Game theory and non-linear dynamics: the Parrondo Paradox case study

In this paper a new research topic is explored on the role of chaos in a particular game problem: the Parrondo Paradox. In the original formulation of this paradox, it has been proved that two separate losing games can be combined following a random or periodic strategy in order to have a resulting winning game. In this paper, three key points will be dealt with. The first one regards the introduction of a strategy based on various chaotic time series: this could improve the gain in the classical two games Parrondo problem. The second one concerns with the introduction of a third loosing game based on the history of the game and not on the capital as in the classical Parrondo two games Problem. Finally, the Parrondo Paradox has been generalized for N games and an algorithm has been proposed in order to investigate through an optimization approach the region of probability parameter space in which Parrondo Paradox can occur.