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Paper   IPM / Biological / 15212
School of Biological Sciences
  Title:   Parrondo's Paradox for Games with Three Players
1.  Nasim Ejlali
2.  Hamid Pezeshk
3.  Yogendra Chaubey
4.  Mehdi Sadeghi
  Status:   Published
  Journal: Technical Report
  No.:  18
  Vol.:  983832/1/ report No. 1/18 (2018)
  Year:  2018
  Pages:   Spectrum: Concordia University, https://spectrum.library.concordia.ca/983832/1/report1-18.pdf
  Supported by:  IPM
Parrondos paradox appears in game theory which asserts that playing two losing games, A and B (say) randomly or periodically may result in a winning expectation. In the original paradox the strategy of game B was capital-dependent. Some extended versions of the original Parrondos game as history dependent game, cooperative Parrondos game and others have been introduced. In all of these methods, games are played by two players. In this paper, we introduce a generalized version of this paradox by considering three players. In our extension, two games are played among three players by throwing a three-sided dice. Each player will be in one of three places in the game. We set up the conditions for parameters under which player one is in the third place in two games A and B. Then paradoxical property is obtained by combining these two games periodically and chaotically and (s)he will be in the first place when (s)he plays the games in one of the mentioned fashions. Mathematical analysis of the generalized strategy is presented and the results are also justified by computer simulations.

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