Game Theory and International Relations: the benefit of alliances
A number of complicated real life situations can be modeled as games. One such example is of interactions between nations, either in economic relationships or in conflict. Some wars are zero sum and can be modeled as zero sum games; a country deciding on a strategy to defend its territory can be zero sum if deciding to defend in one place results in exposing another area (a situation that is simply the Matching Pennies game in another form). More broadly, a conflict between two diametrically opposed powers can be simplistically modeled as a zero sum game, an example of this being the Cold War. Economic or trade relationships are a little more complicated, as they have multiple players with varying wants and incentives that may or may not align with those of other players. Regardless of the complexity of the situation or the type of relationship, however, analyzing the actions of nations through the lens of game theory provides additional, valuable insight into the actions countries can take to achieve their preferred outcome. One finding that has been made through such analysis is that adversarial states have difficulty communicating honestly with each other, as their incentives lead them directly to misleading each other.
Trager analyzes a specific yet fairly common relationship between three states: two states that interact directly with each other, and a third party state allied or associated with one of them. These are, respectively, the “target”, the “protege”, and the “third party”. An example of this arrangement is the relationship between the US, Taiwan, and China, with the US as the third party, Taiwan as the protege, and China as the target. He finds that in certain circumstances, what he refers to as diplomatic signaling can circumvent the incentives that lead to dishonest communication. Diplomatic signaling, in this context, is the support or lack of support from the third party state that can shift the incentives and balance of power between the protege state and the target state, leading to war, better positioning of the protege state, or peace, depending on the specific circumstances of the conflict. This signaling can be public or private. In the end what matters is how it changes the behavior of the protege state towards the target state.
For example, if the protege state takes an aggressive stance towards the target state, the target state can be much more certain that the protege state is acting with the tacit backing of the third party, meaning that if the situation devolves into was the target state will have to fight not only the protege but also the third party. This might happen if the third party has an incentive to protect the protege from occupation, like if the protege state is the land between the target and the third party and having the protege state be occupied is dangerous to the third party. Conversely, it might benefit the third party for the protege to come out worse, and so they might withhold support, signaled by the protege’s less aggressive demands from a weaker position.
Although the model explained here is not yet statistically tested, Trager’s review of relevant diplomatic relationships between states has shown that the predictions of his model are broadly correct. Through his work, he has managed to show how the fairly simple mechanism of public or private declarations of support from a third party state can change the balance of power between two adversary states that would not otherwise be able to communicate truthfully. This is useful not only to diplomats working to balance the interests of their own nation verses those of allied or “client” states, but also to scholars looking to analyze past conflicts. More broadly, it serves as a good example of how useful game theory models can be in a real life context.
Source: Trager, R. F. (2015). Diplomatic Signaling among Multiple States. The Journal of Politics, 77(3), 635-647.
https://www-jstor-org.proxy.library.cornell.edu/stable/10.1086/681259