Europhys. Lett.
Volume 63, Number 3, August 2003
Page(s) 319 - 325
Section General
Published online 01 November 2003
DOI: 10.1209/epl/i2003-00461-5
Europhys. Lett., 63 (3) , pp. 319-325 (2003)

Optimal strategies in collective Parrondo games

L. Dinis and J. M. R. Parrondo

Grupo Intedisciplinar de Sistemas Complejos (GISC) and Departamento de Física Atómica, Molecular y Nuclear Universidad Complutense de Madrid - 28040 Madrid, Spain

(Received 17 March 2003; accepted in final form 26 May 2003)

We present a modification of the so-called Parrondo's paradox where one is allowed to choose in each turn the game that a large number of individuals play. It turns out that, by choosing the game which gives the highest average earnings at each step, one ends up with systematic losses, whereas a periodic or random sequence of choices yields a steadily increase of the capital. An explanation of this behavior is given by noting that the short-range maximization of the returns is "killing the goose that laid the golden eggs". A continuous model displaying similar features is analyzed using dynamic programming techniques from control theory.

02.50.-r - Probability theory, stochastic processes, and statistics.
02.50.Ey - Stochastic processes.
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.

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