Second Parrondo's Paradox in Scale Free Networks

Parrondo’s paradox occurs in sequences of games in which a winning expectation value of a payoff may be obtained by playing two games in a random order, even though each game in the sequence may be lost when played individually. Several variations of Parrondo’s games apparently with the same paradoxical property have been introduced [5]; history dependence, one dimensional line, two dimensional lattice and so on. I have shown that Parrondo’s paradox does not occur in scale free networks in the simplest case with the same number of parameters as the original Parrondo’s paradox[17]. It suggests that some technical complexities are needed to present Parrondo’s paradox in scale free networks. In this article, I show that a simple modification with the same number of parameters as the original Parrondo’s paradox creates Parrondo’s paradox in scale free. This paradox is, however, created by a quite different mechanism from the original Parrondo’s paradox and a considerably rare phenomenon, where the discrete property of degree of nodes is crucial. I call it the second Parrondo’s paradox. keywords: Parrondo’s paradox, Parrondo’s paradoxCScale free network, Game theory