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

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.