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Splitting an Uncertain (Natural) Capital

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  • Jérémy Laurent-Lucchetti
  • Justin Leroux
  • Bernard Sinclair-Desgagné

Abstract

Most natural commons are subject to discontinuities and threshold effects, so their gradual depletion may result in a sudden irreversible loss of the associated ecological services. Yet, it is often impossible to locate these thresholds with certainty. We analyze this context using a variant of the divide-the-dollar game, in which the amount to be split among players follows a discrete or multimodal probability distribution. “Cautions equilibria” – where agents collectively behave as if the worst-case scenario were certain – are found to coexist with “dangerous equilibria” – where overall demand for ecological services might lead to their collapse – and “dreadful equilibria” – where agents collectively request so much natural capital that a collapse of ecological services is certain, even if all agents are risk averse. Communication/cooperation among agents, however, which raises the possibility of coordinated group deviations, would eliminate dreadful equilibria and reduce the occurrence of dangerous equilibria, while cautions equilibria are robust to such deviations. A direct corollary is that dangerous equilibria are Pareto-dominated by any cautions equilibrium in which all agents claim less natural capital. These results shed light on the management of common-pool resources, international climate change negotiations, and the implementation of precautionary policies.

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Bibliographic Info

Paper provided by CIRPEE in its series Cahiers de recherche with number 1105.

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Date of creation: 2011
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Handle: RePEc:lvl:lacicr:1105

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Keywords: Common-pool resources; ecological thresholds; divide-the-dollar game; coalition-proof Nash equilibrium;

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  1. Sandler, Todd & Sternbenz, Frederic P., 1990. "Harvest uncertainty and the tragedy of the commons," Journal of Environmental Economics and Management, Elsevier, vol. 18(2), pages 155-167, March.
  2. Yann Bramoullé & Nicolas Treich, 2009. "Can Uncertainty Alleviate the Commons Problem?," Journal of the European Economic Association, MIT Press, vol. 7(5), pages 1042-1067, 09.
  3. Levin, Jonathan, 1997. "An Optimal Auction for Complements," Games and Economic Behavior, Elsevier, vol. 18(2), pages 176-192, February.
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  6. Brozovic, Nicholas & Schlenker, Wolfram, 2011. "Optimal management of an ecosystem with an unknown threshold," Ecological Economics, Elsevier, vol. 70(4), pages 627-640, February.
  7. Muradian, Roldan, 2001. "Ecological thresholds: a survey," Ecological Economics, Elsevier, vol. 38(1), pages 7-24, July.
  8. Elinor Ostrom, 2010. "Beyond Markets and States: Polycentric Governance of Complex Economic Systems," American Economic Review, American Economic Association, vol. 100(3), pages 641-72, June.
  9. Boucher, Vincent & Bramoullé, Yann, 2010. "Providing global public goods under uncertainty," Journal of Public Economics, Elsevier, vol. 94(9-10), pages 591-603, October.
  10. Bernheim, B. Douglas & Peleg, Bezalel & Whinston, Michael D., 1987. "Coalition-Proof Nash Equilibria I. Concepts," Journal of Economic Theory, Elsevier, vol. 42(1), pages 1-12, June.
  11. David Malueg, 2010. "Mixed-strategy equilibria in the Nash Demand Game," Economic Theory, Springer, vol. 44(2), pages 243-270, August.
  12. Andre, Catherine & Platteau, Jean-Philippe, 1998. "Land relations under unbearable stress: Rwanda caught in the Malthusian trap," Journal of Economic Behavior & Organization, Elsevier, vol. 34(1), pages 1-47, January.
  13. Therese Lindahl & Magnus Johannesson, 2009. "Bargaining over a Common Good with Private Information," Scandinavian Journal of Economics, Wiley Blackwell, vol. 111(3), pages 547-565, 09.
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Cited by:
  1. Espínola-Arredondo, Ana & Muñoz-García, Félix, 2013. "Asymmetric information may protect the commons: The welfare benefits of uninformed regulators," Economics Letters, Elsevier, vol. 121(3), pages 463-467.

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