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...

For the multi-agent spatial Parrondo’s games, the available theoretical analysis methods based on the discrete-time Markov chain were assumed that the losing and winning states of an ensemble of N players were represented to be the system states. The number of system states was 2N types....

Parrondo’s Paradox has gained a fair amount of attention due to it being counter-intuitive. Given two stochastic processes, both of which are losing in nature, it is possible to have an overall net increase in capital by periodically or randomly alternating between the two processes. In this...

Parrondo’s paradox involves two losing processes producing a winning outcome. We analyze the paradox with an original and novel method in which we start with one process and seek to construct a complementary process to achieve the paradox. We then derive a general condition for the classical...

In Parrondo’s paradox, a winning strategy is formed either by playing two losing games randomly or alternating them periodically. The paradox is commonly analyzed using stochastic matrices. In this paper, we modify the stochastic matrices to allow a more systematic introduction of bias into...

We assume a multi-agent model based on Parrondo’s games. The model consists of game A between individuals and game B. In game A, two behavioral patterns are defined: competition and inaction. A controlled alternation strategy of behavioral pattern that gives a single player the highest return...

Consider a general coherent system with independent or dependent components, and assume that the components are randomly chosen from two different stocks, with the components of the first stock having better reliability than the others. Then here we provide sufficient conditions on the...