Consistency and the core in games with externalities
type: Item
instance of: scholarly article
title: Consistency and the core in games with externalities
zbMATH Open document ID: 1416.91023
author: Takaaki Abe
published in: International Journal of Game Theory
publication date: 2018-04-11T00:00:00Z
review text: The starting point in the author's considerations is a generalization of the classical transferable utility games, called \textit{games with externalities}. Their structure is the following: Let \(N\) be a finite \textit{player set}. A \textit{coalition} \(S\) is any subset of \(N\). Let \(\Pi(S)\) be the set of all partitions of a coalition \(S\). For a coalition \(S\) and a partition \({\mathcal P}\in \Pi(N\setminus S)\), an \textit{embedded coalition} is defined as the pair \((S,{\mathcal P})\). Let \(EC(N)\) be the set of all embedded coalitions of \(N\). A \textit{partition function form game} is a pair \((N,v)\) where a \textit{partition function} \(v\) is a function that assigns a real number to each embedded coalition, that is, \(v: EC(N) \rightarrow \mathbb{R}\). Let \(\Gamma\) be a subset of the set of all partition function form games. Now a \textit{solution on} \(\Gamma\) is defined as any function \(\sigma\) that associates a subset \(\sigma(N,v)\) of \(F(N,v)\) with every game \((N,v)\in \Gamma\), where \(F(N,v)\) is the set of \textit{payoff vectors} of the form \(F(N,v) = \{x\in \mathbb{R}^N | \sum_{j\in N}x_j \leq v(N,\{\emptyset\})\}\). In the context of games with externalities, the author considers some version of a reduced game called the \textit{complement-reduced game}, and notions of a \textit{subset consistency}, \textit{complement-consistency}, and of a \(\psi\)-\textit{core}. In terms of the first three notions, he gets several results describing different properties of a solution \(\sigma\) on \(\Gamma\) and of the \(\psi\)-\textit{core}. The paper also contains a wide discussion about other versions of reduced games, and about several related results from the literature.
reviewed by: Tadeusz Radzik
Mathematics Subject Classification ID: 91A12
zbMATH DE Number: 6858290
zbMATH Keywords: consistency
zbMATH Keywords: core
zbMATH Keywords: games with externalities
zbMATH Keywords: reduced game
MaRDI profile type: Publication
full work available at URL: s00182-017-0581-y
OpenAlex ID: W2626299809
cites work: The non-emptiness of the core of a partition function form game
cites work: AN AXIOM SYSTEM FOR A VALUE FOR GAMES IN PARTITION FUNCTION FORM
cites work: Sequential formation of coalitions in games with externalities and fixed payoff division
cites work: Expectation formation rules and the core of partition function games
cites work: A set of axioms for a value for partition function games
cites work: The kernel of a cooperative game
cites work: Externalities, potential, value and consistency
cites work: The core and consistency properties: A general characterisation
cites work: Efficiency in coalition games with externalities
cites work: Endogenous Formation of Coalitions
cites work: A recursive core for partition function form games
cites work: The coalition structure core is accessible
cites work: Sharing the surplus: An extension of the Shapley value for environments with externalities
cites work: The separability axiom and equal-sharing methods
cites work: Values of games in partition function form
cites work: On the reduced game property and its converse
cites work: Reduced games, consistency, and the core
DOI: 10.1007/S00182-017-0581-Y
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description: scientific article; zbMATH DE number 6858290