Linear criterion for testing the extremity of an exact game based on its finest min-representation

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F18%3A00491060" target="_blank" >RIV/67985556:_____/18:00491060 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.ijar.2018.06.007" target="_blank" >http://dx.doi.org/10.1016/j.ijar.2018.06.007</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.ijar.2018.06.007" target="_blank" >10.1016/j.ijar.2018.06.007</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Linear criterion for testing the extremity of an exact game based on its finest min-representation

Popis výsledku v původním jazyce

A game-theoretical concept of an exact (cooperative) game corresponds to the notion of a discrete coherent lower probability, used in the context of imprecise probabilities. The collection of (suitably standardized) exact games forms a pointed polyhedral cone and the paper is devoted to the recognition of extreme rays of that cone, whose generators are called extreme exact games. We give a necessary and sufficient condition for an exact game to be extreme. Our criterion leads to solving a simple linear equation system determined by a certain min-representation of the game. It has been implemented on a computer and a web-based platform for testing the extremity of an exact game is available, which works with a modest number of variables. The paper also deals with different min-representations of a fixed exact game, which can be compared with the help of the concept of a tightness structure (of a min-representation) introduced in the paper. The collection of tightness structures (of min-representations of a fixed game) is shown to be a finite lattice with respect to a refinement relation. We give a method to obtain a min-representation with the finest tightness structure, which construction comes from the coarsest standard min-representation of the game given by the (complete) list of vertices of the core (polytope) of the game. The newly introduced criterion for exact extremity is based on the finest tightness structure.

Název v anglickém jazyce

Linear criterion for testing the extremity of an exact game based on its finest min-representation

Popis výsledku anglicky

A game-theoretical concept of an exact (cooperative) game corresponds to the notion of a discrete coherent lower probability, used in the context of imprecise probabilities. The collection of (suitably standardized) exact games forms a pointed polyhedral cone and the paper is devoted to the recognition of extreme rays of that cone, whose generators are called extreme exact games. We give a necessary and sufficient condition for an exact game to be extreme. Our criterion leads to solving a simple linear equation system determined by a certain min-representation of the game. It has been implemented on a computer and a web-based platform for testing the extremity of an exact game is available, which works with a modest number of variables. The paper also deals with different min-representations of a fixed exact game, which can be compared with the help of the concept of a tightness structure (of a min-representation) introduced in the paper. The collection of tightness structures (of min-representations of a fixed game) is shown to be a finite lattice with respect to a refinement relation. We give a method to obtain a min-representation with the finest tightness structure, which construction comes from the coarsest standard min-representation of the game given by the (complete) list of vertices of the core (polytope) of the game. The newly introduced criterion for exact extremity is based on the finest tightness structure.

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

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

International Journal of Approximate Reasoning

ISSN

0888-613X

e-ISSN

—

Svazek periodika

101

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

22

Strana od-do

49-68

Kód UT WoS článku

000445987900004

EID výsledku v databázi Scopus

2-s2.0-85049531080