Security and economics are the two main issues considered in the theory and practice of international relations. Acheiving cooperation is difficult in the world politics and economy. There is no common government to enforce rules, and international institutions are weak Scientists have long attempted to understand the fundamental causes of conflict and cooperation, especially when participants are mutally distrastfull. The game theory enabled researchers to analyze this subject. The game theory models strategic confrontations where each player tries to get the maximum payoff, knowing that the other player will also try to do the same. The application of game theory to international relations is not new, but there has been an increase in the particularity of the approaches, associated with new applications of the game theory models to international political economy in addition to their standard role in militarypolitical strategic analysis. The concept of nation-states as independent goal-seeking actors lies in the heart of strategic game analysis. The classical Prisoners' Dilemma game is the most referred to in the field of game theory and international relations and it is often used to show how countries in conflict may lose out due to self interest, rather than cooperate with one another. Theoretical analysis of the iterated, two-player Prisoners' Dilemma show that a strategy based on reciprocity (such as tit-for-tat) can be effective in promoting cooperation. This suggests that states may have incentives to practice reciprocity in a variety of situations that are characterized by mixtures of conflicting and complementary interest and that a strategy based on reciprocity can yield relatively high payoffs against other strategies. Games such as Chicken and Stag Hunt are also significant for analysis of international relations. However, it seems that the classical game theory, its '' games'', and its way of "playing'' the game, are not sufficiently adapted to the specificities of contemporary international relations. New approaches, based on the ''soft '' games, such as the theory of moves, meta games theory, hyper games theory, analysis of confrontation, analysis of options, offer new solutions, but they are not yet sufficiently theoretically elaborated and confirmed.