Positivity and convexity in incomplete cooperative games

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F24%3A00587911" target="_blank" >RIV/67985807:_____/24:00587911 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216208:11320/24:10491183

Výsledek na webu

<a href="https://doi.org/10.1007/s10479-024-06082-6" target="_blank" >https://doi.org/10.1007/s10479-024-06082-6</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10479-024-06082-6" target="_blank" >10.1007/s10479-024-06082-6</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Positivity and convexity in incomplete cooperative games

Popis výsledku v původním jazyce

Incomplete cooperative games generalize the classical model of cooperative games by omitting the values of some of the coalitions. This allows for incorporating uncertainty into the model and studying the underlying games and possible payoff distributions based only on the partial information. In this paper, we conduct a systematic investigation of incomplete games, focusing on two important classes: positive and convex games. Regarding positivity, we generalize previous results from a special class of minimal incomplete games to a general setting. We characterize the non-extendability to a positive game by the existence of a certificate and provide a description of the set of positive extensions using its extreme games. These results also enable the construction of explicit formulas for several classes of incomplete games with special structures. The second part deals with convexity. We begin with the case of non-negative, minimal incomplete games. We establish the connection between incomplete games and the problem of completing partial functions and, consequently, provide a characterization of extendability and a full description of the set of symmetric convex extensions. This set serves as an approximation of the set of convex extensions.

Název v anglickém jazyce

Positivity and convexity in incomplete cooperative games

Popis výsledku anglicky

Incomplete cooperative games generalize the classical model of cooperative games by omitting the values of some of the coalitions. This allows for incorporating uncertainty into the model and studying the underlying games and possible payoff distributions based only on the partial information. In this paper, we conduct a systematic investigation of incomplete games, focusing on two important classes: positive and convex games. Regarding positivity, we generalize previous results from a special class of minimal incomplete games to a general setting. We characterize the non-extendability to a positive game by the existence of a certificate and provide a description of the set of positive extensions using its extreme games. These results also enable the construction of explicit formulas for several classes of incomplete games with special structures. The second part deals with convexity. We begin with the case of non-negative, minimal incomplete games. We establish the connection between incomplete games and the problem of completing partial functions and, consequently, provide a characterization of extendability and a full description of the set of symmetric convex extensions. This set serves as an approximation of the set of convex extensions.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA22-11117S" target="_blank" >GA22-11117S: Globální analýza citlivosti a stabilita v optimalizačních úlohách</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Annals of Operations Research

ISSN

0254-5330

e-ISSN

1572-9338

Svazek periodika

340

Číslo periodika v rámci svazku

2-3

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

25

Strana od-do

785-809

Kód UT WoS článku

001270194400002

EID výsledku v databázi Scopus

2-s2.0-85198393891