AI 中文总结
该研究针对需所有代理人一致参与的多边贸易机制设计问题，提出DSIC与BIC机制并给出福利近似比，还扩展至部分同意场景，得到匹配上下界。
AI 中文摘要
我们引入对“多边贸易”的研究：这是一个机制设计问题，其中一项潜在的单一交易涉及k个代理人，且只有当所有k个代理人都同意参与时，该交易才能执行。经典的k=2情形是被广泛研究的双边贸易问题，即拥有私人价值的卖方和买方必须决定是否交易卖方持有的一件物品。现有对双边贸易的扩展研究主要聚焦于拥有大量买方和卖方的市场，但其中每笔已实现的交易仍为双边交易，仅要求匹配的买方和卖方达成一致。我们的模型捕捉了交易本身需要联合参与的场景，这会耦合代理人的激励并产生新的挑战。我们在该场景下研究满足激励相容、个体理性和预算平衡的福利近似，提出了一种近似比为O(k²)的DSIC（占策略激励相容）机制，以及一种近似比为Õ(k^(3/2))的BIC（贝叶斯激励相容）机制，还证明了至多多对数因子的匹配下界。最后，我们将模型扩展至“k个代理人中至少l个参与”的部分同意场景，即当至少l个代理人参与时交易即可发生，在这种放松模型中，福利保证会随着无需参与的代理人数量（k−l）的增加而平滑提升，且我们得到了至多多对数因子的匹配上界和下界。
英文摘要
We introduce the study of \emph{multilateral trade}: a mechanism-design problem in which a single potential trade involves $k$ agents and can be executed only if all $k$ agents agree to participate. The classical case $k=2$ is the well-studied bilateral trade problem, where a seller and a buyer with private values must decide whether to trade an item initially held by the seller. Existing extensions of bilateral trade have largely focused on markets with many buyers and many sellers, but where each realized transaction is still bilateral, requiring agreement only between the matched buyer and seller. Our formulation captures settings in which the trade itself requires joint participation, coupling the agents' incentives and creating new challenges. We study welfare approximation in this setting under incentive compatibility, individual rationality, and budget balance. We give a DSIC mechanism with approximation ratio $O(k^2)$, and a BIC mechanism with approximation ratio $\widetilde O(k^{3/2})$. We prove matching lower bounds up to polylogarithmic factors. Finally, we extend the model to an $\ell$-out-of-$k$ partial-agreement setting, where the trade may occur once at least $\ell$ agents participate. In this relaxed model, the welfare guarantees improve smoothly as $k-\ell$, the number of agents whose participation is not required, grows, and we obtain matching upper and lower bounds up to polylogarithmic factors.
