (2008) Feedback Nash equilibria for non-linear differential games in pollution control. J Econ Dyn Control 32(4): 1312–1331

    Article  Google Scholar 

  17. Kurz M (1968) The general instability of a class of competitive growth processes. Rev Econ Stud 35(102): 155–174

    Google Scholar 

  18. Lepers E, Lambin EF, Janetos AC, DeFries R, Frederic A, Navin R, Scholes RJ (2005) A synthesis of information on rapid land-cover change for the period 1981–2000. Bioscience 55(2): 115–124

    Article  Google Scholar 

  19. Ludwig D, Jones DD, Holling CS (1978) Qualitative analysis of insect outbreak systems: the spruce budworm and the forest. J Anim Ecol 47: 315–332

    Article  Google Scholar 

  20. Mäler K-G, Xepapadeas A, de Zeeuw A (2003) The economics of shallow lakes. Environ Resour Econ 26(4): 603–624

    Article  Google Scholar 

  21. Manley WA, Hart R, Samuel MJ, Smith M, Waggoner J, Manley J (1997) Vegetation, cattle, and economic responses to grazing strategies and pressures. J Range Manag 50(6): 638–646

    Article  Google Scholar 

  22. Murray J (2002) Mathematical biology, volume 17 of interdisciplinary applied mathematics (3rd edn). Springer-Verlag, New York

    Google Scholar 

  23. Nikaido H (1968) Convex structures and economic theory. Academic Press, London

    Google Scholar 

  24. Ostrom E (1990) Governing the commons—the evolution of institutions for collective action. Political economy of institutions and decisions. Cambidge University Press, New York

    Google Scholar 

  25. Ostrom E (2000) Collective action and the evolution of social norms. J Econ Perspect 14: 137–158

    Article  Google Scholar 

  26. Perrings C, Walker B (1997) Biodiversity, resilience and the control of ecological-economic systems: the case of fire-driven rangelands. Ecol Econ 22: 73–83

    Article  Google Scholar 

  27. Pontryagin L, Boltyanskii V, Gamkrelidze R, Mishchenko E (1964) The mathematical theory of optimal processes (trans: Brown DE). Pergamon Press, New York

  28. Scholes RJ (2003) Convex relationships in ecosystems containing mixtures of trees and grass. J Environ Econ Manag 26(4): 559–574

    Google Scholar 

  29. Scholes R, Archer S (1997) Tree–grass interactions in savannas. Annu Rev Ecol Syst 28: 517–544

    Article  Google Scholar 

  30. Shampine LF, Kierzenka J, Reichelt MW (2000) Solving boundary value problems for ordinary differential equations in MATLAB with bvp4c. http://www.mathworks.com/matlabcentral/fileexchange.

  31. Skiba AK (1978) Optimal growth with a convex–concave production. Econometrica 46(3): 527–539

    Article  Google Scholar 

  32. Steffen W, Sanderson A, Jäger J, Tyson P, Moore BIII, Matson P, Richardson K, Oldfield F, Schellnhuber H-J, Turner II BL, Wasson RE (2004) Global change and the earth system: a planet under pressure. IGBP book series. Springer-Verlag, Heidelberg

    Google Scholar 

  33. Turchin P (2003) Complex population dynamics—a theoretical/empirical analysis, volume 35 of monographs in population biology. Princeton University Press, Princeton

    Google Scholar 

  34. Van Keuren R, Parker C (1967) Better pasture utilization grazing cattle and sheep together. Ohio Rep 57: 12

    Google Scholar 

  35. Wagener F (2003) Skiba points and heteroclinic bifurcation points, with applications to the shallow lake system. J Econ Dyn Control 27(9): 1533–1561

    Article  Google Scholar 

  36. Walker B (1993) Rangeland ecology: understanding and managing change. Ambio 22: 80–87

    Google Scholar 

  37. White R, Murray S, Rohweden M (2000) Pilot analysis of global ecosystems: grassland ecosystems. World Resources Institute, Washington

    Google Scholar 

  38. Zhou H, Zhao X, Tang Y, Gu S, Zhou L (2005) Alpine grassland degradation and its control in the source region of the Yangtze and Yellow rivers, China. Grassl Sci 51: 191–203

    Article  Google Scholar 

Download references

Author information

Affiliations

  1. The Beijer Institute of Ecological Economics, The Royal Swedish Academy of Sciences, Box 50005, 10405, Stockholm, Sweden

    Anne-Sophie Crépin & Therese Lindahl

Authors
  1. Anne-Sophie Crépin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Therese Lindahl
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Therese Lindahl.

Electronic Supplementary Material

The Below is the Electronic Supplementary Material.

ESM 1 (PDF 132 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Crépin, AS., Lindahl, T. Grazing Games: Sharing Common Property Resources with Complex Dynamics. Environ Resource Econ 44, 29–46 (2009). https://doi.org/10.1007/s10640-008-9258-0

Download citation

Keywords

  • Common pool resources
  • Common property
  • Complex ecosystem dynamics
  • Differential games
  • Grasslands
  • Multiple equilibria