Using game theory as a way of modeling strategically motivated decisions has direct implications for understanding basic international relations issues. Prisoners Dilemma, Stag Hunt, Battle of the Sexes, and Chicken are discussed in our text. I will apply them to IR and give an example for each.
We are all familiar with the basic Prisoners Dilemma. Two players, simultaneous decisions. In this example, each player has a dominant strategy. In international relations terms, the states exist in anarchy. They are the only body responsible for their own protection. In a security dilemma, each state cannot trust the other to cooperate. A common example of the Prisoners Dilemma in IR is trade agreements. Both nations can benefit by working together and signing the agreement. One nation can then cheat on the agreement, and receives more of a benefit at the cost of the other. The second player, or nation in this case, has the same option. They can cheat on the agreement and hope to gain more than the first nation, but if the both cheat, they both do very poorly. This is why international trade negotiations are often tense and difficult.
Stag Hunt is a game in which the players must cooperate in order to hunt larger game, and with higher participation, they are able to get a better dinner. If participation is not universal, they cannot surround the stag and it escapes, leaving everyone that hunted stag hungry. However, anyone who hunts rabbit can do so successfully by themselves, but with a smaller meal. The closest approximation of this in International Relations are universal treaties, like the Kyoto Protocol environmental treaty. In the long term, environmental regulation in theory protects us all, but even if most of the countries sign the treaty and regulate, some like China and the US will not for sovereignty reasons, or because they are experiencing great economic gain.
Most events in IR are not mutually beneficial, like in the Battle of the Sexes. For example, most land disputes, like the ongoing Chinese and Japanese dispute over the Senkaku Islands, must be resolved by compromising in other areas of policy in order to achieve the goal.
Finally, in the game of chicken, two sides race to collision in the hopes that the other swerves from the path first. Collision is disastrous for everyone, but swerving is losing bad too. A great example of chicken in IR is the Cuban Missile Crisis. On the face of it, the USSR “Swerved”, but I believe that both sides actually made concessions, although the US made theirs later on, to save face.
These are a few basic examples of modeling IR problems with game theory.