A characterization of the Owen value via sign symmetries

IF 0.9 4区经济学 Q3 ECONOMICS

Theory and Decision Pub Date : 2024-05-10 DOI:10.1007/s11238-024-09985-9

Xinjuan Chen, Minghua Zhan, Zhihui Zhao

引用次数: 0

Abstract

Khmelnitskaya and Yanovskaya (Math Methods Oper Res 66(2):255–261, 2007) characterized the Owen value for TU games with a coalition structure by the axioms of efficiency, marginality, symmetry across coalitions and symmetry within coalitions. Symmetry across components requires that components with equally productive in the game between components obtain the same total payoffs of their members. In this note, inspired by Casajus (Econ Lett 169:59–62, 2018), we weaken the symmetry across components to the sign symmetry across components, which requires only that equally productive components obtain the same sign of total payoffs. We extend the Khmelnitskaya-Yanovskaya’s characterization by using efficiency, marginality, sign symmetry across coalitions, and sign symmetry within coalitions, similarly as it was done by Casajus (Econ Lett 169:59–62, 2018) for the Shapley value for general TU games. At last, we extend the main result to the Winter value for games with level structure

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通过符号对称分析欧文值的特征

Khmelnitskaya 和 Yanovskaya（Math Methods Oper Res 66(2)：255-261，2007 年）通过效率、边际性、跨联盟对称和联盟内对称等公理描述了具有联盟结构的 TU 博弈的欧文值。跨联盟对称要求在联盟间博弈中具有同等生产力的联盟成员获得相同的总收益。在本说明中，受 Casajus（Econ Lett 169:59-62, 2018）的启发，我们将跨成分的对称性弱化为跨成分的符号对称性，即只要求生产率相同的成分获得相同符号的总报酬。我们通过使用效率、边际性、跨联盟的符号对称性和联盟内的符号对称性来扩展 Khmelnitskaya-Yanovskaya 的特征，这与 Casajus（Econ Lett 169:59-62, 2018）对一般 TU 博弈的 Shapley 值所做的类似。最后，我们将主要结果扩展到有水平结构博弈的温特值

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来源期刊

Theory and Decision Multiple-

CiteScore

1.60

自引率

0.00%

发文量

期刊介绍： The field of decision has been investigated from many sides. However, research programs relevant to decision making in psychology, management science, economics, the theory of games, statistics, operations research, artificial intelligence, cognitive science and analytical philosophy have remained separate. Theory and Decision is devoted to all aspects of decision making belonging to such programs, but addresses also possible cross-fertilizations between these disciplines which would represent effective advances in knowledge. The purpose of the journal is to let the engineering of choice gradually emerge both for individual and for collective decision making. Formalized treatments will be favoured, to the extent that they provide new insights into the issues raised and an appropriate modeling of the situation considered. Due to its growing importance, expermentation in decision making as well as its links to the cognitive sciences will be granted special attention by Theory and Decision. Of particular interest are: Preference and belief modeling, Experimental decision making under risk or under uncertainty, Decision analysis, multicriteria decision modeling, Game theory, negotiation theory, collective decision making, social choice, Rationality, cognitive processes and interactive decision making, Methodology of the decision sciences. Applications to various problems in management and organization science, economics and finance, computer-supported decision schemes, will be welcome as long as they bear on sufficiently general cases. Analysis of actual decision making processes are also relevant topics for the journal, whether pertaining to individual, collective or negotiatory approaches; to private decisions or public policies; to operations or to strategic choices. Officially cited as: Theory Decis