Bulletin of Mathematical Biology

, Volume 77, Issue 2, pp 281–297 | Cite as

Satisficing Versus Optimality: Criteria for Sustainability

  • Michel De Lara
  • Vincent Martinet
  • Luc Doyen
Original Article


Economic analysis addresses risk and long-term issues with discounted expected utility, focusing on optimality. Viability theory is rooted on satisfying sustainability constraints over time, focusing on feasibility. We build a bridge between these two approaches by establishing that viability is equivalent to an array of degenerate intertemporal optimization problems. First, we focus our attention on the deterministic case. We highlight the connections between the viability kernel and the minimum time of crisis. Carrying on, we lay out stochastic viability, turning the spotlight onto the notions of viable scenario and maximal viability probability. Our conceptual results bring the viability approach closer to the economic approach, especially in the stochastic case and regarding efficiency. We discuss the possible use of viability as a theoretical framework for biodiversity conservation, ecosystem management and climate change issues.


Sustainability Uncertainty Optimality Viability 



The authors are indebted to the Editor and to two Reviewers for their useful comments.


  1. Allais, M. (1953). Le comportement de l’homme rationnel devant le risque: critique des postulats et axiomes de l’école américaine. Econometrica, 21(4), 503–546. MathSciNetCrossRefzbMATHGoogle Scholar
  2. Aubin, J.-P. (1991). Viability theory. Boston: Birkhäuser. 542 pp. zbMATHGoogle Scholar
  3. Aubin, J.-P., & Da Prato, G. (1998). The viability theorem for stochastic differential inclusions. Stoch. Anal. Appl., 16, 1–15. CrossRefzbMATHGoogle Scholar
  4. Baumgärtner, S., & Quaas, M. F. (2009). Ecological-economic viability as a criterion of strong sustainability under uncertainty. Ecol. Econ., 68(7), 2008–2020. CrossRefGoogle Scholar
  5. Béné, C., & Doyen, L. (2008). Contribution values of biodiversity to ecosystem performances: a viability perspective. Ecol. Econ., 68(1–2), 14–23. CrossRefGoogle Scholar
  6. Béné, C., Doyen, L., & Gabay, D. (2001). A viability analysis for a bio-economic model. Ecol. Econ., 36, 385–396. CrossRefGoogle Scholar
  7. Boiteux, M. (1976). À propos de la “critique de la théorie de l’actualisation telle qu’employée en France”. Rev. Econ. Polit., 5. Google Scholar
  8. Buckdahn, R., Quincampoix, M., Rainer, C., & Rascanu, A. (2004). Stochastic control with exit time and contraints, application to small time attainability of sets. Appl. Math. Optim., 49, 99–112. MathSciNetCrossRefzbMATHGoogle Scholar
  9. Chakravorty, U., Moreaux, M., & Tidball, M. (2008). Ordering the extraction of polluting nonrenewable resources. Am. Econ. Rev., 98(3), 1128–1144. CrossRefGoogle Scholar
  10. Chichilnisky, G. (1996). An axiomatic approach to sustainable development. Soc. Choice Welf., 13(2), 219–248. MathSciNetCrossRefGoogle Scholar
  11. Cissé, A., Gourguet, S., Doyen, L., Blanchard, F., & Péreau, J.-C. (2013). A bio-economic model for the ecosystem-based management of the coastal fishery in French Guiana. Environ. Dev. Econ., 18, 245–269. CrossRefGoogle Scholar
  12. Clark, C. W. (1990). Mathematical bioeconomics (2nd ed.). New York: Wiley. zbMATHGoogle Scholar
  13. Dasgupta, P., & Heal, G. (1974). The optimal depletion of exhaustible resources. Rev. Econ. Stud., 41, 1–28. Symposium on the economics of exhaustible resources. CrossRefGoogle Scholar
