Strategy-proof allocation problem with hard budget constraints and income effects : weak efficiency and fairness

• Material Type: 文書・図像類
• Title: Strategy-proof allocation problem with hard budget constraints and income effects : weak efficiency and fairness
• Author/Editor: Wakabayashi, Yuya; Sakai, Ryosuke; Shinozaki, Hiroki
• Author Heading: Wakabayashi, Yuya; Sakai, Ryosuke; Shinozaki, Hiroki; https://nrid.nii.ac.jp/nrid/1000000979338
• Publication, Distribution, etc.: Osaka School of International Public Policy, Osaka University
• Publication Date: 2024-05-24
• Publication Date (W3CDTF): 2024-05-24
• Periodical title: OSIPP Discussion Paper
• No. or year of volume/issue: DP-2024-E-003
• Volume: DP-2024-E-003
• Pages: 1-27
• Text Language Code: eng
• Subject Heading: Single-object allocation problem; Non-quasi-linear preference; Hard budget constraint; Efficiency; Fairness; Strategy-proofness; Vickrey rule with reserve prices
• Target Audience: 一般
• Note (General): We consider the single-object allocation problem with monetary transfers. Agents have hard budgets and their utility functions may exhibit income effects. When hard budget constraints exist, it is known that efficiency and strategy-proofness are in-compatible along with individual rationality and no subsidy. Our objectives are (i) to explore which forms of partial efficiency are compatible with strategy-proofness, and (ii) to investigate strategy-proof rules that satisfy some fairness conditions, in-stead of efficiency. We focus on constrained efficiency as a weak efficiency condition, and on weak envy-freeness for equals as a fairness condition. We introduce truncated Vickrey rules with endogenous reserve prices. Some of them may fail to satisfy either constrained efficiency, weak envy-freeness for equal, or strategy-proofness. In order to satisfy the properties, we impose additional conditions:exclusive tie-breaking rules, non-negligible reserve prices, and prioritized tie-breaking rules, respectively. First we show that the truncated Vickrey rule with endogenous reserve prices and with an exclusive and prioritized tie-breaking rule are the only rules satisfying constrained efficiency, individual rationality, no subsidy for losers, and strategy-proofness. Next we show that the truncated Vickrey rules with non-negligible endogenous reserve prices and with a prioritized tie-breaking rule are the only rules satisfying weak envy-freeness for equals, individual rationality, no subsidy for losers and strategy-proofness. This characterization also holds when replacing weak envy-freeness for equals with equal treatment of quals or envy-freeness. Moreover, if endogenous reserve prices are upper anonymous, then the same result holds for anonymity in welfare.
• References (URI): URI; https://www.osipp.osaka-u.ac.jp/archives/DP/2024/DP2024E003.pdf
• Data Provider (Database): 国立情報学研究所 : 学術機関リポジトリデータベース（IRDB）（機関リポジトリ）; https://irdb.nii.ac.jp
• Original Data Provider (Database): 大阪大学 : 大阪大学学術情報庫 桜華