Introduction: Probability and Finance as a Game
1 Jean Ville (1910–1988) as a student at thé Ecole Normale Supérieure in Paris. His study of martingales helped inspire our framework for probability. We propose a framework for the theory and use of mathematical probability that rests more on game theory than on measure theory. This new framework merits attention on purely mathematical grounds, for it captures the basic intuitions of probability simply and effectively. It is also of philosophical and practical interest. It goes deeper into probability's conceptual roots than the established measure-theoretic framework, it is better adapted to many practical problems, and it clarifies the close relationship between probability theory and finance theory. From the viewpoint of game theory, our framework is very simple. Its most essential elements were already present in Jean Ville's 1939 book, ´ Etude critique de la notion de collectif, which introduced martingales into probability theory. Following Ville, we consider only two players. They alternate moves, each is immediately informed of the other's moves, and one or the other wins.