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Published in: Social Choice and Welfare 1/2022

05-07-2021 | Original Paper

Does the approval mechanism induce the efficient extraction in common pool resource games?

Authors: Koffi Serge William Yao, Emmanuelle Lavaine, Marc Willinger

Published in: Social Choice and Welfare | Issue 1/2022

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Abstract

Masuda et al. (Games Econ Behav 83:73–85, 2014) showed that the minimum approval mechanism (AM) implements the efficient level of public good theoretically and experimentally in a linear public good game. We extent this result to a two-players common pool resource (CPR) game. The AM adds a second stage into the extraction game. In the first stage, each group member proposes his level of extraction. In the second stage, the proposed extractions and associated payoffs are displayed and each player is asked to approve or to disapprove both proposed extractions. If both players approve, the proposals are implemented. Otherwise, a uniform level of extraction, the disapproval benchmark (DB), is imposed onto each player. We consider three different DBs: the minimum proposal (MIN), the maximum proposal (MAX) and the Nash extraction level (NASH). We derive theoretical predictions for each DB following backward elimination of weakly dominated strategies (BEWDS). We first underline the strength of the AM, by showing that the MIN implements the optimum theoretically and experimentally. The sub-games predicted under the NASH are Pareto improving with respect to the Nash equilibrium. The MAX leads, either to Pareto improving outcomes with respect to the free access extractions, or to a Pareto degradation. Our experimental results show that the MAX and the NASH reduce the level of over-extraction of the CPR. The MAX leads above all to larger reductions of (proposed and realized) extractions than the NASH.

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Appendix
Available only for authorised users
Footnotes
1
The unanimity approval rule is a particular case. One may consider other rules, such as the majority rule.
 
2
A pro-social player aims at maximizing the joint payoff of himself and the other party, as the benevolent social planner. On the other hand, a selfish rational player maximizes only his own payoff without regard to the others payoff. Therefore if the AM induces a social optimum level of extraction for a selfish player, it also does so for any player whose preferences support pro-social behavior.
 
3
Low contributions to public goods, over-extraction from CPRs or high levels of emission of pollutants.
 
4
Under the MIN, voluntariness is satisfied only if total group extraction is above the threshold \(X=(a-p)/b\). However, it is not satisfied under the MAX as mentionned in appendix 6.7.
 
5
1 token is equal to 3 units of CPR extraction level.
 
6
Secondly, we show that Pareto-efficient sub-game \(({\hat{x}}, {\hat{x}})\) weakly dominates other symmetrical sub-games. The two players determine the outcome of the DB in the set of a uniform extraction vectors. To do so, player i maximizes his payoff under the constraint of uniform extraction vector: maximize \(\pi _{i}(x_{i},x_{j})\) wrt \(x_{i}=x_{j}\). The solution of this problem is the Pareto-efficient extraction level \({\hat{x}}=\frac{a-p}{4b}=6\) tokens, \({\hat{\pi }}=\frac{(a-p)^{2}}{8b}+pw=312\) ecus and \({\hat{X}}=\frac{a-p}{2b}=12\) tokens.
 
7
The authors would like to thank Dimitri Dubois, from the Experimental Economic Laboratory of Montpellier (LEEM) for technical support.
 
8
Center for environmental economics - Montpellier.
 
10
The period dummy corresponds to twice 10 periods in order to take into account the 10 periods timing of the game.
 
11
the comparison between NASH and MAX versus MIN, as well as NASH, and MIN versus NASH is not of interest; that is why they are alternatively removed from the sample.
 
12
This test is based on 40 independent observations.
 
13
This test is based on 20 independent observations (10 observations per sequence).
 
14
This test is based on 20 independent observations (10 observations per sequence).
 
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Metadata
Title
Does the approval mechanism induce the efficient extraction in common pool resource games?
Authors
Koffi Serge William Yao
Emmanuelle Lavaine
Marc Willinger
Publication date
05-07-2021
Publisher
Springer Berlin Heidelberg
Published in
Social Choice and Welfare / Issue 1/2022
Print ISSN: 0176-1714
Electronic ISSN: 1432-217X
DOI
https://doi.org/10.1007/s00355-021-01342-x

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