Contextual Approach to Quantum-like Macroscopic Games

In Chapter 8 the QL theory of macroscopic games was developed on the basis of quantum logic. These investigations were initiated by Andrey Grib and then continued in collaboration with me. They induced understanding that games for macroscopic players having all the distinguishing features of “really quantum games” (i.e., games that are based on microscopic sources of randomness such as pairs of entangled photons) can be easily constructed and represented by means of quantum logic. This QL (in fact, quantum logic) program on macroscopic games stimulated the author to apply the contextual statistical model to represent nonclassical (from the probabilistic point of view) games in the contextual form and then, using QLRA, map them into the complex (or even hyperbolic) Hilbert space.