The Opportunity Costs of Conservation with Deterministic and Probabilistic Degradation Externalities


This experimental study examines variations in the opportunity cost of conservation in two linear appropriation games that include symmetric and asymmetric subject payoffs. In the first game, appropriation leads to deterministic degradation in the value of a shared resource. In the second game, appropriation leads to both deterministic and probabilistic degradation, introducing endogenous uncertainty in the value of the opportunity cost of conserving the shared resource. The results show that subjects systematically decrease appropriation the lower the opportunity cost of conservation, and the addition of probabilistic degradation leads to further decreases in group appropriation. As conjectured, the response of individual subjects to the addition of probabilistic degradation is conditional on their expected marginal net benefits to appropriate, which depend in turn on their first order beliefs of others’ appropriation. The overall decreases in appropriation due to probabilistic degradation, however, are not large enough to offset decreases in expected efficiency due to expected losses in the value of the shared resource.

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  1. 1.

    Also see the Economics of Ecosystems and Biodiversity global initiative (; the UK National Ecosystem Assessment (; the Millennium Ecosystem Assessment (; or the Ecosystem Services for Poverty Alleviation (

  2. 2.

    It might be argued that equivalent information could be derived from decisions in the first round of a repeated game. Yet, the first-round decision of subjects in this context might be confounded with strategic signaling of willingness to engage in cooperative play.

  3. 3.

    This game builds on the appropriation game presented by Cox et al. (2013). Other studies using similar games but addressing framing differences between linear provision and appropriation games are Andreoni (1995), Sonnemans et al. (1998) and Dufwenberg et al. (2011).

  4. 4.

    A 50 % reduction in the value of the Group Fund was implemented to avoid the extreme case of a 100 % reduction, while maintaining a reduction that had important implications for experimental earnings. In addition, for experimental control and simplicity, the capacity to appropriate \((e)\) was set equal to 25, as described in Sect. 2.3. Therefore, if all subjects appropriate up to their capacity, the result is a 100 % chance of probabilistic degradation. Note, therefore, that the parameters of the DPD game imply settings with substantial probabilistic losses.

  5. 5.

    Other, less similar, experimental settings provide further evidence related to heterogeneities and levels of cooperation (see Marwell and Ames 1979; Ahn et al. 2007; Reuben and Riedl 2009).

  6. 6.

    Note that although the DPD game has two Nash equilibria when \({\textit{PB}_{i}}\) \(=\) 0.6, the minimum and maximum possible group payoffs used for calculating efficiency are not affected. The minimum payoffs are still those of the Nash equilibrium with appropriation up to capacity.

  7. 7.

    Examining the effects of asymmetries in appropriation games has focused primarily on players’ positions rather than marginal incentives. Hackett et al. (1994) and Holahan (2011) examine CPR settings where subjects have communication or voting opportunities to facilitate cooperation, where subjects receive differential returns from agreements that are linked to the capacity to appropriate. Cardenas et al. (2011) and Janssen et al. (2012) examine settings where CPR users face sequential decisions, introducing asymmetries through the position (order) each subject has in making appropriation decisions.

  8. 8.

    Average earnings (in US$), including the forecast bonus, were for the DD games 13.96 (DD-MedPB), 14.83 (DD-HighPB), 13.40 (DD-LowPB), 16.22 (DD-Asym(PB\(_{i}=1.4\))), and 11.36 (DD-Asym(PB\(_{i}=0.6\))). For the DPD games, average earnings, with the forecast bonus, were 9.71 (DPD-MedPB), 11.61 (DPD-HighPB), 9.36 (DPD-LowPB), 11.71 (DPD-Asym(PB\(_{i}=1.4\))), and 7.44 (DPD-Asym(PB\(_{i}=0.6\))). In addition to these experimental earnings, subjects received a show-up payment of $ 2.83.

  9. 9.

