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arXiv · 2109.12039

Products of synchronous games

Laura Mančinska·Vern I. Paulsen·Ivan G. Todorov·Andreas Winter
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Abstract

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.

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Laura Mančinska, Vern I. Paulsen, Ivan G. Todorov, Andreas Winter. 2021-09-24. Products of synchronous games. https://doi.org/10.4064/sm221201-19-4

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