Hidden variable models for entanglements can or cannot have a local component?

Understand

A recent article of Colbeck and Renner tackled the problem whether entanglements may be explained by combined models of local and non-local hidden variables.

• To the difference from previous works they considered models in which each pair of entangled particles behaves in the same way, and the particles in the pair are equivalent, i.e.
• each of them produces its response to a measurement according to both local and non-local hidden variables.
• Their article aimed at proving that the local hidden variable component in such models has no effect on the measurement results, i.e.