  14. De Lara, M., & Martinet, V. (2009). Multi-criteria dynamic decision under uncertainty: a stochastic viability analysis and an application to sustainable fishery management. Math. Biosci., 217(2), 118–124. MathSciNetCrossRefzbMATHGoogle Scholar
  15. De Lara, M., & Doyen, L. (2008). Sustainable Management of Natural Resources. Mathematical Models and Methods. Berlin: Springer. Google Scholar
  16. De Lara, M., Ocaña Anaya, E., Oliveros-Ramos, R., & Tam, J. (2012). Ecosystem viable yields. Environ. Model. Assess., 17(6), 565–575. CrossRefGoogle Scholar
  17. Doyen, L., & De Lara, M. (2010). Stochastic viability and dynamic programming. Syst. Control Lett., 59(10), 629–634. CrossRefzbMATHGoogle Scholar
  18. Doyen, L., & Martinet, V. (2012). Maximin, viability and sustainability. J. Econ. Dyn. Control, 36(9), 1414–1430. MathSciNetCrossRefGoogle Scholar
  19. Doyen, L., & Péreau, J.-C. (2009). The precautionary principle as a robust cost-effectiveness problem. Environ. Model. Assess., 14(1), 127–133. CrossRefGoogle Scholar
  20. Doyen, L., & Saint-Pierre, P. (1997). Scale of viability and minimum time of crisis. Set-Valued Anal., 5, 227–246. MathSciNetCrossRefzbMATHGoogle Scholar
  21. Doyen, L., De Lara, M., Ferraris, J., & Pelletier, D. (2007). Sustainability of exploited marine ecosystems through protected areas: a viability model and a coral reef case study. Ecol. Model., 208(2–4), 353–366. CrossRefGoogle Scholar
  22. Doyen, L., Thébaud, O., Béné, C., Martinet, V., Gourguet, S., Bertignac, M., Fifas, S., & Blanchard, F. (2012). A stochastic viability approach to ecosystem-based fisheries management. Ecol. Econ., 75, 32–42. CrossRefGoogle Scholar
  23. Dubbins, L. E., & Savage, L. J. (1965). How to gamble if you must: inequalities for stochastic processes. New York: McGraw-Hill. Google Scholar
  24. Ellsberg, D. (1961). Risk, ambiguity, and the Savage axioms. Q. J. Econ., 75, 643–669. CrossRefzbMATHGoogle Scholar
  25. Gollier, C. (2008). Discounting with fat-tailed economic growth. J. Risk Uncertain., 37(2), 171–186. CrossRefzbMATHGoogle Scholar
  26. Gourguet, S., Macher, C., Doyen, L., Thébaud, O., Bertignac, M., & Guyader, O. (2013). Managing mixed fisheries for bio-economic viability. Fish. Res., 140, 46–62. CrossRefGoogle Scholar
  27. Hardy, P.-Y., Béné, C., Doyen, L., & Schwarz, A.-M. (2013). Food security versus environment conservation: a case study of Solomon islands’ small-scale fisheries. Environ. Dev., 8, 38–56. CrossRefGoogle Scholar
  28. Heal, G. (1998). Valuing the future, economic theory and sustainability. New York: Columbia University Press. Google Scholar
  29. Howarth, R. (1995). Sustainability under uncertainty: a deontological approach. Land Econ., 71(4), 417–427. CrossRefGoogle Scholar
  30. ICES (2004). Report of the ICES advisory committee on fishery management and advisory committee on ecosystems, 2004. ICES Advice, vol. 1, 1544 pp. Google Scholar
  31. Kahneman, D., & Tversky, A. (1979). Prospect theory: an analysis of decision under risk. Econometrica, 47(2), 263–292. CrossRefzbMATHGoogle Scholar
  32. Koopmans, T. (1965). On the concept of optimal economic growth. Acad. Sci. Scr. Var., 28, 225–300. Google Scholar
  33. Krawczyk, J., & Kim, K. (2009). Satisficing solutions to a monetary policy problem: a viability theory approach. Macroeconomic Dynamics, 13(1), 46–80. CrossRefzbMATHGoogle Scholar
