guest ::
| Home > Conference materials > Papers > On attempts to characterize facet-defining inequalities of the cone of exact games |
Original title:
On attempts to characterize facet-defining inequalities of the cone of exact games
Authors: Studený, Milan ; Kroupa, Tomáš ; Kratochvíl, Václav
Document type: Papers
Conference/Event: Workshop on Uncertainty Processing (WUPES’18), Třeboň (CZ), 20180606
Year: 2018
Language: eng
Abstract: 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.
Keywords: balanced; exact game; extremity; irreducible
Project no.: GA16-12010S (CEP)
Funding provider: GA ČR
Host item entry: Proceedings of the 11th Workshop on Uncertainty Processing (WUPES’18), ISBN 978-80-7378-361-7
Institution: Institute of Information Theory and Automation AS ČR (web)
Document availability information: Fulltext is available at external website.
External URL: http://library.utia.cas.cz/separaty/2018/MTR/studeny-0490915.pdf
Original record: http://hdl.handle.net/11104/0285278
Permalink: http://www.nusl.cz/ntk/nusl-383516
The record appears in these collections:
Research > Institutes ASCR > Institute of Information Theory and Automation
Conference materials > Papers
Authors: Studený, Milan ; Kroupa, Tomáš ; Kratochvíl, Václav
Document type: Papers
Conference/Event: Workshop on Uncertainty Processing (WUPES’18), Třeboň (CZ), 20180606
Year: 2018
Language: eng
Abstract: 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.
Keywords: balanced; exact game; extremity; irreducible
Project no.: GA16-12010S (CEP)
Funding provider: GA ČR
Host item entry: Proceedings of the 11th Workshop on Uncertainty Processing (WUPES’18), ISBN 978-80-7378-361-7
Institution: Institute of Information Theory and Automation AS ČR (web)
Document availability information: Fulltext is available at external website.
External URL: http://library.utia.cas.cz/separaty/2018/MTR/studeny-0490915.pdf
Original record: http://hdl.handle.net/11104/0285278
Permalink: http://www.nusl.cz/ntk/nusl-383516
The record appears in these collections:
Research > Institutes ASCR > Institute of Information Theory and Automation
Conference materials > Papers
Record created 2018-07-30, last modified 2021-11-24