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Resource Economics

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Handbook of Dynamic Game Theory

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Abstract

This chapter provides a selective survey of dynamic game models of exploitation of natural resources. It covers both renewable resources and exhaustible resources. In relation to earlier surveys (Long, A survey of dynamic games in economics, World Scientific, Singapore, 2010; Long, Dyn Games Appl 1(1):115–148, 2011), the present work includes many references to new developments that appeared after January 2011 and additional suggestions for future research. Moreover, there is a greater emphasis on intuitive explanation.

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Notes

  1. 1.

    For a review of the game theoretic approach to water resources, see Dinar and Hogarth (2015). For some recent models of differential games involving water transfer between two countries, see Cabo et al. (2014) and in particular Cabo and Tidball (2016) where countries cooperate in the infrastructure investment stage but play a noncooperative game of water transfer in a second stage. Cabo and Tidball (2016) design a time-consistent imputation distribution procedure to ensure cooperation, along the lines of Jørgensen and Zaccour (2001).

  2. 2.

    Dictionnaire LE ROBERT, Société du Nouveau Littré, Paris: 1979.

  3. 3.

    However, as pointed out by Ostrom (1990), in some societies, thanks to good institutions, the commons are efficiently managed.

  4. 4.

    See Fudenberg and Tirole (1991) on the comparison of the concepts of open-loop equilibrium and feedback or Markov-perfect equilibrium.

  5. 5.

    It has been estimated that about 80 % of fish stocks are exploited at or beyond their maximum sustainable yields. See FAO (2009).

  6. 6.

    We assume that the upper bound constraint on effort is not binding at the steady state.

  7. 7.

    If the amount harvested depends only on the effort level and not on the level of the stock, i.e., h i  = γ L i , then in an open-loop equilibrium, there is no dynamic overcrowding production externality. In that case, it is possible that open-loop exploitation is Pareto efficient; see Chiarella et al. (1984).

  8. 8.

    The farsightedness concept was formalized in Greenberg (1990) and Chwe (1994) and has been applied to the literature on public goods (Ray and Vohra 2001) and international environmental agreements (de Zeeuw 2008; Diamantoudi and Sartzetakis 2015).

  9. 9.

    For ownership risks, see Bohn and Deacon (2000).

  10. 10.

    In contrast, in the standard models, where all utility functions are concave, it can be shown that the equilibrium trajectory of the state variable must eventually become monotone. See Dutta and Sundaram (1993b).

  11. 11.

    Sundaram and Dutta (1993b) extend this “no tragedy” result to the case with mild discounting: as long as the discount rate is low enough, if players use discontinuous strategies that threaten to make a drastic increase in consumption when the stock falls below a certain level, they may be able to lock each other into a stock level that is dynamically inefficient and greater than the cooperative steady state.

  12. 12.

    Except possibly the cooperative steady state (Dutta and Sundaram 1993b, Theorem 3).

  13. 13.

    Dockner and Sorger (1996), Lemma 1.

  14. 14.

    Dockner and Long (1993) find similar results in a pollution game.

  15. 15.

    Efficiency can also be ensured if players can resort to trigger strategies, see Cave (1987) and Benhabib and Radner (1992), or if there exist countervailing externalities, as in Martin and Rincón-Zapareto (2005).

  16. 16.

    See e.g. Fudenberg and Levine (2006, 2012).

  17. 17.

    See Salo and Tahvonen (2001) for the modeling of economic exhaustion in a duopoly.

  18. 18.

    See Gaudet (2007) for the theory and empirics related to the Hotelling Rule.

  19. 19.

    For a proof of the time inconsistency of open-loop Stackelberg equilibrium, see, for example, Dockner et al. (2000), or Long (2010).

  20. 20.

    See also Lewis and Schmalensee (1980).

  21. 21.

    This corresponds to the result that, in a closed economy, the market power of an oil monopolist with zero extraction cost disappears when the elasticity of demand is constant. See, e.g., Stiglitz (1976).

  22. 22.

    This is confirmed in Brander and Djajic (1983), who consider a two-country world in which both countries use oil to produce a consumption good, but only one of them is endowed with oil.

  23. 23.

    See also Karp (1984) and Maskin and Newbery (1990) for the time-inconsistency issue.

  24. 24.

    For discussions of the concept of global feedback Stackelberg equilibrium, see Basar and Olsder (1982) and Long and Sorger (2010). An alternative notion is the stagewise Stackelberg leadership, which will be explained in more detail in Sect. 3.3 below.

  25. 25.

    In a stagewise Stackelberg equilibrium, no commitment of any significant length is possible. The leader can only commit to the current period decision.

  26. 26.

    This result is confirmed by Rubio and Estriche (2001) who modify the model of Tahvonen (1996) by assuming that the per-unit extraction cost in period t is c × (S(0) − S(t)), where c is a positive parameter.

  27. 27.

    Dasgupta and Heal (1979, Ch. 12) consider the open-loop Nash equilibrium of a similar seepage problem, with just two firms, and reach similar results.

  28. 28.

    Sinn (1984) considers a different concept of equilibrium in the seepage model: each firm is committed to achieve a given time path of its stock.

  29. 29.

    Bolle (1980) obtains a similar result, assuming that there is only one common stock that all m firms have equal access.

  30. 30.

    The case of open-loop Nash equilibrium was addressed by Kolstad (1994) and Keutiben (2014).

  31. 31.

    This is related to the so-called SLOSS debate in ecology, in which authors disagree as to whether a single large or several small (SLOSS) reserves would be better for conservation.

  32. 32.

    Myerson and Weibull (2015) formalize the idea that “social conventions usually develop so that people tend to disregard alternatives outside the convention.”

  33. 33.

    For a sample of papers that deal with evolutionary dynamics, see Bala and Long (2005), ?, and Sethi and Somanathan (1996).

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Authors and Affiliations

  1. McGill University, Montreal, QC, Canada

    Ngo Van Long

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  1. Ngo Van Long
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Correspondence to Ngo Van Long .

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Editors and Affiliations

  1. Center for Advanced Study, University of Illinois Urbana-Champaign, Urbana, Illinois, USA

    Tamer Basar

  2. GERAD, HEC Montréal, Montreal, Québec, Canada

    Georges Zaccour

Section Editor information

  1. Coordinated Science Laboratory, University of Illinois, 1308 West Main, 61801, Urbana, Illinois, USA

    Tamer Basar

  2. Département de sciences de la décision, HEC Montreal, Montreal, Canada

    Georges Zaccour

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Long, N. (2016). Resource Economics. In: Basar, T., Zaccour, G. (eds) Handbook of Dynamic Game Theory. Springer, Cham. https://doi.org/10.1007/978-3-319-27335-8_15-1

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