对福利最大化自动竞价均衡的紧近似性分析
Tight Inapproximability for Welfare-Maximizing Autobidding Equilibria
AI总结：
该研究证明了在自动竞价拍卖中，计算接近最优福利和收益的均衡是NP难的，并揭示了近似性阈值与价格无效率之间的紧密联系。
摘要：
我们研究了在受回报率支出（RoS）约束的自动竞价第二价格拍卖中，计算福利和收益最大化均衡的复杂性。我们证明，对于任何常数ε>0，计算一个近似福利最优解的因子为2-ε的自动竞价均衡是NP难的。此外，决定是否存在一个达到最优福利1/2+ε分数的自动竞价均衡（不受均衡约束限制）也是NP难的，对于任何常数ε>0。这一难度结果在价格无效率（PoA）最大为2的背景下是紧的，表明决定是否存在非平凡的自动竞价均衡——即使比最坏保证略好——也是难以处理的。在收益方面，我们建立了更强的对数近似性，而在投影游戏猜想下，我们的减少规则出乎意料地排除了甚至多项式近似因子。这些结果显著加强了李和唐（AAAI '24）的APX难问题。此外，我们在存在机器学习建议的情况下细化了我们的减少，再次揭示了近似性阈值与PoA界限之间的紧密联系。最后，我们研究了由简单学习算法获得的放松均衡概念，证明了收益和福利的常数近似性。
英文摘要：
We examine the complexity of computing welfare- and revenue-maximizing equilibria in autobidding second-price auctions subject to return-on-spend (RoS) constraints. We show that computing an autobidding equilibrium that approximates the welfare-optimal one within a factor of $2 - ε$ is NP-hard for any constant $ε> 0$. Moreover, deciding whether there exists an autobidding equilibrium that attains a $1/2 + ε$ fraction of the optimal welfare -- unfettered by equilibrium constraints -- is NP-hard for any constant $ε> 0$. This hardness result is tight in view of the fact that the price of anarchy (PoA) is at most $2$, and shows that deciding whether a non-trivial autobidding equilibrium exists -- one that is even marginally better than the worst-case guarantee -- is intractable. For revenue, we establish a stronger logarithmic inapproximability, while under the projection games conjecture, our reduction rules out even a polynomial approximation factor. These results significantly strengthen the APX-hardness of Li and Tang (AAAI '24). Furthermore, we refine our reduction in the presence of ML advice concerning the buyers' valuations, revealing again a close connection between the inapproximability threshold and PoA bounds. Finally, we examine relaxed notions of equilibrium attained by simple learning algorithms, establishing constant inapproximability for both revenue and welfare.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