  34. Lopes, L. L. (1996). When time is of the essence: averaging, aspiration, and the short run. Organ. Behav. Hum. Decis. Process., 65(3), 179–189. CrossRefGoogle Scholar
  35. Mäler, K. G. (2002). Environment, uncertainty, and option values. Beijer Institute working paper. Google Scholar
  36. Martin, S. (2004). The cost of restoration as a way of defining resilience: a viability approach applied to a model of lake eutrophication. Ecology and Society, 9(2), 8. Google Scholar
  37. Martinet, V., & Doyen, L. (2007). Sustainable management of an exhaustible resource: a viable control approach. Resour. Energy Econ., 29(1), 19–37. CrossRefGoogle Scholar
  38. Martinet, V., Doyen, L., & Thébaud, O. (2007). Defining viable recovery paths toward sustainable fisheries. Ecol. Econ., 64(2), 411–422. CrossRefGoogle Scholar
  39. Martinet, V., Thébaud, O., & Rapaport, A. (2010). Hare or Tortoise? Trade-offs in recovering sustainable bioeconomic systems. Environ. Model. Assess., 15(6), 503–517. CrossRefGoogle Scholar
  40. Morris, W. F., & Doak, D. F. (2003). Quantitative conservation biology: theory and practice of population viability analysis. Sunderland: Sinauer. Google Scholar
  41. Mouysset, L., Doyen, L., & Jiguet, F. (2014). From population viability analysis to coviability of farmland biodiversity and agriculture. Conserv. Biol., 28(1), 187–201. CrossRefGoogle Scholar
  42. Péreau, J.-C., Doyen, L., Little, L. R., & Thébaud, O. (2012). The triple bottom line: meeting ecological, economic and social goals with individual transferable quotas. J. Environ. Econ. Manag., 63(3), 419–434. CrossRefGoogle Scholar
  43. Philibert, C. (1999). The economics of climate change and the theory of discounting. Energy Policy, 27(15), 913–927. CrossRefGoogle Scholar
  44. Philibert, C. (2006). Discounting the future. In D. Pannell & S. Schilizzi (Eds.), Discounting and discount rates in theory and practice (pp. 136–148). Cheltenham: Edward Elgar. Chap. 10. Google Scholar
  45. Savage, L. J. (1972). The foundations of statistics (2nd ed.). New York: Dover. zbMATHGoogle Scholar
  46. Simon, H. (1957). A behavioral model of rational choice. In Models of man, social and rational: mathematical essays on rational human behavior in a social setting. New York: Wiley. Google Scholar
  47. Solow, R. M. (1974). Intergenerational equity and exhaustible resources. Rev. Econ. Stud., 41, 29–45. Symposium on the economics of exhaustible resources. CrossRefGoogle Scholar
  48. Stern, N. (2006). The economics of climate change. Cambridge: Cambridge University Press. Google Scholar
  49. Sterner, T., & Persson, U. M. (2008). An even sterner review: introducing relative prices into the discounting debate. Rev. Environ. Econ. Policy, 2(1), 61–76. CrossRefGoogle Scholar
  50. Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: cumulative representation of uncertainty. J. Risk Uncertain., 5(4), 297–323. CrossRefzbMATHGoogle Scholar
  51. von Neuman, J., & Morgenstern, O. (1947). Theory of games and economic behaviour (2nd ed.). Princeton: Princeton University Press. Google Scholar
  52. Weitzman, M. L. (2007). A review of the Stern review on the economics of climate change. J. Econ. Lit., 45(3), 703–724. CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 2014

Authors and Affiliations

  1. 1.CERMICS (ENPC)Université Paris-EstMarne-la-ValléeFrance
  2. 2.INRAUMR210 Economie PubliqueThiverval-GrignonFrance
  3. 3.CNRS, GREThAUniversity of Bordeaux 4Pessac CedexFrance

Personalised recommendations