Spacetime games subsume causal contextuality scenarios

Abstract

We show that a category of causal contextuality scenarios with no cycles, unique causal bridges, and causally secured covers is equivalent to a category containing a subclass of the formerly published spacetime games, which generalize game theory to decisions arbitrarily located in Minkowski spacetime. This insight leads to certain constructs and proofs being shorter, simpler, and more intuitive when expressed in the spacetime game framework than in the causal contextuality scenario framework. The equivalence of categories and the modular structure of causal contextuality theory also implies that it is possible to build (pure) strategy sheaves, mixed strategy presheaves (equivalent to distribution presheaves) and empirical models on top of spacetime games: the obstruction to a global section in the presence of contextuality corresponds to the non-existence of a mixed strategy in the sense of the Nash game theory framework. This shows that the insights of both frameworks taken together can contribute positively to advancing the field of quantum foundations.