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Published in: Dynamic Games and Applications 2/2017

23-03-2016

International Fisheries Agreements with a Shifting Stock

Authors: Florian K. Diekert, Emmi Nieminen

Published in: Dynamic Games and Applications | Issue 2/2017

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Abstract

When a fish stock shifts from one nation to another nation, e.g., due to climate change, the nation that loses the resource has incentives to deplete it, while the other nation, receiving the resource, has incentives to conserve it. We propose an analytical model to study under which circumstances self-enforcing agreements can align incentives. Our setup allows to distinguish between a fast and a slow shift and between a smooth or a sudden shift in ownership. We show that the shorter the expected duration of the transition, the higher the total equilibrium exploitation rate. Similarly, a sudden shift implies—by and large—more aggressive non-cooperative exploitation than a gradual shift. However, a self-enforcing agreement without side-payments is more likely for a sudden than for a smooth shift. Further, the scope for cooperation increases with the expected duration of the transition, and it decreases with the renewability of the resource and the discount rate. Most importantly, we show that concentrating on in-kind transfers can be very detrimental for shifting renewable resources: In some cases, there is no efficient bargaining solution without side-payments, even when there are only two players.

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Appendix
Available only for authorised users
Footnotes
1
Note that at this level of abstraction, we do not differentiate between producer surplus and consumer surplus, or any positive externalities such as cultural or touristic values derived from, for example, a picturesque fishing industry. The decrease in marginal utility could thus capture increasing harvesting costs, a supply side effect on the landings price, or other more general effects. However, we require that no utility can be derived from the resource when it is not harvested (i.e., there are no existence values). We further discuss this latter aspect in Sect. 6.
 
2
In the coming pages, we will introduce a number of short-hand variables to simplify the notation. For the reader’s convenience, an overview of the fundamental and derived variables that we use is given in the Appendix in Table 2.
 
3
Let \(i_\mathrm{min}\) be the lowest extraction rate of player i and let \(d_\mathrm{max}\) be the largest equilibrium total extraction rate. Then a condition that guarantees nonnegative objective function values is \(i_\mathrm{min}M\left( (1-d_\mathrm{max})M\right) ^{\frac{\alpha }{1-\alpha }} \ge 1\) for \(i = A,B\).
 
4
We refer to a standard mathematic textbook for economists, e.g., [35, p.391]. To see the solution more clearly, it is useful to change variables so that we start counting from the terminal stage T. That is, we introduce a new variable \(n = 0,1,2,\ldots \) so that \(n = 0 \equiv \tau = T\). This means that Eq. (6) is written as: \(k_{n+1}^{i} = l + m k_{n}^{i}\) which can be solved to get \(k_n^i=m^n k_0 + l(\sum (m^n))\). As we have a geometric series in the brackets, the solution of the equation can be rewritten as: \(k_n^i=\frac{l(1-m^n)}{1-m}+mk_0 \Leftrightarrow k_n^i=m^n[k_0 - \frac{ l}{1-m}] + \frac{ l}{1-m}\), where \(\frac{l}{1-m} = \frac{1}{1-\alpha \beta q} \frac{1}{1-\frac{\alpha \beta (1-q)}{1-\alpha \beta q}} = \frac{1}{1-\alpha \beta q} \frac{1}{\frac{(1-\alpha \beta q) - \alpha \beta (1-q)}{1-\alpha \beta q}} = \frac{1}{1-\alpha \beta q - \alpha \beta + \alpha \beta q} = \frac{1}{1- \alpha \beta }\).
 
5
The legal principle that treaties must be honored (pacta sunt servanda) is understood to be contingent on the current state of affairs when the treaty was made (rebus sic stantibus).
 
6
We provide the source codes (using [33]) to replicate all figures of this paper as an online appendix. These scripts also allow the interested reader to explore the state space further than the examples that we provide here.
 
7
In a sense, the lower Z, the stronger is the effect of an increase in T on q. For example if \(Z = 3\), T can only take the values 1, 2 and 3. If \(T=1\), \(q=\frac{2}{3}\) and \(d_\mathrm{max} = 0.49\). When \(T = 2\), \(q=\frac{1}{3}\) and \(d_{\max } = 0.62\), and when \(T = 3\), \(q= 0\) and \(d_{\max } = 0.62\). Now when \(Z = 50\), \(q = 0.3\) when \(T = 35\) and \(q= 0.28\) when \(T=36\). The associated change in \(d_{\max }\) will be much smaller.
 
8
Interestingly, a pessimistic shift in one player’s prior may exacerbate the problem of the commons due to the strategic interactions.
 
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Metadata
Title
International Fisheries Agreements with a Shifting Stock
Authors
Florian K. Diekert
Emmi Nieminen
Publication date
23-03-2016
Publisher
Springer US
Published in
Dynamic Games and Applications / Issue 2/2017
Print ISSN: 2153-0785
Electronic ISSN: 2153-0793
DOI
https://doi.org/10.1007/s13235-016-0184-4

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