一般注記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.
連携機関・データベース国立情報学研究所 : 学術機関リポジトリデータベース（IRDB）（機関リポジトリ）