On attempts to characterize facet-defining inequalities of the cone of exact games

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F18%3A00490915" target="_blank" >RIV/67985556:_____/18:00490915 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
On attempts to characterize facet-defining inequalities of the cone of exact games
Original language description
The sets of balanced, totally balanced, exact and supermodular games play an important role in cooperative game theory. These sets of games are known to be polyhedral cones. The (unique) non-redundant description of these cones by means of the so-called facet-defining inequalities is known in cases of balanced games and supermodular games, respectively. The facet description of the cones of exact games and totally balanced games are not known and we present conjectures about what are the facet-defining inequalities for these cones. We introduce the concept of an irreducible min-balanced set system and conjecture that the facet-defining inequalities for the cone of totally balanced games correspond to these set systems. The conjecture concerning exact games is that the facet-defining inequalities for this cone are those which correspond to irreducible min-balanced systems on strict subsets of the set of players and their conjugate inequalities. A consequence of the validity of the conjectures would be a novel result saying that a game m is exact if and only if m and its reflection are totally balanced.
Czech name
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Czech description
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Project
<a href="/en/project/GA16-12010S" target="_blank" >GA16-12010S: Conditional independence structures: combinatorial and optimization methods</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Proceedings of the 11th Workshop on Uncertainty Processing (WUPES’18)
ISBN
978-80-7378-361-7
ISSN
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e-ISSN
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Number of pages
11
Pages from-to
177-187
Publisher name
MatfyzPress, Publishing House of the Faculty of Mathematics and Physics Charles University
Place of publication
Praha
Event location
Třeboň
Event date
Jun 6, 2018
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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