Quantum Games of Macroscopic Partners

Examples where quantum Nash Equilibrium has been found are considered. It turned out that under certain conditions opportunist behavior leads to a greater gain than non-opportunist one. Besides, the analysis of the structure of the quantum game has shown that it is isomorphic to a sum of two inter-connected classical games. This link named “quantum cooperation” is expressed by means of a non-linear relation between the probabilities of the choice of corresponding pure strategies. The difference between the quantum cooperation and the usual correlation has been demonstrated. Mixed strategies for participants of these games are calculated using probability amplitudes according to the rules of quantum mechanics in spite of the macroscopic nature of the game and absence of the Planck’s constant. Possible role of quantum logical lattices for existence of macroscopic quantum equilibria is discussed. The games modelling opportunist behavior have the structure that is characteristic of the description of microparticles with a spin equal to $\frac12$ and $1$ when additional variables are measured.