Randomized strategies and terminal distributions (Q2759593)

A pure strategy in a D-S gambling problem may be considered as a sequence of gambles selected from the individual gambles at each stage of the game. So there are two ways of selecting a strategy at random, namely first by selecting the individual gamble at random, second by choosing the entire strategy at random from the set of pure strategies. These two approaches are shown to be equivalent. Finally the authors characterize the set of all possible terminal distributions obtained by stopping the underlying process at random. Two ways of randomizing are shown to be equivalent for this problem, a third one which consists in that the decision to stop is done at random at each stage, is shown to need further conditions.NEWLINENEWLINEFor the entire collection see [Zbl 0971.00065].