{"title":"Decomposition of interaction indices: alternative interpretations of cardinal–probabilistic interaction indices","authors":"Sébastien Courtin, Rodrigue Tido Takeng , Frédéric Chantreuil","doi":"10.1007/s11238-023-09970-8","DOIUrl":null,"url":null,"abstract":"<p>In cooperative game theory, the concept of interaction index is an extension of the concept of one-point solution that takes into account interactions among players. In this paper, we focus on cardinal–probabilistic interaction indices that generalize the class of semivalues. We provide two types of decompositions. With the first one, a cardinal–probabilistic interaction index for a given coalition equals the difference between its external interaction index and a weighted sum of the individual impact of the remaining players on the interaction index of the considered coalition. The second decomposition, based on the notion of the \"decomposer\", splits an interaction index into a direct part, the decomposer, which measures the interaction in the coalition considered, and an indirect part, which indicates how all remaining players individually affect the interaction of the coalition considered. We propose alternative characterizations of the cardinal–probabilistic interaction indices.</p>","PeriodicalId":47535,"journal":{"name":"Theory and Decision","volume":"7 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory and Decision","FirstCategoryId":"96","ListUrlMain":"https://doi.org/10.1007/s11238-023-09970-8","RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ECONOMICS","Score":null,"Total":0}
引用次数: 0
Abstract
In cooperative game theory, the concept of interaction index is an extension of the concept of one-point solution that takes into account interactions among players. In this paper, we focus on cardinal–probabilistic interaction indices that generalize the class of semivalues. We provide two types of decompositions. With the first one, a cardinal–probabilistic interaction index for a given coalition equals the difference between its external interaction index and a weighted sum of the individual impact of the remaining players on the interaction index of the considered coalition. The second decomposition, based on the notion of the "decomposer", splits an interaction index into a direct part, the decomposer, which measures the interaction in the coalition considered, and an indirect part, which indicates how all remaining players individually affect the interaction of the coalition considered. We propose alternative characterizations of the cardinal–probabilistic interaction indices.
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
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