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Strength in Numbers Robust Mechanisms for Public Goods with Many Agents

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Document pages: 41 pages

Abstract: This study examines the mechanism design problem for public goods in a modelwith independent private values. We propose a class of informationally robust,dominant-strategy incentive compatible (DSIC), and ex post individual rational(EPIR) mechanisms that are asymptotically ex ante budget balanced (AEABB) andasymptotically efficient (AE) as the population grows. The decision rule isconstructed in two steps: First, each valuation is transformed with anincreasing function and centered to be mean zero. Then the public good isallocated if the sum of transformed valuations exceeds a threshold that onlydepends on the population size $n$. The increasing function can be chosenarbitrarily. For example, it can simply be the identity function. Our resultsshow that the rate of change of the threshold is the key to characterizing thetrade-off between budget balance and efficiency. In particular, using themultivariate Berry-Esseen theorem, our results demonstrate that when this rateis controlled within the range from $ sqrt{n}$ to $ sqrt{n log n}$, themechanism can be AEABB and AE at the same time as long as the cost does notgrow too rapidly. One advantage of the proposed mechanisms is theirinformational robustness as they depend only on certain moments of thevaluation distributions. In contrast, previous mechanisms proposed to solvethis question, such as the second-best mechanism, typically require theknowledge of the entire valuation distribution. Also, our study extends theresults to non-binary decision environments with general utility functions.Lastly, we show that if the threshold is instead set equal to the cost, theproposed mechanism can achieve a non-negligible fraction of the optimal profitin the limit, where the fraction is the correlation between the virtual valueand the aforementioned transformed value.

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