Investigation of Chaotic Switching Strategies in Parrondo's Games

Tang, Tze Wei; Allison, Andrew; Abbott, Derek

doi:10.1142/s021947750400221x

Cited by 18 publications

(9 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition, the Parrondo effect has inspired the studies of the negative-mobility phenomena [5], the reliability theory [6], the noise-induced synchronization [7] and the controlling chaos [8]. In biological systems, Parrondo’s paradox may be related to the dynamics of gene transcription in GCN4 protein and the dynamics of transcription errors in DNA [2].…”

Section: Introductionmentioning

confidence: 99%

Parrondo’s Games Based on Complex Networks and the Paradoxical Effect

Wang

Xie

2013

PLoS ONE

View full text Add to dashboard Cite

Parrondo’s games were first constructed using a simple tossing scenario, which demonstrates the following paradoxical situation: in sequences of games, a winning expectation may be obtained by playing the games in a random order, although each game (game A or game B) in the sequence may result in losing when played individually. The available Parrondo’s games based on the spatial niche (the neighboring environment) are applied in the regular networks. The neighbors of each node are the same in the regular graphs, whereas they are different in the complex networks. Here, Parrondo’s model based on complex networks is proposed, and a structure of game B applied in arbitrary topologies is constructed. The results confirm that Parrondo’s paradox occurs. Moreover, the size of the region of the parameter space that elicits Parrondo’s paradox depends on the heterogeneity of the degree distributions of the networks. The higher heterogeneity yields a larger region of the parameter space where the strong paradox occurs. In addition, we use scale-free networks to show that the network size has no significant influence on the region of the parameter space where the strong or weak Parrondo’s paradox occurs. The region of the parameter space where the strong Parrondo’s paradox occurs reduces slightly when the average degree of the network increases.

show abstract

Section: Introductionmentioning

confidence: 99%

Parrondo’s Games Based on Complex Networks and the Paradoxical Effect

Wang

Xie

2013

PLoS ONE

View full text Add to dashboard Cite

show abstract

“…Hereafter we consider two examples of aperiodic games in more detail. Games generated by chaotic dynamical systems have already been considered in the past [34].…”

Section: Aperiodic Gamesmentioning

confidence: 99%

Parrondo games as disordered systems

Luck

2019

Eur. Phys. J. B

View full text Add to dashboard Cite

Parrondo's paradox refers to the counter-intuitive situation where a winning strategy results from a suitable combination of losing ones. Simple stochastic games exhibiting this paradox have been introduced around the turn of the millennium. The common setting of these Parrondo games is that two rules, A and B, are played at discrete time steps, following either a periodic pattern or an aperiodic one, be it deterministic or random. These games can be mapped onto 1D random walks. In capitaldependent games, the probabilities of moving right or left depend on the walker's position modulo some integer K. In history-dependent games, each step is correlated with the Q previous ones. In both cases the gain identifies with the velocity of the walker's ballistic motion, which depends non-linearly on model parameters, allowing for the possibility of Parrondo's paradox. Calculating the gain involves products of non-commuting Markov matrices, which are somehow analogous to the transfer matrices used in the physics of 1D disordered systems. Elaborating upon this analogy, we study a paradigmatic Parrondo game of each class in the neutral situation where each rule, when played alone, is fair. The main emphasis of this systematic approach is on the dependence of the gain on the remaining parameters and, above all, on the game, i.e., the rule pattern, be it periodic or aperiodic, deterministic or random. One of the most original sides of this work is the identification of weak-contrast regimes for capital-dependent and history-dependent Parrondo games, and a detailed quantitative investigation of the gain in the latter scaling regimes. P

show abstract

“…These sequences are deterministic. In principle, the player can perform an exhaustive search for small N and use other search algorithms including genetic algorithms for large N sequences [11]. Here we would like to endow the player with finite short-term memory, so that he or she has some extra information in the decision on the choice of game played next, as opposed to random switching or deterministic switching in a pre-set sequence.…”

Section: Edward's Ab Game With One-step Memorymentioning

confidence: 99%

“…Tang et al [11]. Apart from the original Parrondo game, other types of Parrondo game have been constructed such as the quantum Parrondo game [12], history-dependent Parrondo game [13] and extended Parrondo game that incorporate dierent B games without the diusive A game [14].…”

Section: Introductionmentioning

confidence: 99%

Winning in sequential Parrondo games by players with short-term memory

Cheung¹,

Fai²,

Wu³

et al. 2016

J. Stat. Mech.

View full text Add to dashboard Cite

Abstract. The original Parrondo game, denoted as AB3, contains two independent games: A and B. The winning or losing of A and B game is defined by the change of one unit of capital. Game A is a losing game if played continuously, with winning probability p = 0.5 − ǫ, where ǫ = 0.003. Game B is also losing and it has two coins: a good coin with winning probability p g = 0.75 − ǫ is used if the player's capital is not divisible by 3, otherwise a bad coin with winning probability p b = 0.1 − ǫ is used. Parrondo paradox refers to the situation that the mixture of A and B game in a sequence leads to winning in the long run. The paradox can be resolved using Markov chain analysis. We extend this setting of Parrondo game to involve players with one-step memory. The player can win by switching his choice of A or B game in a Parrondo game sequence. If the player knows the identity of the game he plays and the state of his capital, then the player can win maximally. On the other hand, if the player does not know the nature of the game, then he is playing a (C,D) game, where either (C=A, D=B), or (C=B,D=A). For player with one-step memory playing the AB3 game, he can achieve the highest expected gain with switching probability equal to 3/4 in the (C,D) game sequence. This result has been found first numerically and then proven analytically. Generalization to AB mod(M ) Parrondo game for other integer M has been made for the general domain of parameters p b < p = 0.5 = p A < p g . We find that for odd M , Parrondo effect does exist. However, for even M , there is no Parrondo effect for two cases: initial game is A and initial capital is even, or initial game is B and initial capital is odd. There is still a possibility of Parrondo effect for the other two cases when M is even: initial game is A and initial capital is odd, or initial game is B and initial capital is even. These observations from numerical experiments can be understood as the factorization of the Markov chains into two distinct cycles. Discussion of these effects on games is also made in the context of feedback control of the Brownian ratchet.

show abstract

Investigation of Chaotic Switching Strategies in Parrondo's Games

Cited by 18 publications

References 16 publications

Parrondo’s Games Based on Complex Networks and the Paradoxical Effect

Parrondo’s Games Based on Complex Networks and the Paradoxical Effect

Parrondo games as disordered systems

Winning in sequential Parrondo games by players with short-term memory

Contact Info

Product

Resources

About