Ústav teorie informace a automatizace

Jste zde

Bibliografie

Conference Paper (international conference)

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

Studený Milan, Kroupa Tomáš, Kratochvíl Václav

: Proceedings of the 11th Workshop on Uncertainty Processing (WUPES’18), p. 177-187 , Eds: Kratochvíl Václav, Vejnarová Jiřina

: Workshop on Uncertainty Processing (WUPES’18), (Třeboň, CZ, 20180606)

: GA16-12010S, GA ČR

: exact game, extremity, irreducible, balanced

: http://library.utia.cas.cz/separaty/2018/MTR/studeny-0490915.pdf

(eng): 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.

: BA

: 10101

07.01.2019 - 08:39