Completely mixed linear games corresponding to Z-transformations over self-dual cones
dc.contributor.author | Gowda, M. Seetharama | |
dc.date.accessioned | 2023-11-20T15:02:22Z | |
dc.date.available | 2023-11-20T15:02:22Z | |
dc.date.issued | 2023-10-20 | |
dc.description.abstract | In 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.uri | https://arxiv.org/abs/2310.13464 | |
dc.format.extent | 32 pages | |
dc.genre | journal articles | |
dc.genre | preprints | |
dc.identifier.uri | https://doi.org/10.48550/arXiv.2310.13464 | |
dc.identifier.uri | http://hdl.handle.net/11603/30799 | |
dc.language.iso | en_US | |
dc.relation.isAvailableAt | The University of Maryland, Baltimore County (UMBC) | |
dc.relation.ispartof | UMBC Mathematics Department Collection | |
dc.relation.ispartof | UMBC Faculty Collection | |
dc.rights | This 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.title | Completely mixed linear games corresponding to Z-transformations over self-dual cones | |
dc.type | Text | |
dcterms.creator | https://orcid.org/0000-0001-5171-0924 |