Assignment games with population monotonic allocation schemes

IF 0.5 4区经济学 Q4 ECONOMICS

Social Choice and Welfare Pub Date : 2023-08-21 DOI:10.1007/s00355-023-01477-z

Tamás Solymosi

引用次数: 0

Abstract

Abstract We characterize the assignment games which admit a population monotonic allocation scheme (PMAS) in terms of efficiently verifiable structural properties of the nonnegative matrix that induces the game. We prove that an assignment game is PMAS-admissible if and only if the positive elements of the underlying nonnegative matrix form orthogonal submatrices of three special types. In game theoretic terms it means that an assignment game is PMAS-admissible if and only if it contains either a veto player or a dominant veto mixed pair, or the game is a composition of these two types of special assignment games. We also show that in PMAS-admissible assignment games all core allocations can be extended to a PMAS, and the nucleolus coincides with the tau-value.

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具有人口单调分配方案的分配对策

摘要利用诱导博弈的非负矩阵的有效可验证的结构性质，刻画了一类具有种群单调分配方案的分配博弈。证明了一个赋值对策当且仅当其下非负矩阵的正元素构成三种特殊类型的正交子矩阵时是pmas可容许的。用博弈论的术语来说，这意味着一个分配博弈当且仅当它包含一个否决参与者或一个优势否决混合对，或者该博弈是这两种类型的特殊分配博弈的组合时，是pmas可接受的。我们还证明了在PMAS允许分配对策中，所有核分配都可以扩展到一个PMAS，并且核仁与tau值重合。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Social Choice and Welfare Multiple-

CiteScore

1.60

自引率

11.10%

发文量

期刊介绍： Social Choice and Welfare explores all aspects, both normative and positive, of welfare economics, collective choice, and strategic interaction. Topics include but are not limited to: preference aggregation, welfare criteria, fairness, justice and equity, rights, inequality and poverty measurement, voting and elections, political games, coalition formation, public goods, mechanism design, networks, matching, optimal taxation, cost-benefit analysis, computational social choice, judgement aggregation, market design, behavioral welfare economics, subjective well-being studies and experimental investigations related to social choice and voting. As such, the journal is inter-disciplinary and cuts across the boundaries of economics, political science, philosophy, and mathematics. Articles on choice and order theory that include results that can be applied to the above topics are also included in the journal. While it emphasizes theory, the journal also publishes empirical work in the subject area reflecting cross-fertilizing between theoretical and empirical research. Readers will find original research articles, surveys, and book reviews.Officially cited as: Soc Choice Welf