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Parrondo's paradox via redistribution of wealth

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Parrondo's paradox via redistribution of wealth
2.	Creator	Author's name, affiliation, country	Stewart N. Ethier; University of Utah; United States
2.	Creator	Author's name, affiliation, country	Jiyeon Lee; Yeungnam University; Korea, Republic Of
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Parrondo's capital-dependent games; Markov chain; stationary distribution; fundamental matrix; strong law of large numbers; central limit theorem
3.	Subject	Subject classification	60J20; 60F05
4.	Description	Abstract	In Toral's games, at each turn one member of an ensemble of $N\ge2$ players is selected at random to play.  He plays either game $A'$, which involves transferring one unit of capital to a second randomly chosen player, or game $B$, which is an asymmetric game of chance whose rules depend on the player's current capital, and which is fair or losing.  Game $A'$ is fair (with respect to the ensemble's total profit), so the \textit{Parrondo effect} is said to be present if the random mixture $\gamma A'+(1-\gamma)B$ (i.e., play game $A'$ with probability $\gamma$ and play game $B$ otherwise) is winning.  Toral demonstrated the Parrondo effect for $\gamma=1/2$ using computer simulation.  We prove it, establishing a strong law of large numbers and a central limit theorem for the sequence of profits of the ensemble of players for each $\gamma\in(0,1)$.  We do the same for the nonrandom pattern of games $(A')^r B^s$ for all integers $r,s\ge1$.  An unexpected relationship between the random-mixture case and the nonrandom-pattern case occurs in the limit as $N\to\infty$.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2012-03-14
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/1867
10.	Identifier	Digital Object Identifier	10.1214/EJP.v17-1867
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 17
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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