Nonlocal Teams and Information Structures

Abstract

We look at Bell inequalities from the lens of information structures in stochastic teams. We consider the usual CHSH game and a dynamic variant of the same to study how various classes of strategies, classical, projective and quantum, behave under team theoretic solution concepts. We find that projective strategies (where each player performs projective measurements) enjoy important properties in the usual CHSH game, but they do not carry over to its dynamic version. These results shed light on the delicate interplay of information structure in quantum strategies and the fragility of some well known ideas under changes of information structure.