AI 中文总结
该研究针对策略智能体，提出自筹资金市场的机制设计问题，证明现有 truthful auction 近似性能上限，给出序贯 auction 实现对数级近似，还设计 auction 实现最大最小份额基准的常数级近似。
AI 中文摘要
我们提出了激励策略智能体形成自筹资金市场的机制设计问题。在我们的模型中，若智能体\textit{i}付出努力\textit{x}\textsubscript{i}∈[0,1]，则会产生成本\textit{x}\textsubscript{i}·\textit{c}\textsubscript{i}（其中\textit{c}\textsubscript{i}对机制设计者未知），并产生收益\textit{x}\textsubscript{i}·\textit{r}\textsubscript{i}；关键在于，\textit{c}\textsubscript{i}可大于或小于\textit{r}\textsubscript{i}。每个努力配置\textbf{x}产生价值\textit{v}(\textbf{x})，目标是选择努力向量以最大化价值，同时确保每个智能体\textit{i}获得支付\textit{p}\textsubscript{i}≥\textit{x}\textsubscript{i}·\textit{c}\textsubscript{i}，且\textbf{x}是预算平衡的，即∑\textsubscript{i}\textit{p}\textsubscript{i}≤∑\textsubscript{i}\textit{x}\textsubscript{i}·\textit{r}\textsubscript{i}。该问题推广了已被广泛研究的预算可行机制设计问题，后者要求∑\textsubscript{i}\textit{p}\textsubscript{i}≤\textit{B}，其中\textit{B}为预定预算。为评估此类机制的性能，我们首先考虑最优基准（无任何私人信息时可实现的最优价值），并证明无 truthful auction 能实现该基准的有界近似。此外，即使在受限设定中，也无 auction 能实现优于对数级的近似。我们通过提出一类序贯 auction 补充这些结果，其子博弈完美均衡保证该基准的对数级近似。随后，我们引入另一基准——最大最小份额（MMS），其能更好地体现市场的厚度，我们提供的 auction 其子博弈完美均衡可实现该基准的常数级近似。
英文摘要
We introduce the problem of designing mechanisms that incentivize strategic agents to form self-funded marketplaces. In our model, if agent $i$ exerts effort $x_i\in [0,1]$, they incur a cost of $x_i\cdot c_i$ (where $c_i$ is unknown to the mechanism designer) and they generate revenue $x_i\cdot r_i$; crucially, $c_i$ can be greater or smaller than $r_i$. Each effort profile $\mathbf{x}$ yields value $v(\mathbf{x})$ and the objective is to choose an effort vector that maximizes the value while ensuring that every agent $i$ receives a payment $p_i\geq x_i\cdot c_i$ and that $\mathbf{x}$ is budget-balanced, i.e., $\sum_{i} p_i \leq \sum_{i} x_i\cdot r_i$. This problem generalizes the well-studied budget-feasible mechanism design problem, where the requirement is that $\sum_{i} p_i \leq B$ for some predetermined budget $B$. To evaluate the performance of such mechanisms, we first consider the first-best benchmark (the optimal value achievable in the absence of any private information) and show that no truthful auction can achieve a bounded approximation of this benchmark. Also, even in restricted settings, no auction can achieve better than a logarithmic approximation. We complement these results by proposing a class of sequential auctions whose subgame perfect equilibria guarantee a logarithmic approximation of this benchmark. We then introduce an alternative benchmark, the maximin share (MMS), that better captures the thickness of the market and we provide an auction whose subgame perfect equilibria achieve a constant approximation of this benchmark.
CommentsExtended Abstract accepted 27th ACM Conference on Economics and Computation (ACM EC 2026)
