Products of synchronous games

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.