Impossibility results for parametrized notions of efficiency and strategy-proofness in exchange economies

• 成果类型: Article
• 署名作者: Cho, Wonki Jo
• 署名单位: University of Manchester
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2014.03.003
• 发表日期: 2014
• 页码: 26-39
• 关键词: Exchange economy; individual rationality; delta-Efficiency; delta-Strategy-proofness

摘要

We study a standard model of exchange economies with individual endowments. It is well known that no rule is individually rational, efficient, and strategy-proof. In order to quantify the extent of this impossibility, we parametrize axioms on allocation rules. Given an axiom A, a parametrization of A is a continuum of axioms {delta-A}(delta is an element of[0,1]) such that (i) delta-A is equivalent to A if and only if delta = 1; (ii) delta-A is vacuous if and only if delta = 0; and (iii) for each pair delta,delta' is an element of [0, 1] with delta < delta'-A implies delta-A. Thus, as delta decreases from 1 to 0, delta-A weakens monotonically, eventually to a vacuous requirement. We consider two parametrizations {delta-efficiency}(delta is an element of [0,1]) and {delta-strategy-proofness}(delta is an element of [0, 1]), and investigate their compatibility with individual rationality for the class of two-agent economies defined on the linear preference domain. We show that (i) for each delta is an element of (0, 1], no rule is individually rational, delta-efficient, and strategy-proof; and (ii) for each delta is an element of (0, 1], no rule is individually rational, efficient, and delta-strategy-proof. (C) 2014 Elsevier Inc. All rights reserved.