Winning combinations of history-dependent games.

Abstract

The Parrondo effect describes the seemingly paradoxical situation in which two losing games can, when combined, become a winning game [Parrondo, Harmer, and Abbott, Phys. Rev. Lett. 85, 24 (2000)]. Here, we generalize this analysis to the case where both games are history dependent, i.e., there is an intrinsic memory in the dynamics of each game. Results are presented for the cases of both random and periodic switching between the two games.