Abstract
In a laboratory experiment we test three regulations imposed on a common-pool resource game with heterogeneous users: an access fee and subsidy scheme, transferable quotas and non-transferable quotas. We calibrate the game so that all regulations improve users’ profits compared to free-access extraction. We compare the regulations according to five criteria: resource preservation, individual profits, profit difference, Pareto-improvement from free-access and sorting of the most efficient users. One of the main findings is that, even though it performs better in sorting out the most efficient subjects, the fee and subsidy scheme is not more profitable than tradable quotas.
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Notes
Apesteguia (2006) studied behavioral consequences of two degrees of information on CPR (complete vs. incomplete information) and found that information does not alter behaviors, i.e., both levels of information lead to the convergence of the aggregate effort towards the Nash equilibrium.
This repeated “Partners” design is more realistic as agents share common pool resources repeatedly. Moreover, with two groups per session, we double the number of independent observations compared to a “Strangers” design.
A special feature of CPRs is that by investing \(x\) units of extracting effort, an individual obtains a share \(\frac{x}{X}\) of total extraction (or harvest) \(X\phi (X)\). The linear form \(a-bX\) is standard in CPR experiments (Janssen and Ostrom 2006).
As pointed out above, our intension is not to test behaviors in the FA regime but rather to assess the performance of regulations in improving welfare from a non-cooperative equilibrium of the FA benchmark. That is why we set up quite a straightforward benchmark game.
Since the average product \(\phi (X)\) is decreasing with CPR extraction \(X\), the return on the CPR \(\phi (X)\) is always lower than on the outside option \(c_i\) for player of type \(i=A,B\) for any \(X \le 32\).
Note that the first best CPR extraction level is \(X=12\). Implementing the first-best would require one to assign \(1.5\) quota units to each subject and, therefore, to divide the quotas.
Due to the lump-sum nature of \((\tau ,\sigma )\), all other incentive-compatibility constraints can be ignored. By the other incentive-compatible constraints, we mean those that prevent any player from investing only part of his or her endowment in the CPR, rather than all (for types \(A\)) or nothing (for types \(B\)).
Recall that the TQ game is dynamic since it involves two decisions in turn: a strategy in the quota market and an investment decision. Given the market equilibrium outcome, the investment strategy described is a Nash equilibrium of the investment subgame. In the previous market stage, given the selling and buying strategy of the other players, a type \(A\) (resp. type B) player’s best response is to buy (resp. to sell) 2 quotas.
Ambec and Sebi (2011) provide a more complete theoretical comparison of all three instruments, including the Pareto-improvement criteria and fairness considerations.
When the number of bids differs from the number of asks, the bidders or sellers not supplied are determined randomly.
Based on the estimated coefficients for model (1), the predicted Nash deviation in absolute value for period 5 is 0.5 compared to 0.42 for period 7. At the first period it is equal to 0.9.
We have also considered some other specifications of the model including higher lags (\(T=2, 3\)) and the strategy used each player in the previous period. Results are consistent with the ones presented in Table 2.
Subjects do not seek the social optimum which is obtained in our setup when the four players \(A\) extract at their maximum capacity and when the four players \(B\) extract one unit each: only 3 % of players \(B\) extract fewer than 2 units.
Consequent to the results of the learning equation estimates in the previous section, we performed the Wilcoxon signed rank tests without taking into account the first three periods. The results stress the ones that we report with 7 periods: \(p \ge 0.1439\) for NTQ and FS, \(p \ge 0.6246\) for NTQ and TQ and \(p \ge 0.1214\) for FS and TQ.
We get a pseudo \(\mathrm{R}^2\) equal to 0.2 which corresponds to a relatively poor predictive power of the logit model. However, at a probability cutoff equal to 0.50, 74 % of the subjects are well classified by the model.
These results are robust even if we exclude the first periods for which the learning effect has been shown to be strong. For instance, if we restrict the sample to periods 3–7, we obtain some estimated coefficients for \(TYPE_B\) and \(TREAT_{FS}\) significant at 1 % and respectively equal to 0.244 and 1.661.
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We wish to thank Jean-Loup Dupuis for technical assistance with the computer laboratory and Liz Libbrecht for editorial assistance. We thank the Editor and two anonymous referees for useful suggestions that improved the paper. We also acknowledge the participants in various conferences (including EAERE 2008) and seminars for comments. This research received financial support from the French National Research Agency through the project ANR-08-JCJC-0111-01.
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Ambec, S., Garapin, A., Muller, L. et al. Comparing Regulations to Protect the Commons: An Experimental Investigation. Environ Resource Econ 58, 219–244 (2014). https://doi.org/10.1007/s10640-013-9700-9
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DOI: https://doi.org/10.1007/s10640-013-9700-9