Completely mixed linear games corresponding to Z-transformations over self-dual cones

dc.contributor.authorGowda, M. Seetharama
dc.date.accessioned2023-11-20T15:02:22Z
dc.date.available2023-11-20T15:02:22Z
dc.date.issued2023-10-20
dc.description.abstractIn the setting of a self-dual cone in a finite dimensional inner product space, we consider (zero-sum) linear games. In our previous work, we showed that a Z-transformation with positive value is completely mixed. In the present paper, we consider the case when the value is zero. Motivated by the result (in the classical setting) that a Z-matrix with value zero is completely mixed if and only if it is irreducible, we formulate our general results based on the concepts of cone-irreducibility and space-irreducibility. In the setting of a symmetric cone (in a Euclidean Jordan algebra), we show that the space-irreducibility condition is necessary for a Z-transformation with value zero to be completely mixed and that it is sufficient when the Z-transformation is the difference of a Lyapunov-like transformation and a positive transformation. Additionally, we show that cone-irreducibility and space-irreducibility are equivalent for a positive transformation on a symmetric cone.
dc.description.urihttps://arxiv.org/abs/2310.13464
dc.format.extent32 pages
dc.genrejournal articles
dc.genrepreprints
dc.identifier.urihttps://doi.org/10.48550/arXiv.2310.13464
dc.identifier.urihttp://hdl.handle.net/11603/30799
dc.language.isoen_US
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Mathematics Department Collection
dc.relation.ispartofUMBC Faculty Collection
dc.rightsThis item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.
dc.titleCompletely mixed linear games corresponding to Z-transformations over self-dual cones
dc.typeText
dcterms.creatorhttps://orcid.org/0000-0001-5171-0924

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