Parrondo’s paradox for games with three players and its potential application in combination therapy for type II diabetes

Nasim Ejlali, Hamid Pezeshk, Yogendra P. Chaubey, Mehdi Sadeghi, Ali Ebrahimi and Abbas Nowzari-Dalini

Physica A: Statistical Mechanics and its Applications, 2020, vol. 556, issue C

Abstract: 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 1 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. A potential application of the model in treatment of type II diabetes is presented. In this theoretical work, we consider two types of treatments as two games which are played among three different players. The player 1 is considered as the treatment success index, the player 2 is the insulin deficiency index and the player 3 is assumed to be the insulin resistance index. It is shown that certain combinations of two losing games for player 1 (unsuccessful treatments) will result in a win (successful treatment).

Keywords: Parrondo’s paradox; Game theory; Combined game; Type II diabetes; Combination therapy (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437120303496
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:556:y:2020:i:c:s0378437120303496

DOI: 10.1016/j.physa.2020.124707

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().