Facets of the cone of totally balanced games

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Facets of the cone of totally balanced games

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Facets of the cone of totally balanced games

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA16-12010S" target="_blank" >GA16-12010S: Struktury podmíněné nezávislosti: kombinatorické a optimalizační metody</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Mathematical Methods of Operations Research

ISSN

1432-2994

e-ISSN

—

Svazek periodika

90

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

29

Strana od-do

271-300

Kód UT WoS článku

000496600500006

EID výsledku v databázi Scopus

2-s2.0-85066154003