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

Public Library of Science
Publication Date
DOI: 10.1371/journal.pone.0067924
  • Research Article
  • Computer Science
  • Computer Modeling
  • Computerized Simulations
  • Mathematics
  • Applied Mathematics
  • Complex Systems
  • Game Theory
  • Mathematical Computing
  • Probability Theory
  • Probability Distribution
  • Statistics
  • Statistical Theories
  • Scaling Theory
  • Social And Behavioral Sciences
  • Sociology
  • Social Networks
  • Mathematics


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.

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