Game Theory in the Cold War
https://www.spaceship.com.au/blog/2017/game-theory-cold-war/
This article discusses the role of game theory during the profileration of nuclear weapons in the Cold War. This connects to our discussions on Nash Equilibria, as the article seems to suggest that the large-scale trends of the Cold War can be viewed as the USA and the Soviet Union taking actions to settle in an equilibrium point.
The article notes that the general Cold War conditions can be described by a 2×2 payoff matrix, where the Soviet Union and the United States both choose between attacking and not attacking. If both countries attack each other with nuclear weapons, both receive an infinite negative payoff since they would be destroyed by a massive nuclear attack. If neither countries attack, they both receive a payoff of zero since nothing occurs. However, if only one country attacks, the attacker receives a positive payoff as they have eliminated an enemy, and the receiving country receives a finite negative payoff as they suffer military defeat.
In the case of the Soviet Union, these decisions look like:
However, if one closely examines this game, the case where neither country attacks is not a stable equilibrium, as either country could attack for a higher payoff. Another interesting point is that if the United States is attacked, it would be better off surrendering and suffering military defeat (finite negative payoff) than retaliating and wiping out much of the world’s population in nuclear war (infinite negative payoff). However, we know the Cold War ended with neither country attacking – so how did this happen? The article notes that both countries implemented a “doomsday device” that would automatically trigger retaliation upon any foreign attack. This ensures that if an opponent chooses to attack, it must choose to proceed while knowing that the action will result in mutually assured destruction – making the choice much less attractive. This behavior allows a Nash Equilibrium to form in the case where neither country attacks.
This question can be further extended beyond what is discussed in the article as the rules of the game change drastically over time, with the addition of anti-missile technology, the addition of more countries which may or may not have nuclear capabilities, and ability to gain asymmetric information about the choices of one’s opponents. It seems that military strategists must closely consider game theory when making decisions.