Prisoner's Dilemma is a famous paradoxical-ish thought experiment type example given to try and explain Game Theory. Two partners in crime have been captured and held separately and charged with various crimes. They are given an opportunity to exonerate themselves, by snitching on the other guy. The outcomes are that either both prisoners don't snitch and they both get a shorter sentence for the crimes committed, or one of them snitches and goes free while the other gets a long jail term, or they both snitch on each other and they both go to jail for long jail terms. 

The obvious best-case scenario is that neither snitches and they both finish their short sentences and step back into a life of crime or whatever. But an important thing to keep in mind is that neither knows what the other is planning. There is no honor among thieves, and they both doubt each other and seek to protect themselves.

A Zero-Sum Game is one where one clearly wins, and one clearly loses. There is no intersection in their gains or losses, one prisoner snitches the other gets stitches. Non-Zero Sum games are those where the losses and gains are not balanced out. Both could win, both could lose, trade is a great example.

The terms come from the fact that a win is counted as a +1 and a loss as a -1, and when they both are equally distributed, it sums up to 0. Non-Zero Sums then suggest that the +1 and -1 are not equally distributed, one agent gets or loses more than the other gains or loses. An important thing to mention is that a game can always have more than two playas. 

Another more practical example is voting. You could vote, prompting more people to vote. While your individual contribution is sort of meaningless, your not contributing is much worse. You could preempt a really low turnout and not vote yourself. But if that instead motivated you to go out and vote, perhaps other people around you would also be motivated to vote. But the cinch here is that no one knows what the other person's assessment of the situation is.

When Cortez (Spanish boi) landed in Mexico to invade the Aztec Empire (the Mayans and Aztecs were Mexicans - South Americans were Inca), he burnt his ships to make sure that the soldiers would stand their ground and fight, and not calculate their individual gains in aborting mission and running away. Aztecs were not a peaceful race of people, and when they saw some foreigners come to their lands with a meager fighting force and burning their only options for a retreat, they lost their shit and ran away and Cortez very easily took over the capital Tenochtitlan. 

 The funnest way (IMO) game theory is used is scheduling broadcasts for television, and movie releases. How do you schedule which program with these numbers of average viewership, taking into consideration the rival channels' schedules and numbers.

So game theory is a very intuitive concept that way - we inherently know what the logic is. Game theory also happens to be the reason for society evolving into its present form. Thomas Hobbes was a famous philosopher who came up with a theory of social contract. IDK if you remember, but Social Contract theories are theories behind the conception of a government or state authority. He believed that social life has no guarantees. If my helping you is conditional on you helping me, then there's really no way to ensure you keep up your side of the bargain once I do what I was supposed to do. This doubt means I might take some extreme action to ensure your cooperation, and it could turn into a vicious cycle of jungle raaj, where the one with the most power wins. That's why we introduce a state to enforce contracts. 

The point of that tangent is that game theory has a lot more applications than you would think it does, and possibly made us who we are now. 

The math of game theory is most easily resolved through matrices. I hope you remember what a matrix is, I am not sure how to explain it here. But you basically make a matrix and figure in the losses and gains (payoffs) of each scenario for each agent and form an equation to see which is the most conducive scenario for all agents.

I think game theory is amaze-balls because of how super intuitive it is - inherently, we know what's the best outcome for a situation based on everyone's unique position and maximizing everyone's gains. Which just goes to show that math rally is the unique language underlying our existence. Someone once said that math is the language of the universe, and I think it really absolutely is: U+I=69

Series of letters for my manfriend who has a three-second attention span, during lockdown so he wouldn't leave me or forget me. Edited to take the XXX bits out, if you see an accidental yucky cheese moment pls ignore.