Game Theory Applied to Arms Races
In international relations, the question of why do states develop arm races always remain a puzzle. In a world of anarchy, having military power allow a nation to get its way. Military power is relative, as a state only makes a relative gain against a rival if it builds its military and its rival country does not. Given the cost of building arms is high, an arms race is considered a classic application of prisoner’s dilemma in real life.
The passage linked below discusses that it is always in the best interest of a state to build its armies regardless of the rival state’s status. Therefore, each player’s dominant strategy is to choose high arms and the Nash equilibrium of the game is for both states to choose high. The outcome of the game thus becomes worse for both players than if they both choose low arms, given that they maintain the power balance and spend extra cost on their arm-building.
However, in reality, the “game” is different than in an imagined, perfectly rational world. Arm-building usually does not happen at once, it is more like an ongoing series of decisions and a prolonged game. This fits into the model of “iterated prisoner’s dilemma,” which is a classic game repeatedly played by the same players.
The British physicist and psychologist Lewis Fry Richardson proposed the Richardson model, which describes an arms race between two countries where each country sets its military expenditure or arms acquisition level in each period based on its own and its rival’s level in the previous period. in an “action-reaction” pattern.
According to the passage, the Richardson model can be modeled in this way:
Here, M1t and M2t are the military spending levels of country 1 and country 2 in years t and t-1. Coefficients a1 and a2 are “fatigue” coefficients, representing the difficulty of maintaining high levels of military spending. Coefficients b1 and b2 are “reaction” coefficients, showing the tendency of each country to respond to the military spending of its enemy. The constants g1 and g2 are autonomous “grievance” or “ambition” terms, representing each country’s desire for military capability apart from the rivalry. The arms race will either reach an equilibrium or loses control depending on the fatigue coefficients and reaction coefficients.
There are several questions that arise with Richardson’s model. For example, how do you interpret M1 and M2, and the motives for their actions? They might be countries, alliances, decision-makers, or other types of players. Their hostility might arise due to bureaucratic policies and many other sources that cannot be generalized. Most importantly, there is no way to stop the process of the arms race suggested by the model.
The passage indicated that the Richardson model does not take the changing relationship between states into account and considers its parameters to be constant. Thus, no single conclusion about the international arms race can be made, and it is a complicated matter requiring more research and analysis.
https://www.britannica.com/topic/arms-race/Prisoners-dilemma-models