Applications of Genetic Algorithm on Optimal Sequence for Parrondo Games

Parrondo game, which introduction is inspired by the flashing Brownian ratchet, presents an apparently paradoxical situation where there are ways to combine two losing games into a winning one. The original Parrondo game consists of two individual games, game A and game B. Game A is a slightly losing coin-tossing game. Game B has two coins, with an integer parameter M. If the current cumulative capital (in discrete unit) is a multiple of M, an unfavorable coin pb is used, otherwise a favorable pg coin is used. Game B is also a losing game if played alone. Paradoxically, combination of game A and game B could lead to a winning game, either through random mixture, or deterministic switching. In deterministic switching, one plays according to a sequence such as ABABB. Exhaustive search and backward induction have been applied to the search for optimal finite game sequence. In this paper, we apply genetic algorithm (GA) to search for optimal game sequences with a given length N for large N. Based on results obtained through a problem-independent GA, we adapt the point mutation operator and one-point crossover operator to exploit the structure of the optimal game sequences. We show by numerical results the adapted problem-dependent GA has great improvement in