动态社会选择问题中真实报告的风险最小化GUE实现

中文摘要 AI 辅助

保证效用机制（GUM）被引入用于在动态社会选择问题中实现保证效用均衡（GUE）下的效率。我们证明该机制还具有先前未知的与风险最小化的联系。固定一个有效的决策策略，我们研究在真实报告的GUE实现类别中，方差最小化的预算平衡转移规则。当不存在公共状态时，GUM的对称化版本（sym-GUM）在真实报告下最小化各代理效用方差之和。当存在公共状态时，对该规则进行轻微修改即可得到同一目标下的最小化规则。然而，sym-GUM并不最小化转移风险。该问题的最小化规则反而是密切相关的一种类GUM转移规则的对称化版本。在这两个问题中，最小化的真实总转移在代理特定常数之和为零及概率为零的事件意义下是唯一的。

英文摘要

The Guaranteed Utility Mechanism (GUM) was introduced to implement efficiency in Guaranteed Utility Equilibrium (GUE) in dynamic social choice problems. We show that this mechanism also has a previously unknown connection to risk minimization. Fixing an efficient decision policy, we study variance-minimizing budget-balanced transfer rules in the class of GUE-implementations of truthful reporting. A symmetrized version of GUM (sym-GUM) minimizes the sum of the agents' utility variances under truthful reporting when there is no public state. When a public state is present, a slight modification of this rule yields the minimizer for the same objective. Sym-GUM, however, does not minimize transfer risk. The minimizer for that problem is instead the symmetrized version of a closely related GUM-like transfer rule. In both problems, the minimizing truthful total transfers are unique up to agent-specific constants summing to zero and events of probability zero.

发表机构

• Alfréd Rényi Institute of Mathematics（阿尔弗雷德·雷尼数学研究所）
• ELTE Faculty of Science（厄特沃什·罗兰大学理学院）

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