    Using our notation, the baseline appropriation game of Cox et al. (2013) is parameterized with \({\textit{PB}_{i}}=1\) and \(g=3\). Based on the relative value of \(g/PB_i= 3/1\), our decision setting LowPB (where \(g/h=2/0.6=3.33\)) comes closest to matching the marginal incentives in their appropriation game. Cox et al. observe an average individual appropriation of 38.1 % of maximum appropriation capacity, nearly identical to the 37.8 % observed in LowPB decision setting in our study.

  10. 10.

    Across all decision settings, 18.26 % of the forecasts of the per-person appropriation of other group members are identical to the decision makers’ own decision. Table 2 shows that the mean forecasts of others’ individual appropriation levels (potentially ranging between 0 and 25) follow a pattern across decision settings that is very similar to the pattern observed for average individual appropriation levels. However, across all decision settings, there is a clear “upward shift” in average per-person forecasts relative to actual appropriation levels. Thus, on average subjects’ beliefs of the cooperative behavior of other group members are overly pessimistic. Further, for the same value of \({\textit{PB}_{i}}\), forecasts for symmetric and asymmetric decisions are very similar; and lower for the DPD games relative to the DD games.

  11. 11.

    Other results regarding the average group effect in asymmetric decision settings are somewhat mixed. As shown in Table 3 panel A for the DD game, average appropriation in the asymmetric decision settings with an average value of PB \(=\) 1 (DD-Asym(pooled PB)) is not statistically different to that of symmetric decision settings where \({\textit{PB}_{i}}\) \(=\) 1 (DD-MedPB). However, for the same decision settings in the DPD game, as shown in Table 3 panel B, there is a weakly significant effect (at the 10 % level of significance) due to asymmetry, with average appropriation being higher in the asymmetric decision setting.

  12. 12.

    Based on the first order beliefs, for the DPD games, the percentage of subjects that forecasted a group appropriation greater than 50 tokens is 26.56 % for DPD-LowPB, 39.84 % for DPD-MedPB, 53.13 % for DPD-HighPB, 20.31 % for DPD-Asym(PB\(_{i}=0.6\)) and 20.31 % for DPD-Asym(PB\(_{i}=1.4\)).

  13. 13.

    For the asymmetric treatment condition DPD-Asym(pooled), individual specific PB values were used for computing \(\hbox {MNB}_\mathrm{i}^{\prime }\). The results for the perceived \(\hbox {MNB}_\mathrm{i}^{\prime }\) at the individual level are robust to computing the value of the \(\hbox {MNB}_\mathrm{i}^{\prime }\) based only on forecasts of the other 3 group members’ appropriation.

  14. 14.

    In order to assess the potential existence of interaction effects between asymmetry and probabilistic degradation, an additional analysis for the pooled asymmetric treatment was conducted that included a dummy variable for low-PB, the continuous variable \(\hbox {MNB}_\mathrm{i}^{\prime }\), and the interaction of these two variables. As expected, the coefficients found in this analysis correspond to those presented in columns 4 and 5 of Table 6. The constant term and the coefficients for the low-PB dummy and the \(\hbox {MNB}_\mathrm{i}^{\prime }\) variable are statistically significant. The interaction term, however, is not significant. Thus, the latter result does not support the existence of robust differential responses to \(\hbox {MNB}_\mathrm{i}^{\prime }\) between high and low-PB subjects in the asymmetric treatments.


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Financial support was provided by the University of Innsbruck. The authors also acknowledge the support of the National Science Foundation (Grant Number SES-0849551). We are grateful to Paula Andrea Zuluaga, Adriana Beltran and Tobias Haller for their outstanding assistance and to Glenn Dutcher, Brock Stoddard, and participants in the 5th World Congress of Environmental and Natural Resource Economists and in the Experimental Reading Group of the University of Innsbruck for comments on previous versions of this paper.

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Correspondence to Esther Blanco.

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Blanco, E., Lopez, M.C. & Walker, J.M. The Opportunity Costs of Conservation with Deterministic and Probabilistic Degradation Externalities. Environ Resource Econ 64, 255–273 (2016).

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  • Asymmetry
  • Social dilemma
  • Cooperation
  • Laboratory experiment

JEL Classfication

  • D7
  • H4
  • C90