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On the performance of rule-based contribution schemes under endowment heterogeneity

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Abstract

We experimentally test different rule-based contribution mechanisms in a repeated 4-player public goods game with endowment heterogeneity and compare them to a VCM, distinguishing between a random and an effort-based allocation of endowments. We find that endowment heterogeneities limit the efficiency gains from these rule-based contribution schemes under random allocation. Under effort-based allocations, substantial efficiency gains relative to a VCM occur. These are largely driven by significant reductions of contributions in VCM, while the rule-based mechanisms generate stable efficiency levels, even though falling short in realizing the maximal efficiency gains. Our results indicate that the procedure of endowment allocation impacts the perception of what constitutes a fair burden sharing.

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Notes

  1. For the case of homogeneous marginal benefits, the payoff equation simplifies to \(\pi_{i} = e_{i} - q_{i} + bQ\) and correspondingly \(\sum\nolimits_{j = 1}^{n} {b_{j} = nb}\). Throughout the paper, we keep the notation \(b_{i}\) to allow for a more general application of our model. The Electronic Supplementary Material to this paper reports findings from an additional treatment to investigate the robustness of the eqpay rule in a setting with heterogeneous marginal benefits.

  2. Multiples of four are required.

  3. For deriving minimum individual contribution levels, integer numbers are required.

  4. Note that, given a specific binding \(Q^{min}\), voluntary contributions by high-type agents would be smaller in E-eqcont than under R-eqcont, but might be increased through the smaller \(Q^{min}\). As such, no prediction on the ranking for voluntary contributions is possible.

  5. It should be noted, however, that under effort-based allocation, eqcont may be expected to perform better than eqpay if high-type players feel to deserve a higher income than others: the distance in payoff between high- and low-types is constant in the range \(Q^{min} < 40\) in eqcont, while it decreases in eqpay (see Fig. 1). As such, high-type agents under effort-based allocation may block coordinating on positive minimum contribution levels.

  6. We observe the typical downward trends in contributions both under random and effort-based allocation (see also test for time trends in Table 7). Importantly, the gap in cooperative behavior between effort-based and random allocation persists over time.

  7. Considering the distribution of proposals allows gaining insights into possible motivation for this decline: under random allocation, 51% of low-type players’ suggestions correspond to their (potentially) payoff maximizing group contribution level (\(Q = 80\)), while less than 4% suggest a level which maximizes high-type players’ payoffs (\(Q = 40\)). Under effort-based endowment allocation, the rate of low-type players suggestions at \(Q = 80\) drops to 26%, while 13% of suggestions are at \(Q = 40\).

  8. It is noteworthy that players voluntarily go beyond the minimum contribution requirement. Under the equal-contribution rule, this applies particularly to high-type players (1.4), and less to low-types (0.7). Under the equal-payoff rule, this is reversed such that voluntary contributions largely stem from low-types (0.7) rather than high-types (0.1). As such, the equal-contribution rule appears to be seen as requiring disproportionately large contributions from low-types, while the equal-payoff rule may require too much from high-types.

  9. As can be seen from Fig. 4, average payoffs rather tend to decline over time, most notably in the last 5 periods.

  10. This is partly surprising, since even though binding minimum contribution levels on average remain in the range \(Q^{min} < 40\) where the distance in payoffs between both type of players decreases (see Fig. 1) high-type agents under effort-based allocation do not appear to block coordinating on positive minimum contribution levels.

  11. The corresponding Wald Test for the parameters estimated in regression (Table 6, column 5) confirm this finding for low-type players only for the eqpay rule but not for the eqcont rule (p[minQ + effXminQ = 0] = 0.23 and p[minQeq + effXminQeq] < 0.01).

  12. As a robustness check to the interpretation of our results for the equal-payoff rule under effort-based allocation, we carried out an additional treatment E-MPCR-eqpay which introduced heterogeneity with respect to the MPCR in addition to unequal endowments. For a discussion of the results, see the Electronic Supplementary Material to this paper.

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Acknowledgements

Financial support by the German Federal Ministry of Education and Research (FKZ 01UN1016A) is gratefully acknowledged. We thank the MaXLab team for their support in conducting the experiment.

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Authors and Affiliations

  1. Centre for European Economic Research (ZEW), Mannheim, Germany

    Martin Kesternich, Andreas Lange & Bodo Sturm

  2. University of Hamburg, Hamburg, Germany

    Andreas Lange

  3. Leipzig University of Applied Sciences, Leipzig, Germany

    Bodo Sturm

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  1. Martin Kesternich
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  2. Andreas Lange
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  3. Bodo Sturm
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Correspondence to Andreas Lange.

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Kesternich, M., Lange, A. & Sturm, B. On the performance of rule-based contribution schemes under endowment heterogeneity. Exp Econ 21, 180–204 (2018). https://doi.org/10.1007/s10683-017-9535-2

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