Are Parrondos games really anything to do with traditional game theory?
The question here is pointing out that Parrondo’s original games do not involve decisions of conflict between players, and therefore cannot be game theory proper. There are two answers to this point. One way of answering it is to say “well, that may be the case but mathematicians, such as Behrends in Germany, are now leading the way with adding Markov decision theory to the games.” Another different answer is to say “well, who says game theory has to have decisions in it?” That is game theory in the von Neumann sense. In the Blackwell sense, game theory includes simple coin tossing games. The book on game theory by Blackwell and Girshick (1954) was another great landmark after the book by von Neumann and Morgenstern (1948).
