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Parrondo's Paradox for Games with Three Players


Parrondo's Paradox for Games with Three Players

Ejlali, Nasim, Pezeshk, Hamid, Chaubey, Yogendra P. ORCID: https://orcid.org/0000-0002-0234-1429 and Sadeghi, Mehdi (2018) Parrondo's Paradox for Games with Three Players. Technical Report. Concordia University. Department of Mathematics and Statistics, Montreal, Quebec.

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Parrondo’s 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 Parrondo’s game as history dependent game, cooperative Parrondo’s 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.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Monograph (Technical Report)
Authors:Ejlali, Nasim and Pezeshk, Hamid and Chaubey, Yogendra P. and Sadeghi, Mehdi
Series Name:Department of Mathematics & Statistics.Technical Report No. 1/18
Corporate Authors:Concordia University. Department of Mathematics and Statistics
Institution:Concordia University
Date:26 April 2018
  • Natural Sciences and Engineering Research Council
Keywords:Parrondo’s paradox, Combined game, Game theory.
ID Code:983832
Deposited By: Yogen Chaubey
Deposited On:07 May 2018 13:24
Last Modified:07 May 2018 13:29


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