Narrow Results

We introduce a new family of Parrondo's games of alternating losing strategies in order to get a winning result. In our version of the games we consider an ensemble of players and use "social" rules in which the probabilities of the games are defined in terms of the actual state of the neighbors of a given player.

We present new versions of the Parrondo's paradox by which a losing game can be turned into winning by including a mechanism that allows redistribution of the capital amongst an ensemble of players. This shows that, for this particular class of games, redistribution of the capital is beneficial for everybody. The same conclusion arises when the redistribution goes from the richer players to the poorer.

A discrete-time Markov chain solution with exact rules for general computation of transition probabilities of the one-dimensional cooperative Parrondo's games is presented. We show that winning and the occurrence of the paradox depends on the number of players. Analytical results are compared to the results of the computer simulation and to the results based on the mean-field approach.

Inspired by asynchronous cooperative Parrondo's games we introduce two new types of games in which all players simultaneously play game A or game B or a combination of these two games. These two types of games differ in the way a combination of games A and B is played. In the first type of synchronous games, all players simultaneously play the same game (either A or B), while in the second type players simultaneously play the game of their choice, i.e. A or B. We show that for these games, as in the case of asynchronous games, occurrence of the paradox depends on the number of players. An analytical result and an algorithm are derived for the probability distribution of these games.