次优双边贸易的样本复杂度
Sample Complexity of the Second-Best Bilateral Trade
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中文总结 AI 辅助
该研究聚焦满足BIC、IIR、WBB的次优双边贸易机制，推导了正则乘积分布、乘性近似及满足MHR的无界分布下的样本复杂度上下界，明确了复杂度对次优贸易收益等基准的依赖关系。
中文摘要 AI 辅助
我们研究学习近最优双边贸易机制的样本复杂度。与先前学习简单或固定价格双边贸易机制的工作不同，我们关注满足贝叶斯激励相容（BIC）、中期个体理性（IIR）和事前弱预算平衡（WBB）的机制。换言之，我们的目标是设计一种基于样本的机制，使其达到次优贸易收益（second-best gains-from-trade）基准。我们在三种场景中给出了匹配或近乎匹配的上下界：对于[0,h]²上的正则乘积分布，加性ε近似的样本复杂度为$\boldsymbol{\tilde{\theta}}(h^2/\boldsymbol{\theta}^2)$；在相同假设下的乘性(1-α)近似中，样本复杂度为$\boldsymbol{\tilde{\theta}}(h/(\text{SB}(D)\boldsymbol{\theta}^2))$，该复杂度与基准相关，不可避免地依赖于次优贸易收益$\text{SB}(D)$；我们还研究了满足单调风险率（MHR）假设的无界分布，其样本复杂度依赖于比率$\boldsymbol{\tilde{\theta}}_\boldsymbol{\theta}(D)=\boldsymbol{\theta}(D)/\text{SB}(D)$，其中$\boldsymbol{\theta}(D)$是买方期望价值与卖方期望成本之和。
英文摘要
We study the sample complexity of learning near-optimal bilateral trade mechanisms. Unlike previous work on learning simple or fixed-price bilateral-trade mechanisms, we focus on mechanisms satisfying Bayesian incentive compatibility (BIC), interim individual rationality (IIR), and ex-ante weak budget balance (WBB). In other words, our target is to design a sample-based mechanism that achieves the second-best gains-from-trade benchmark. We give matching or nearly matching upper and lower bounds in three regimes. For regular product distributions on $[0,h]^2$, additive $\varepsilon$-approximation has sample complexity $\widetildeΘ(h^2/\varepsilon^2)$. For multiplicative $(1-α)$-approximation under the same assumptions, we find that the sample complexity is $\widetildeΘ(h/(\mathrm{SB}(D)α^2))$, which is benchmark-sensitive with unavoidable dependence on the second-best gains from trade $\mathrm{SB}(D)$. We also investigate unbounded distributions under a monotone hazard rate (MHR) assumption. The sample complexity depends on the ratio $χ_μ(D)=μ(D)/\mathrm{SB}(D)$, where $μ(D)$ is the sum of the buyer's expected value and the seller's expected cost.
