Products of synchronous games
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866912041507225600 |
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| author | Mančinska, Laura Paulsen, Vern I. Todorov, Ivan G. Winter, Andreas |
| author_facet | Mančinska, Laura Paulsen, Vern I. Todorov, Ivan G. Winter, Andreas |
| contents | We show that the *-algebra of the product of two synchronous games is the tensor product of the corresponding *-algebras. We prove that the product game has a perfect C*-strategy if and only if each of the individual games does, and that in this case the C*-algebra of the product game is *-isomorphic to the maximal C*-tensor product of the individual C*-algebras. We provide examples of synchronous games whose synchronous values are strictly supermultiplicative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_12039 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Products of synchronous games Mančinska, Laura Paulsen, Vern I. Todorov, Ivan G. Winter, Andreas Operator Algebras 81P45, 46L89, 91A12 We show that the *-algebra of the product of two synchronous games is the tensor product of the corresponding *-algebras. We prove that the product game has a perfect C*-strategy if and only if each of the individual games does, and that in this case the C*-algebra of the product game is *-isomorphic to the maximal C*-tensor product of the individual C*-algebras. We provide examples of synchronous games whose synchronous values are strictly supermultiplicative. |
| title | Products of synchronous games |
| topic | Operator Algebras 81P45, 46L89, 91A12 |
| url | https://arxiv.org/abs/2109.12039 |