Second-order productivity, second-order payoffs, and the Banzhaf value

IF 0.6 4区 经济学 Q4 ECONOMICS International Journal of Game Theory Pub Date : 2024-04-07 DOI:10.1007/s00182-024-00893-4
André Casajus, Rodrigue Tido Takeng
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Abstract

First, we suggest and discuss second-order versions of properties for solutions for TU games used to characterize the Banzhaf value, in particular, of standardness for two-player games, of the dummy player property, and of 2-efficiency. Then, we provide a number of characterizations of the Banzhaf value invoking the following properties: (i) [second-order standardness for two-player games or the second-order dummy player property] and 2-efficiency, (ii) standardness for one-player games, standardness for two-player games, and second-order 2-efficiency, (iii) standardness for one-player games, [second-order standardness for two-player games or the second-order dummy player property], and second-order 2-efficiency. These characterizations also work within the classes of simple games, of superadditive games, and of simple superadditive games.

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二阶生产力、二阶报酬和班查夫值
首先,我们提出并讨论用于描述班扎夫值的 TU 博弈解的二阶版本的性质,特别是双人博弈的标准性、假棋子性质和 2 效率。然后,我们引用以下性质对班扎夫值进行了描述:(i) [二阶二人博弈标准性或二阶假棋手性质] 和 2-效率,(ii) 一人博弈标准性、二人博弈标准性和二阶 2-效率,(iii) 一人博弈标准性、[二阶二人博弈标准性或二阶假棋手性质] 和二阶 2-效率。这些特征也适用于简单博弈类、超加性博弈类和简单超加性博弈类。
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来源期刊
International Journal of Game Theory
International Journal of Game Theory 数学-数学跨学科应用
CiteScore
1.30
自引率
0.00%
发文量
9
审稿时长
1 months
期刊介绍: International Journal of Game Theory is devoted to game theory and its applications. It publishes original research making significant contributions from a methodological, conceptual or mathematical point of view. Survey articles may also be considered if especially useful for the field.
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