[论文解读] Optimal dynamic mechanisms with ex-post IR via bank accounts

Vahab Mirrokni, Renato Paes Leme+2 more|arXiv (Cornell University)|May 28, 2016

Auction Theory and ApplicationsDecision Sciences参考文献 20被引用 19

一句话总结

本文提出了银行账户机制——一种简单且可实现的动态机制，在多阶段设置中实现最优收益，且满足事后个体理性。通过使用银行账户追踪各阶段的效用盈余与赤字，作者证明此类机制可在常数因子内近似最优收益，并为离散类型空间提供了FPTAS。

ABSTRACT

Lately, the problem of designing multi-stage dynamic mechanisms has been shown to be both theoretically challenging and practically important. In this paper, we consider the problem of designing revenue optimal dynamic mechanism for a setting where an auctioneer sells a set of items to a buyer in multiple stages. At each stage, there could be multiple items for sale but each item can only appear in one stage. The type of the buyer at each stage is thus a multi-dimensional vector characterizing the buyer's valuations of the items at that stage and is assumed to be stage-wise independent. In particular, we propose a novel class of mechanisms called bank account mechanisms. Roughly, a bank account mechanism is no different from any stage-wise individual mechanism except for an augmented structure called bank account, a real number for each node that summarizes the history so far. We first establish that the optimal revenue from any dynamic mechanism in this setting can be achieved by a bank account mechanism, and we provide a simple characterization of the set of incentive compatible and ex-post individually rational bank account mechanisms. Based on these characterizations, we then investigate the problem of finding the (approximately) optimal bank account mechanisms. We prove that there exists a simple, randomized bank account mechanism that approximates optimal revenue up to a constant factor. Our result is general and can accommodate previous approximation results in single-shot multi-dimensional mechanism design. Based on the previous mechanism, we further show that there exists a deterministic bank account mechanism that achieves constant-factor approximation as well. Finally, we consider the problem of computing optimal mechanisms when the type space is discrete and provide an FPTAS via linear and dynamic programming.

研究动机与目标

• 解决在多阶段物品销售中设计简单、收益最优的动态机制以满足事后个体理性的挑战。
• 克服现有动态机制因高承诺要求而复杂且不切实际，且缺乏个体理性的局限。
• 开发一种机制类别，实现在各阶段间进行效用存贷，同时保持激励相容与个体理性。
• 提供一种计算高效的近似方法，用于离散类型空间中的最优收益。
• 建立常数因子近似与通过FPTAS实现精确计算的理论基础。

提出的方法

• 提出银行账户机制，通过引入一个实值银行账户追踪累积效用偏差，扩展阶段内机制。
• 利用银行账户存储并抵消前期阶段的效用赤字或盈余，实现长期效用平衡。
• 通过分配与支付规则的结构约束，刻画激励相容且事后个体理性的银行账户机制。
• 设计一种随机化银行账户机制，实现最优收益的常数因子近似。
• 构建银行账户机制的确定性变体，同样实现常数因子近似。
• 针对离散类型空间，利用线性与动态规划技术，开发一种FPTAS以计算最优机制。

实验结果

研究问题

• RQ1 是否存在一种简单、可实现的动态机制，可在确保事后个体理性的同时实现最优收益？
• RQ2 是否存在一种机制类别，允许在各阶段间进行效用存贷，而不牺牲激励相容性？
• RQ3 与最优动态机制相比，随机化银行账户机制可实现的近似比是多少？
• RQ4 确定性银行账户机制是否能实现与随机版本相同的常数因子近似？
• RQ5 是否存在一种高效算法，可在离散类型空间中计算近似最优机制？

主要发现

• 在多阶段设置中，任何动态机制的最优收益均可通过银行账户机制实现。
• 一种简单且随机化的银行账户机制可实现最优收益的常数因子近似。
• 确定性银行账户机制同样可实现最优收益的常数因子近似。
• 对于离散类型空间，本文通过线性与动态规划技术，提供了计算最优机制的FPTAS。
• 近似过程所需的查询次数被限制在 O(max_ξ φ(ξ)/δ + log(β_a - β_b)/(-β_b)) 以内，确保了效率。
• 通过银行账户允许效用向前结转，机制设计确保了事后个体理性，防止在任何历史后出现负效用盈余。