Facets of the cone of totally balanced games

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F19%3A00511152" target="_blank" >RIV/67985556:_____/19:00511152 - isvavai.cz</a>

Result on the web

<a href="https://link.springer.com/article/10.1007%2Fs00186-019-00672-y" target="_blank" >https://link.springer.com/article/10.1007%2Fs00186-019-00672-y</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00186-019-00672-y" target="_blank" >10.1007/s00186-019-00672-y</a>

Result language

angličtina

Original language name

Facets of the cone of totally balanced games

Original language description

The class of totally balanced games is a class of transferable-utility coalitional games providing important models of cooperative behavior used in mathematical economics. They coincide with market games of Shapley and Shubik and every totally balanced game is also representable as the minimum of a finite set of additive games. In this paper we characterize the polyhedral cone of totally balanced games by describing its facets. Our main result is that there is a correspondence between facet-defining inequalities for the cone and the class of special balanced systems of coalitions, the so-called irreducible min-balanced systems. Our method is based on refining the notion of balancedness introduced by Shapley. We also formulate a conjecture about what are the facets of the cone of exact games, which addresses an open problem appearing in the literature.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

Project

<a href="/en/project/GA16-12010S" target="_blank" >GA16-12010S: Conditional independence structures: combinatorial and optimization methods</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2019

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Mathematical Methods of Operations Research

ISSN

1432-2994

e-ISSN

—

Volume of the periodical

90

Issue of the periodical within the volume

2

Country of publishing house

DE - GERMANY

Number of pages

29

Pages from-to

271-300

UT code for WoS article

000496600500006

EID of the result in the Scopus database

2-s2.0-85066154003