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Maximizing Gains from Trade in Two-Sided Markets through Two-Sided Recruitment


Core Concepts
Augmenting a two-sided market with a constant number of additional buyers and sellers can enable a simple, prior-independent mechanism to achieve gains from trade at least as high as the optimal mechanism in the original market.
Abstract
The paper studies the problem of maximizing the gains from trade (GFT) in two-sided markets, where there are m unit-demand buyers and n unit-supply sellers. The authors consider the double auction setting and focus on the GFT as the measure of efficiency. The key insights are: Seller Trade Reduction (STR), a variant of the Trade Reduction mechanism, can achieve GFT at least as high as the first-best GFT in the original market by augmenting the market with a constant number of additional buyers and sellers, when the buyers' value distribution first-order stochastically dominates the sellers' distribution. For any ε > 0 and any set of O(1/ε) buyers and O(1/ε) sellers where the buyers' value exceeds the sellers' value with constant probability, augmenting these agents into any market allows the Trade Reduction mechanism to achieve a (1-ε)-approximation of the optimal GFT in the augmented market, without any knowledge of the original market. The key technical contributions are: Constructing carefully designed "good" and "bad" events to analyze the GFT difference between STR and the first-best allocation in the augmented market. Developing a coupling argument to show that the optimal GFT comes mainly from instances where there are a large number of trades, enabling a constant-factor approximation result.
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Key Insights Distilled From

by Yang Cai,Chr... at arxiv.org 04-01-2024

https://arxiv.org/pdf/2307.03844.pdf
The Power of Two-sided Recruitment in Two-sided Markets

Deeper Inquiries

How can the results be extended to settings with multi-dimensional or combinatorial valuations

The results obtained in the paper can be extended to settings with multi-dimensional or combinatorial valuations by considering a more complex valuation structure for the buyers and sellers. In multi-dimensional settings, each agent's value is determined by multiple attributes or dimensions, leading to a more intricate valuation space. The Trade Reduction mechanism can still be applied in these settings, but the optimization problem becomes more challenging due to the increased complexity of the valuation space. To extend the results to multi-dimensional valuations, the mechanism designer would need to consider how to match agents based on their multidimensional values while ensuring incentive compatibility, individual rationality, and budget balance. This may involve developing new algorithms or mechanisms that can handle the multidimensional nature of the valuations and still achieve a good approximation to the optimal GFT.

What are the implications of these results on the design of practical two-sided market mechanisms

The implications of these results on the design of practical two-sided market mechanisms are significant. By showing that augmenting the market with a constant number of buyers and sellers can lead to a good approximation of the optimal GFT using the Trade Reduction mechanism, the research provides insights into how to improve efficiency in two-sided markets without requiring detailed knowledge of the agents' distributions. Practically, these results suggest that platform operators in two-sided markets can enhance their market outcomes by recruiting additional participants on both sides of the market. This recruitment strategy can lead to increased competition, better matching of buyers and sellers, and ultimately higher gains from trade. By implementing simple and prior-independent mechanisms like Trade Reduction, market operators can achieve close-to-optimal results without the need for complex and distribution-specific mechanisms. The findings also highlight the importance of understanding the structure of two-sided markets and the potential benefits of increasing the number of participants to improve market efficiency and outcomes.

Can similar techniques be applied to analyze the revenue-maximizing objective in two-sided markets

Similar techniques can be applied to analyze the revenue-maximizing objective in two-sided markets by adapting the approach used in the paper to focus on revenue optimization rather than gains from trade. The key idea would be to explore how augmenting the market with additional buyers and sellers can impact revenue generation in two-sided markets. The research could investigate how the Trade Reduction mechanism or other simple mechanisms can be used to maximize revenue in two-sided markets by recruiting additional participants. By studying the revenue-maximizing objective and considering the impact of augmentation on revenue outcomes, insights can be gained into how platform operators can design mechanisms to optimize revenue while maintaining incentive compatibility and market efficiency. Overall, applying similar techniques to revenue optimization in two-sided markets can provide valuable insights into how market mechanisms can be designed to maximize revenue while ensuring a fair and efficient marketplace for all participants.
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