Abstract
Agents interacting on a body of water choose between technologies to catch fish. One is harmless to the resource, as it allows full recovery; the other yields high immediate catches, but low(er) future catches. Strategic interaction in one ‘objective’ resource game may induce several ‘subjective’ games in the class of social dilemmas. Which unique ‘subjective’ game is actually played depends crucially on how the agents discount their future payoffs. We examine equilibrium behavior and its consequences on sustainability of the common-pool resource system under exponential and hyperbolic discounting. A sufficient degree of patience on behalf of the agents may lead to equilibrium behavior averting exhaustion of the resource, though full restraint (both agents choosing the ecologically or environmentally sound technology) is not necessarily achieved. Furthermore, if the degree of patience between agents is sufficiently dissimilar, the more patient is exploited by the less patient one in equilibrium. We demonstrate the generalizability of our approach developed throughout the paper. We provide recommendations to reduce the enormous complexity surrounding the general cases.
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Notes
None of the ideas and effects to be presented depend on the specific mathematical form of this connection, hence if empirical research offer a precise causal relationship it can easily substitute our assumed one.
The PD is due to Merrill Flood and Melvin Dresher and received its name and famous interpretative anecdote by Albert Tucker (cf, e.g., Campbell 1985, p.3). The CH also known as Snowdrift (cf., e.g., Skyrms 1996) appeared first in Kahn (1965). The name of the PG is due to Heckathorn (1996) inspired by Olson (1965). The SH can be traced back to at least Hume (1739), Hobbes (1651) and Rousseau (1755). An SH is also called an Assurance (Sen 1967) or Trust Game (Liebrand 1983).
Efficient algorithms to obtain large sets of feasible \(\beta \)-discounted rewards are lacking.
To save computing time the infinite sum was cut off after \(t=250\); \( \underline{m}=0,\) \(n_{1}=3,\) \(n_{2}=2,\) \(q=5,\) \(a=4,\) \(b=\frac{7}{2 }\), \(c=6\), \(d=\frac{11}{2}.\)
I thank Christian Cordes for reminding me of this fact.
Rubinstein (2003) notes that the criticism leading to a rejection of standard constant discount utility functions can easily reject hyperbolic discounting as well.
To speed up computations, we set \(T=75.\)
In a Fish War off Newfoundland, a deal between Canada and Spain was struck in which Canadian fishermen received quota which were lower than in an earlier agreement broken by the Spanish. A real world example of the patient being exploited by the impatient? Another example can be found in Kennedy (1987, p. 7) where the Australian government considered lowering Australian quota in case Japanese catch was not curtailed sufficiently, this being deemed in the interest of Australia itself.
For the sake of brevity, we only refer to the exponential discounting approach.
See Sect. 3.1 for motivations.
An anonymous referee advised us to make clear that agents here as in our earlier models, are the collective fishermen of countries, villages or cooperatives taking decisions together. According to Hillis and Wheelan (1994) individual fishermen are quite myopic.
Olson (1965, p. 2) challenged communis opinio at that point in time that group benefit would inevitably trigger collective action to achieve that benefit: “unless there is coercion or some other special devise to make individuals act in their common interest, rational self-interested individuals will not act to achieve their common or group interests”.
Benevolent as in wishing to do ‘justice’ to the agents as well as desiring to preserve the resource with as little intervention as possible.
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Acknowledgments
I thank Ulrich Witt, Christian Cordes, Sebastiaan Morssinkhof and Berend Roorda for comments.
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Joosten, R. Social dilemmas, time preferences and technology adoption in a commons problem. J Bioecon 16, 239–258 (2014). https://doi.org/10.1007/s10818-014-9182-z
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DOI: https://doi.org/10.1007/s10818-014-9182-z
Keywords
- Stochastic renewable resource games
- Hyperbolic and exponential discounting
- Social dilemmas
- Sustainability