We present a best-response based algorithm for computing verifiable $\varepsilon$-perfect Bayesian equilibria for sequential auctions with combinatorial bidding spaces and incomplete information. Previous work has focused only on computing Bayes-Nash equilibria for static single-round auctions, which our work captures as a special case. Additionally, we prove an upper bound $\varepsilon$ on the utility loss of our approximate equilibria and present an algorithm to efficiently compute $\varepsilon$ based on the immediate loss at each subgame. We evaluate the performance of our algorithm by reproducing known results from several auctions previously introduced in the literature, including a model of combinatorial split-award auctions used in procurement.

翻译：我们提出了一种基于最优反应的算法，用于计算组合竞价空间和不完全信息下序贯拍卖的可验证 $\varepsilon$-完美贝叶斯均衡。以往工作仅关注静态单轮拍卖中的贝叶斯-纳什均衡计算，而我们的工作将其作为特例纳入。此外，我们证明了近似均衡的效用损失上界 $\varepsilon$，并给出了一种基于每个子博弈即时损失高效计算 $\varepsilon$ 的算法。通过复现文献中多个已有拍卖模型（包括采购中使用的组合分标拍卖模型）的已知结果，我们评估了算法的性能。