Products of synchronous games
Volume 272 / 2023
Studia Mathematica 272 (2023), 299-317
MSC: Primary 81P45; Secondary 46L89, 91A12.
DOI: 10.4064/sm221201-19-4
Published online: 10 August 2023
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.
