Facets of the cone of exact games

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F22%3A00556097" target="_blank" >RIV/67985556:_____/22:00556097 - isvavai.cz</a>

Result on the web

<a href="https://link.springer.com/article/10.1007/s00186-022-00770-4" target="_blank" >https://link.springer.com/article/10.1007/s00186-022-00770-4</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00186-022-00770-4" target="_blank" >10.1007/s00186-022-00770-4</a>

Result language

angličtina

Original language name

Facets of the cone of exact games

Original language description

The class of exact transferable utility coalitional games, introduced in 1972 by Schmeidler, has been studied both in the context of game theory and in the context of imprecise probabilities. We characterize the cone of exact games by describing the minimal set of linear inequalities defining this cone. These facet-defining inequalities for the exact cone appear to correspond to certain set systems (= systems of coalitions). We noticed that non-empty proper coalitions having non-zero coefficients in these facet-defining inequalities form set systems with particular properties.nnMore specifically, we introduce the concept of a semi-balanced system of coalitions, which generalizes the classic concept of a balanced coalitional system in cooperative game theory. The semi-balanced coalitional systems provide valid inequalities for the exact cone and minimal semi-balanced systems (in the sense of inclusion of set systems) characterize this cone. We also introduce basic classification of minimal semi-balanced systems, their pictorial representatives and a substantial concept of an indecomposable (minimal) semi-balanced system of coalitions. The main result of the paper is that indecomposable semi-balanced systems are in one-to-one correspondence with facet-defining inequalities for the exact cone. The second relevant result is the rebuttal of a former conjecture claiming that a coalitional game is exact iff it is totally balanced and its anti-dual is also totally balanced. We additionally characterize those inequalities which are facet-defining both for the cone of exact games and for the cone of totally balanced games.

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/GA19-04579S" target="_blank" >GA19-04579S: Conditonal independence structures: methods of polyhedral geometry</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2022

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

1432-5217

Volume of the periodical

95

Issue of the periodical within the volume

1

Country of publishing house

CH - SWITZERLAND

Number of pages

46

Pages from-to

35-80

UT code for WoS article

000757714500001

EID of the result in the Scopus database

2-s2.0-85124749808