Stochastic Modelings of Social Phenomena: Pedestrian Counter Flow and Tournaments

We present here two examples of stochastic modelings of social phenomena. The first topic is pedestrian counter flow. Two groups of model pedestrians move in opposite directions and create congestions. It will be shown that this congestion becomes worst where individuals are given certain stochastic freedom to avoid another in front compared to the case that they are bound to more strict rules. The second example model tournaments. We present here a rather unexpected feature of tournaments that the probability to reach the top position is higher than that of finishing up at lower positions for not only the number one ranked player, but also for a range of top players. This "inversion characteristics" are shown to be observed with simple mathematical model tournaments as well as in the real tournaments.