Annals of Operations Research

, Volume 220, Issue 1, pp 159–180 | Cite as

Consistent conjectures in a dynamic model of non-renewable resource management

Article

Abstract

We consider a model of non-renewable resource extraction where players do not know their opponents’ utility functions and form conjectures on the behavior of others. Two forms of beliefs are introduced, one based on the state of the resource, the other on this state and on the others’ strategy (their consumption). We focus on consistent equilibria, where beliefs must be consistent with observed past plays. Closed form expressions of the optimal policies are derived. Comparisons are made with the full information benchmark case. With strategy and state based beliefs, the agents may behave more (respectively, less) aggressively than in the non-cooperative benchmark depending on the initial consumption level. When initial consumption is low, the optimal consumption path lies below that of the cooperative benchmark. We conclude the analysis by discussing the impact of public policies on the agents’ choice of consumption patterns, and the robustness of the results for the case of renewable resources.

Keywords

Dynamic game Dynamic resource management Non probabilistic beliefs Conjectural variations 

References

  1. Benhabib, J., & Radner, R. (1992). The joint exploitation of a productive asset: a game-theoretic approach. Economic Theory, 2, 155–190. CrossRefGoogle Scholar
  2. Bischi, G.-I., Kopel, M., & Szidarowszky, F. (2005). Expectation-stock dynamics in multi-agent fisheries. Annals of Operations Research, 137, 299–329. CrossRefGoogle Scholar
  3. Dixon, H., & Somma, E. (2003). The evolution of consistent conjectures. Journal of Economic Behavior & Organization, 51, 523–536. CrossRefGoogle Scholar
  4. Dutta, P., & Sundaram, R. (1993). The tragedy of the commons? Economic Theory, 3, 413–426. CrossRefGoogle Scholar
  5. Fershtman, C., & Kamien, M. (1985). Conjectural equilibrium and strategy spaces in differential games. In Optimal control theory and economic analysis (Vol. 2, pp. 569–579). Amsterdam: Elsevier. Google Scholar
  6. Figuières, C., Jean-Marie, A., Quérou, N., & Tidball, M. (2004). Theory of conjectural variations. In Monograph series in mathematical economics and game theory. Singapore: World Scientific Publishing. Google Scholar
  7. Fischer, R., & Mirman, L. (1992). Strategic dynamic interactions: fish wars. Journal of Economics Dynamics & Control, 16, 267–287. CrossRefGoogle Scholar
  8. Fischer, R., & Mirman, L. (1996). The complete fish wars: biological and dynamic interactions. Journal of Environmental Economics and Management, 30, 34–42. CrossRefGoogle Scholar
  9. Friedman, J. (1977). Oligopoly and the theory of games. Amsterdam: North-Holland. Google Scholar
  10. Friedman, J., & Mezzetti, C. (2002). Bounded rationality, dynamic oligopoly, and conjectural variations. Journal of Economic Behavior & Organization, 49, 287–306. CrossRefGoogle Scholar
  11. Houba, H., Sneek, K., & Vardy, F. (2000). Can negotiations prevent fish wars? Journal of Economic Dynamics & Control, 24, 1265–1280. CrossRefGoogle Scholar
  12. Jean-Marie, A., & Tidball, M. (2005). Consistent conjectures, equilibria and dynamic games. In A. Haurie & G. Zaccour (Eds.), Dynamic games: theory and applications (pp. 93–109). Berlin: Springer. Google Scholar
  13. Jean-Marie, A., & Tidball, M. (2006). Adapting behaviors through a learning process. Journal of Economic Behavior & Organization, 60, 399–422. CrossRefGoogle Scholar
  14. Kalashnikov, V., Kemfert, C., & Kalashnikov, V. (2009). Conjectural variations equilibrium in a mixed duopoly. European Journal of Operational Research, 192, 717–729. CrossRefGoogle Scholar
  15. Koulovatianos, C., Mirman, L., & Santugini, M. (2009). Optimal growth and uncertainty: learning. Journal of Economic Theory, 144, 280–295. CrossRefGoogle Scholar
  16. Laitner, J. (1980). Rational duopoly equilibria. Quarterly Journal of Economics, 641–662. Google Scholar
  17. Levhari, D., & Mirman, L. (1980). The Great Fish War: an example using a dynamic Cournot-Nash solution. The Bell Journal of Economics, 11, 322–334. CrossRefGoogle Scholar
  18. Lindh, T. (1992). The inconsistency of consistent conjectures. Coming back to Cournot. Journal of Economic Behavior & Organization, 18, 69–90. CrossRefGoogle Scholar
  19. Lopez de Haro, S., Sanchez Martín, P., de la Hoz Ardiz, J. E., & Fernandez Caro, J. (2007). Estimating conjectural variations for electricity market models. European Journal of Operational Research, 181, 1322–1338. CrossRefGoogle Scholar
  20. McKitrick, R. (1999). A Cournot mechanism for pollution control under asymmetric information. Environmental & Resource Economics, 14, 353–363. CrossRefGoogle Scholar
  21. Muller, W., & Normann, H.-T. (2005). Conjectural variations and evolutionary stability: a rationale for consistency. Journal of Institutional and Theoretical Economics, 161, 491–502. CrossRefGoogle Scholar
  22. Possajennikov, A. (2009). The evolutionary stability of constant consistent conjectures. Journal of Economic Behavior and Organization, 72, 21–29. CrossRefGoogle Scholar
  23. Quérou, N., & Tidball, M. (2010). Incomplete information, learning, and natural resource management. European Journal of Operational Research, 204, 630–638. CrossRefGoogle Scholar
  24. Slade, M. (1995), Empirical games: the oligopoly case. Revue Canadienne D’Economique 28, 368–402. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.CNRSUMR 5474 LAMETAMontpellierFrance
  2. 2.INRAUMR 1135 LAMETAMontpellierFrance

Personalised recommendations