We provide the first separation in the approximation guarantee achievable by truthful and non-truthful combinatorial auctions with polynomial communication. Specifically, we prove that any truthful mechanism guaranteeing a $(\frac{3}{4}-\frac{1}{240}+\varepsilon)$-approximation for two buyers with XOS valuations over $m$ items requires $\exp(\Omega(\varepsilon^2 \cdot m))$ communication, whereas a non-truthful algorithm by Dobzinski and Schapira [SODA 2006] and Feige [2009] is already known to achieve a $\frac{3}{4}$-approximation in $poly(m)$ communication. We obtain our separation by proving that any {simultaneous} protocol ({not} necessarily truthful) which guarantees a $(\frac{3}{4}-\frac{1}{240}+\varepsilon)$-approximation requires communication $\exp(\Omega(\varepsilon^2 \cdot m))$. The taxation complexity framework of Dobzinski [FOCS 2016] extends this lower bound to all truthful mechanisms (including interactive truthful mechanisms).

中文翻译：

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分离真实和非真实组合拍卖的传播复杂性

我们提供了可通过多项式通信的真实和非真实组合拍卖实现的近似保证中的第一次分离。具体来说，我们证明了任何保证 $(\frac{3}{4}-\frac{1}{240}+\varepsilon)$-近似值的 XOS 估值超过 $m$ 物品的两个买家的真实机制都需要 $\ exp(\Omega(\varepsilon^2 \cdot m))$ 通信，而 Dobzinski 和 Schapira [SODA 2006] 和 Feige [2009] 的非真实算法已经知道实现 $\frac{3}{4 }$-$poly(m)$ 通信中的近似值。我们通过证明任何保证 $(\frac{3}{4}-\frac{1}{240}+\varepsilon)$-approximation 的 {simultaneous} 协议（{不一定是真实的）需要通信来获得我们的分离$\exp(\Omega(\varepsilon^2 \cdot m))$。