Positivity and convexity in incomplete cooperative games
The result's identifiers
Result code in 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>
Alternative codes found
RIV/00216208:11320/24:10491183
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Positivity and convexity in incomplete cooperative games
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA22-11117S" target="_blank" >GA22-11117S: Global sensitivity analysis and stability in optimization problems</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Annals of Operations Research
ISSN
0254-5330
e-ISSN
1572-9338
Volume of the periodical
340
Issue of the periodical within the volume
2-3
Country of publishing house
DE - GERMANY
Number of pages
25
Pages from-to
785-809
UT code for WoS article
001270194400002
EID of the result in the Scopus database
2-s2.0-85198393891