Spacetime games subsume causal contextuality scenarios

TL;DR

This paper demonstrates an equivalence between causal contextuality scenarios and spacetime games, simplifying proofs and enabling new constructs that bridge quantum foundations and game theory in Minkowski spacetime.

Contribution

It establishes a categorical equivalence between causal contextuality scenarios and spacetime games, facilitating simpler proofs and new theoretical constructs in quantum foundations.

Findings

Category equivalence simplifies causal contextuality analysis.

Spacetime games generalize decision-making in Minkowski spacetime.

Obstruction to global sections relates to Nash mixed strategies.

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.