  This work explores dynamics existing in interactions between players. The
dynamic system of games is a new attitude to modeling in which an event is
modeled using several games. The model allows us to analyze the interplay
capabilities and the feasibility objectives of each player after a conflict
with other players objectives and capabilities. As an application, we model
relations between the Soviet Union and America after World War II to October
1962, by using the dynamic system of games. The dynamic system of games as an
important insight clearly has significant implications for modeling strategic
interactions in which player pursue goals for increasing their personal
interests. In addition, we introduce a new game in which there is a dilemma
which this dilemma occurs in most societies. We investigate depends on the
claim that each player in this dilemma is hyper-rational. In the concept of
hyper-rational, the player thinks about profit or loss of other actors in
addition to his personal profit or loss and then will choose an action which is
desirable to him. In this dilemma, a weak trust has been created between
players, but it is fragile.
