Quantum game interpretation for a special case of Parrondo’s paradox

By using the discrete Markov chain method, Parrondo’s paradox is studied by means of theoretical analysis and computer simulation, built on the case of game AB played in alternation with modulus M=4. We find that such a case does not have a definite stationary probability distribution and that payoffs of the game depend on the parity of the initial capital. Besides, this paper reveals the phenomenon that “processing in order produces non-deterministic results, while a random process produces deterministic results”. The quantum game method is used in a further study. The results show that the explanation of the game corresponding to a stationary probability distribution is that the probability of the initial capital has reached parity.