This paper studies the robust mechanism design problem of a public good when there are many agents . We propose a class of dominant strategy incentive compatible (DSIC)  and ex post individual rational (EPIR) mechanisms that balance the budget and approximates the first-best welfare level when the number of participants is large . The decision rule is based on thresholding the sum of transformed valuations of the agents. We show that the rate of change of the threshold is the key to characterizing the trade-off between balancing the budget and maximizing the welfare . In particular, we find that when this rate is controlled in a certain range , the two goals can be achieved to \sqrt{n \log n}, the mechanism can be AEABB and AE } at the same time asymptotically. The proposed mechanisms are robust in two ways: first, they depend on the valuation distributions only through certain moments ; second, they allow for asymmetric and irregular valuation distributions. More specifically, we show that the Myerson regularity condition plays no role in this constrained problem of welfare approximation. In addition to welfare approximation, we also study profit approximation using similar mechanisms but with a different threshold and show that a fraction of the optimal profit can be achieved with a large number of participants. Lastly, we extend the model to accommodate for non-binary decision and general utility functions .
This study examines the mechanism design problem for public goods in a model with 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) and asymptotically efficient (AE) as the population grows . The decision rule is constructed in two steps: First, each valuation is transformed with an increasing function and centered to be mean zero. Then the public good is allocated if the sum of transformed valuations exceeds a threshold that only depends on the population size n. The increasing function can be chosen arbitrarily. For example, it can simply be the identity function. Our results show that the rate of change of the threshold is the key to characterizing the trade-off between budget balance and efficiency . In particular, using the multivariate Berry-Esseen theorem, our results demonstrate that when this rate is controlled within the range from \sqrt{n to \sqrt{n \log n}, the mechanism can be AEABB and AE } at the same time as long as the cost does not grow too rapidly. One advantage of the proposed mechanisms is their informational robustness as they depend only on certain moments of the valuation distributions. In contrast, previous mechanisms proposed to solve this question, such as the second-best mechanism, typically require the knowledge of the entire valuation distribution. Also, our study extends the results to non-binary decision environments with general utility functions. Lastly, we show that if the threshold is instead set equal to the cost, the proposed mechanism can achieve a non-negligible fraction of the optimal profit in the limit, where the fraction is the correlation between the virtual value and the aforementioned transformed value .
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of a public good when there are many agents
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balance the budget and approximates the first-best welfare level when the number of participants is large
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constructed in two steps: First, each valuation is transformed with an increasing function and centered to be mean zero. Then the public good is allocated if the
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of the agents. We
exceeds a threshold that only depends on the population size n. The increasing function can be chosen arbitrarily. For example, it can simply be the identity function. Our results
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balancing the budget and maximizing the welfare
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using the multivariate Berry-Esseen theorem, our results demonstrate
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in a certain range , the two goals can be achieved
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asymptotically. The proposed mechanisms are robust in two ways: first, they depend on the valuation distributions only through certain moments ; second, they allow for asymmetric and irregular
as long as the cost does not grow too rapidly. One advantage of the proposed mechanisms is their informational robustness as they depend only on certain moments of the
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More specifically, we show that the Myerson regularity condition plays no role in this constrained problem of welfare approximation. In addition to welfare approximation, we also study profit approximation using similar mechanisms but with a different threshold and show that a
In contrast, previous mechanisms proposed to solve this question, such as the second-best mechanism, typically require the knowledge of the entire valuation distribution. Also, our study extends the results to non-binary decision environments with general utility functions. Lastly, we show that if the threshold is instead set equal to the cost, the proposed mechanism can achieve a non-negligible
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can be achieved with a large number of participants. Lastly, we extend the model to accommodate for non-binary decision and general utility functions
in the limit, where the fraction is the correlation between the virtual value and the aforementioned transformed value