EconPapers    
Economics at your fingertips  
 

Parity effect of the initial capital based on Parrondo’s games and the quantum interpretation

Lu Wang, Neng-gang Xie, Yong-fei Zhu, Ye Ye and Rui Meng

Physica A: Statistical Mechanics and its Applications, 2011, vol. 390, issue 23, 4535-4542

Abstract: In our previous study [Zhu et al., Quantum game interpretation for a special case of Parrondo’s paradox, Physica A 390 (2011) 579], the capital-dependent Parrondo’s game where one game depends on the capital modulus M=4 was shown not to have a definite stationary probability distribution and that payoffs of the game depended on the parity of the initial capital. This paper presents a generalization of these results to even M greater than 4. An intuitive explanation for producing this phenomenon is that the discrete-time Markov chain of the game is divided into two completely unrelated inner and outer rings. The process taking the inner ring or outer ring of the game is determined by the initial capital of parity and then a win or loss of the game is determined. Quantum game theory is used to further analyze the phenomenon. The results show that the explanation of the game corresponding to a stationary probability distribution is that the probability of the initial capital has reached parity.

Keywords: Parrondo’s game; Markov chain; Computer simulation; Quantum game (search for similar items in EconPapers)
Date: 2011
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437111005929
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:390:y:2011:i:23:p:4535-4542

DOI: 10.1016/j.physa.2011.07.043

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 (repec@elsevier.com).

 
Page updated 2024-12-28
Handle: RePEc:eee:phsmap:v:390:y:2011:i:23:p:4535-4542