Game Theory
Learn the math behind making the perfect choices. Whether you're playing board games, trading Pokémon cards, or sharing a pizza, Game Theory helps you win.
How to Play Perfect
Game theory isn't just about video games. It's the math of predicting what other people will do. If you and your friend both want the last slice of pizza, what's the fairest way to split it? (Hint: One person cuts, the other chooses the slice!)
The Prisoner's Dilemma
Imagine you and your partner get caught pulling a prank. The principal puts you in separate rooms. If you both stay silent, you get 1 day of detention. If you blame your partner and they stay silent, you get zero detention and they get a week! What do you do? This puzzle explains how humans handle trust.
Nash Equilibrium
Named after mathematician John Nash, this is the 'sweet spot' in any game where nobody wants to change their strategy because they're doing the best they possibly can against their opponent. Once you find the equilibrium, you've essentially 'solved' the game.
Things worth remembering.
Rock-Paper-Scissors has a perfect mathematical strategy: just be completely random!
Game theory is used by video game developers to balance characters and weapons.
Animals use evolutionary game theory to decide whether to fight or share food.
Many economists have won the Nobel Prize for using Game Theory to study how people spend money.
Practice problems.
In Tic-Tac-Toe, if both players play perfectly, what is the result?
Show hint
Think about your own games. Has anyone ever won when both of you were really paying attention?
You're playing a game where you and a friend pick a number from 1 to 10. The person who picks the lower number wins that many coins. What number should you pick?
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If you pick 10, they pick 9. If they pick 9, you pick 8. Where does this cycle stop?
How can you win a game of Rock-Paper-Scissors against someone who always plays Rock 50% of the time?
Show hint
If they play Rock half the time, what move should you start spamming?
