Cold War is one of the most controversial and darkest eras in history of humanity which lasted over 4 decades. Starting from 1947 an intense Arms race began between the two superpowers of the time, United States of America and the Soviet Union. This conflict spanned from subtle espionage in the biggest cities of the world to violent combat in the tropical jungles of Vietnam. Both countries were aggressively developing new nuclear weapons which were becoming more and more destructive as developments moved forward. It was in this era that one of the most important mathematical ways of modelling behaviour came in to play. You guessed it! Game Theory. Game Theory was a key component that both countries used in order to model the behaviour of the one another and come with the best strategy possible in response to the strategy one another, however Game Theory was not the only component that leaders of the world considered when they made their decisions at the time. We are going to explore what could happen if each country chose strategies with having minimal to no information about the decision of one another PURLY abed on Game Theory and Rational Thinking. Stay tight and you will find out how a simple matrix and Game Theory could end the life on earth forever!
During the cold war, USA and USSR were both ready and armed to teeth to get in a nuclear war with one another. “On September 26, 1983, Lt. Colonel Stanislav Petrov was in command at Serpukhov-15, a bunker where the Soviets monitored their satellite-based detection systems. Shortly after midnight, panic broke out when an alarm sounded signaling that the United States had fired five Intercontinental Ballistic Missiles, or ICBMs, toward Russia. The warning was a false alarm—one of the satellites had misinterpreted the glint of sunlight off clouds near Montana as a missile launch—but to the Soviets, it appeared the United States had started a nuclear war.” However, Colonel Stanislav Petrov trusted its instincts instead of acting rationally, and didn’t fire soviet nuclear missile and saved the world from a nuclear war close call. However, we would like to see what could happen if he would think rationally about the situation.
Source: Wikipedia
This can be imagined as a game and can be roughly modelled with the tools game theory provides us. Imagine USA and USSR being two rational agents, and both assume that the other is thinking rationally about the situation. In this game setup both agents, USA and USSR, have two strategy that they can come up with in response to one another. Strategy one is: Attack, and strategy two is: Not Attack. Obviously either one of the countries (rational agents) choosing to Attack would start the third world war. Please note that in this era both countries considered one another a threat to the free world and wanted to eliminate each other. With that note in mind we assign pay off values to each strategy. Remember that payoff is a tuple of numbers which first coordinate represents pay off for first agent and second one represents the payoff for the second agent, in this example let agent one be USA and agent two be USSR. Payoff for coordinate AA of matrix (both countries choose to Attack) is (-infinity, -infinity). For coordinate AN (agent one chooses to Attack and agent two chooses not to Attack) is (1, -infinity) and for coordinate NA is (-infinity, 1). And finally, for coordinate NN (both countries choose Not Attack) is (0,0). And this is the game setup and components.
Now, why did we choose the payoff numbers the way they are? well, the explanation is actually pretty simple, -infinity represents permanent elimination or taking TOO MUCH time to repair and revive the life in that are, 0 represents no destruction at all (Nothing changes), and 1 represents they gain a point for eliminating the thereat and it becomes the only superpower in the world. Remember, this is nuclear weapons we are talking about here so -infinity sounds about right for as payoff because if one country attacks the other it takes way TOO LONG to return to normal state for that country.
Now, how each county is choosing their strategy? Well, since both countries are thinking rationally, and both want to eliminate the threat the choose to Attack regardless of what the other country is choosing. The reason is because (1) if one country attacks the other, the other country will attack too, and (2) If one country attacks and the other one doesn’t that country becomes the only superpower and eliminates the threat at the same time (gains a point). Therefore, both countries choose to attack regardless of what the other chooses. Hence, we notice that both countries have a Dominant Strategy.
There is something wrong with the game above and it is that, coordinates NN (Both countries choosing not to Attack) is the best option for all people in the world and nothing would change, and peace would remain in the world. However, making decisions only based on Game Theory, never gets us to both countries choosing not to attack each other, but instead leads to AA (Both countries attacking each other), which is Nash equilibrium in this model, and that would end of life on earth.
With all above being said, Colonel Stanislav Petrov would fire the missiles with the setup we gave, and world would be much more different than what it is right now. So, we explored what would happen if during cold war both countries made their political decisions purely based on Game Theory, and we can see that Game Theory alone could end the life and we wouldn’t exist right now if that happened! Considering all that said, you can go and enjoy your life and be happy that diplomacy is not only based on purely rational decisions, and leaders of the world look further and think about the future of the world and how it could look like before making a decision just like what happened in 1991 and both countries chose to come to peace at the end and save the free world that me and you are living in right now.
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