Europhys. Lett., 63 (3) , pp. 319-325 (2003)
Optimal strategies in collective Parrondo gamesL. 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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