Construction of Compromise Values for Cooperative Games

Fuente: arXiv
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Main Authors: Gilles, Robert P., Brink, René van den
Format: Preprint
Published: 2025
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author Gilles, Robert P.
Brink, René van den
author_facet Gilles, Robert P.
Brink, René van den
contents We explore a broad class of values for cooperative games in characteristic function form, known as \emph{compromise values\/}. These values efficiently allocate payoffs by linearly combining well-specified upper and lower bounds on payoffs. We identify subclasses of games that admit non-trivial efficient allocations within the considered bounds, which we call \emph{bound-balanced games}. Subsequently, we define the associated compromise value. We also provide an axiomatisation of this class of compromise values using variants of the minimal rights property and restricted proportionality. We introduce two construction methods for properly devised compromise values. Under mild conditions, one can use either a lower or an upper bound to construct a well-defined compromise value. We construct and axiomatise various well-known and new compromise values based on these methods, including the $τ$-, the $χ$-, the Gately, the CIS-, the PANSC-, the EANSC-, and the new KM-values. We conclude that this approach establishes a common foundation for a wide range of different values.
format Preprint
id arxiv_https___arxiv_org_abs_2503_05381
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Construction of Compromise Values for Cooperative Games
Gilles, Robert P.
Brink, René van den
Theoretical Economics
Computer Science and Game Theory
We explore a broad class of values for cooperative games in characteristic function form, known as \emph{compromise values\/}. These values efficiently allocate payoffs by linearly combining well-specified upper and lower bounds on payoffs. We identify subclasses of games that admit non-trivial efficient allocations within the considered bounds, which we call \emph{bound-balanced games}. Subsequently, we define the associated compromise value. We also provide an axiomatisation of this class of compromise values using variants of the minimal rights property and restricted proportionality. We introduce two construction methods for properly devised compromise values. Under mild conditions, one can use either a lower or an upper bound to construct a well-defined compromise value. We construct and axiomatise various well-known and new compromise values based on these methods, including the $τ$-, the $χ$-, the Gately, the CIS-, the PANSC-, the EANSC-, and the new KM-values. We conclude that this approach establishes a common foundation for a wide range of different values.
title Construction of Compromise Values for Cooperative Games
topic Theoretical Economics
Computer Science and Game Theory
url https://arxiv.org/abs/2503.05381