In this sense, the theory of games is the analysis of the strategic elements of a game rather than that of the chance elements, which mathematicians have studied over a much longer period in probability . But game theory is not an abstract activity, not pure mathematics. Nor is it a game, though it is useful for explaining the logic of many social games. It is mostly deployed to explore such complex and serious topics as the logic of arms races, the behaviour of agents in imperfect markets, and the behaviour of political parties and coalitions. In this sense the whole of economic theory, and much political theory, are subsets of game theory.
Game theorists classify games by their nature and their pay-offs.
The aim of the analyst is to find the equilibrium solutions to the game. Game theorists also classify games by whether or not they are zero-sum or not. In the social sciences most focus has been on non zero-sum games. The most famous is the two-person prisoner's dilemma which has an apparently paradoxical property. In this game each player has a dominant strategy, that is, one course of action which leads to the best possible pay-off against whichever of two options the opponent chooses.