Game Theory
by Jessica Sedgewick, Economics major
Nash equilibrium
We start with the concept of Nash Equilibrium, made famous in the 2001 film A Beautiful Mind. We end with the concept of Nash Equilibrium as well, because we do not understand it. That was a good movie, though, wasn't it?
Zero-sum games
If you've ever gambled on sports or tried your chops at poker, you've played a zero-sum game. If you've ever won an additional $4000 on a game show by making an irrational wager, and your wager caused a popular wagering blogger to rack up $4000 worth of damages in the rampage he went on at his gym after watching, you've also played a zero-sum game.
Minimax and backward induction
In sequential games like chess, where players move one at a time, we can use backward induction to calculate the optimal outcome - and in doing so, figure out what we should do first. In Jeopardy! wagering, we can use backward induction to calculate that because $4000 is always the best wager, it is the best wager in any particular situation.
Mixed-strategy Nash equilibrium
Sometimes, a game will have no readily-apparent Nash equilibrium. This is especially true if you do not understand Nash equilibria. In such a case, both players have two choices: wager $4000, or go home penniless, sad, and unloved.
Expected value, independent events, and The Gambler's Fallacy
Here, I'll show you how to calculate the expected value of a situation - even when you're looking for more than one thing to happen, such as the probability of flipping "heads" multiple times in a row. Don't expect this to make you a hit at parties.
Dominance
When you're given two rational options, and you always prefer one, we say that your choice "dominates" the other. When you're given the option of wagering $4000 or not wagering $4000, we say that your choice to wager $4000 makes you "dominant" at life.
First-mover advantage
What do the Wu-Tang Clan, CVS pharmacies, and the popular app Threes! have in common? We were unable to obtain celebrity endorsements from any of them for Just Wager $4000!. We're pretty sure they'd all be into it, though.