When states interact with each other in the international arena, they do so in a variety of strategic settings. In the context of an arms competition, states feel an imperative to keep up with their adversary, and surpass them, if possible. In international trade, states often have an incentive to protect domestic industries but a conflicting interest to widen markets for their exports. States attempting to coordinate on an international standard wish to harmonize their policies, but preferably on their own terms.
Each setting will present states with a different set of incentives and strategic opportunities. The primary question of interest in each case is how states will respond to these incentives and opportunities, or how they will behave. Some outcomes, called equilibria, will be stable or self reinforcing, in that if the players think they will occur, they have an incentive to fulfill that expectation and make them occur. Not all outcomes in a strategic setting have this property. Non-equilibrium outcomes are thought to be less likely to occur than equilibria, so by locating equilibria we can begin to make predictions about behavior.
More specifically, we can ask whether states will cooperate. Keohane (1984, 51) defined cooperation as a process by which policies that were not in harmony to start with are brought into conformity through a process of policy coordination. More formally, we can identify cooperation with the achievement of Pareto efficient outcomes by the players in a setting in which inefficient outcomes exist. That is, if a setting is positive sum, so that there is a possibility for joint gains, then it can serve as a model of a cooperation problem. If a Pareto optimal outcome is also an equilibrium, then cooperation is more likely in that setting than if the Pareto optimal outcomes are not equilibria.
These different strategic settings can be represented by simple two player, two strategy normal form games.