Experimental Economics

, Volume 17, Issue 4, pp 649–672 | Cite as

Time and uncertainty in resource dilemmas: equilibrium solutions and experimental results

  • Anabela Botelho
  • Ariel Dinar
  • Lígia M. Costa Pinto
  • Amnon Rapoport
Original Paper


Most common pool resource (CPR) dilemmas share two features: they evolve over time and they are managed under environmental uncertainties. We propose a stylized dynamic model that integrates these two dimensions. A distinguishing feature of our model is that the duration of the game is determined endogenously by the users’ collective decisions. In the proposed model, if the resource stock level below which the irreversible event occurs is known in advance, then the optimal resource use coincides with a unique symmetric equilibrium that guarantees survival of the resource. As the uncertainty about the threshold level increases, resource use increases if users adopt decision strategies that quickly deplete the resource stock, but decreases if they adopt path strategies guaranteeing that the unknown threshold level is never exceeded. We show that under relatively high uncertainty about resource size, CPR users frequently implement decision strategies that terminate the game immediately. When this uncertainty is reduced, they maintain a positive resource level for longer durations.


Common pool resources Social dilemmas Uncertainty Sustainability 

Supplementary material

10683_2013_9388_MOESM1_ESM.pdf (481 kb)
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  1. Bailey, M., Sumaila, U. R., & Lindroos, M. (2010). Application of game theory to fisheries over three decades. Fisheries Research, 102, 1–8. CrossRefGoogle Scholar
  2. Barrett, S., & Dannenberg, A. (2012). Climate negotiations under scientific uncertainty. Proceedings of the National Academy of Sciences of the United States of America, 109(43), 17372–17376. CrossRefGoogle Scholar
  3. Brown, G. M. (2001). Renewable natural resource management and use without markets. Journal of Economic Literature, 38, 875–914. CrossRefGoogle Scholar
  4. Budescu, D. V., Rapoport, A., & Suleiman, R. (1995). Common pool resource dilemmas under uncertainty: qualitative tests of equilibrium solutions. Games and Economic Behavior, 10, 171–201. CrossRefGoogle Scholar
  5. Clarke, H. R., & Reed, W. J. (1994). Consumption/pollution tradeoffs in an environment vulnerable to pollution-related catastrophic collapse. Journal of Economic Dynamics & Control, 18, 991–1010. CrossRefGoogle Scholar
  6. Dutta, P. (1995). Collusion, discounting and dynamic games. Journal of Economic Theory, 66, 289–306. CrossRefGoogle Scholar
  7. Fischbacher, U. (2007). Z-Tree: Zurich toolbox for ready-made economic experiments. Experimental Economics, 10(2), 171–178. CrossRefGoogle Scholar
  8. Gardner, R., & Walker, J. M. (1992). Probabilistic destruction of common-pool resources: experimental evidence. The Economic Journal, 102(414), 1149–1161. CrossRefGoogle Scholar
  9. Gordon, H. S. (1954). The economic theory of a common property resource: the fishery. Journal of Political Economy, 62, 124–142. CrossRefGoogle Scholar
  10. Gustafsson, M., Biel, A., & Garling, T. (1999). Overharvesting of resources of unknown size. Acta Psychologica, 103, 47–64. CrossRefGoogle Scholar
  11. Hardin, G. (1968). The tragedy of the commons. Science, 162, 1243–1248. CrossRefGoogle Scholar
  12. Herr, A., Gardner, R., & Walker, J. M. (1997). An experimental study of time-independent and time-dependent externalities in the commons. Games and Economic Behavior, 19(1), 77–96. CrossRefGoogle Scholar
  13. Hey, J. D., Neugebauer, T., & Sadrieh, A. (2009). An experimental analysis of optimal renewable resource management: the fishery. Environmental & Resource Economics, 44, 263–285. CrossRefGoogle Scholar
  14. Hine, D. W., & Gifford, R. (1996). Individual restraint and group efficiency in commons dilemmas: the effects of two types of environmental uncertainty. Journal of Applied Social Psychology, 26, 993–1009. CrossRefGoogle Scholar
  15. Koundouri, P. (2004). Current issues in the economics of groundwater resource management. Journal of Economic Surveys, 18, 703–738. CrossRefGoogle Scholar
  16. Mason, C. F., & Phillips, O. R. (1997). Mitigating the tragedy of the commons through cooperation: an experimental evaluation. Journal of Environmental Economics and Management, 34(2), 148–172. CrossRefGoogle Scholar
  17. Messick, D. M., & McClelland, C. L. (1983). Social traps and temporal traps. Personality & Social Psychology Bulletin, 9, 105–110. CrossRefGoogle Scholar
  18. Muradian, R. (2001). Ecological thresholds: a survey. Ecological Economics, 38, 7–24. CrossRefGoogle Scholar
  19. Oehlert, G. W. (1992). A note on the delta method. American Statistician, 46, 27–29. Google Scholar
  20. Osés-Eraso, N., Udina, F., & Viladrich-Grau, M. (2008). Environmental versus human-induced scarcity in the commons: do they trigger the same response? Environmental & Resource Economics, 40, 529–550. CrossRefGoogle Scholar
  21. Ostrom, E., Gardner, R., & Walker, J. (1994). Rules, games, & common-pool resources. Ann Arbor: University of Michigan Press. Google Scholar
  22. Papke, L. E., & Wooldridge, J. M. (1996). Econometric methods for fractional response variables with an application to 401(K) plan participation rates. Journal of Applied Econometrics, 11, 619–632. CrossRefGoogle Scholar
  23. Rapoport, A., & Suleiman, R. (1992). Equilibrium solutions for resource dilemma. Group Decision and Negotiation, 1, 269–294. CrossRefGoogle Scholar
  24. Reinganum, J. F., & Stokey, N. L. (1985). Oligopoly extraction of a common property natural resource: the importance of the period of commitment in dynamic games. International Economic Review, 26(1), 161–173. CrossRefGoogle Scholar
  25. Shapley, L. (1953). Stochastic games. Proceedings of the National Academy of Sciences of the United States of America, 39, 1095–1100. CrossRefGoogle Scholar
  26. Sobel, M. J. (1971). Noncooperative stochastic games. The Annals of Mathematical Statistics, 42, 1930–1935. CrossRefGoogle Scholar
  27. Suleiman, R., & Rapoport, A. (1988). Environmental and social uncertainty in single-trial resource dilemmas. Acta Psychologica, 68, 99–112. CrossRefGoogle Scholar
  28. Tsur, Y., & Zemel, A. (1995). Uncertainty and irreversibility in groundwater resource management. Journal of Environmental Economics and Management, 29, 149–161. CrossRefGoogle Scholar
  29. Yin, R., & Newman, D. H. (1996). The effect of catastrophic risk on forest investment decisions. Journal of Environmental Economics and Management, 31, 186–197. CrossRefGoogle Scholar

Copyright information

© Economic Science Association 2014

Authors and Affiliations

  • Anabela Botelho
    • 1
  • Ariel Dinar
    • 2
  • Lígia M. Costa Pinto
    • 1
  • Amnon Rapoport
    • 3
  1. 1.University of Minho and NIMABragaPortugal
  2. 2.Water Science and Policy Center, Department of Environmental SciencesUniversity of CaliforniaRiversideUSA
  3. 3.A. Gary Anderson School of Business AdministrationUniversity of CaliforniaRiversideUSA

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