# Gaming the System

Fundamentals of Game Theory

Artwork credit to ncase.me/trust - an interactive demo of prisoner's dilemma

## Game Theory

"... is the study of mathematical models of strategic interaction between **rational** decision-makers. It has applications in all fields of social science, as well as in logic and computer science."

## The Prisoner's Dilemma

"... is a standard example of a game analyzed in game theory that shows why two completely rational individuals might not cooperate, even if it appears that it is in their best interests to do so."

## The Game

"Two members of a criminal gang are arrested and imprisoned. Each prisoner is given the opportunity either to betray the other by testifying against them, or to cooperate with the other by remaining silent."

## Choice and Consequence

## Tournament Rules

- Form groups of 2 players each
- Each group will make 5 decisions total
- Take your points after each decision
- After the last decision, count your points
- In each group, the player with the fewest points is
**ELIMINATED**
- Any
**TIES** are settled with a coin toss
- Form new groups of 2 players each and continue until one player remains

## Changing the Rules

- Form groups of 2 players each
- Each group will make 5 decisions total
- Take your points after each decision
- After the last decision, count and write your points on a piece of paper
**ALL PLAYERS CONTINUE**
- Form a new group with a different player and start a new match
- The tournament ends after 4 matches have been played
- The player with the most points wins!

## What's the Best Strategy?

- Depends on the rules of the system
- In the
**elimination** tournament?
- To
**always cheat** is the best strategy
- In the
**every player continues** tournament?
**Cooperate then copy the last move of the other player** - also known as "Tit for Tat" - is the best strategy

## Real-World Applications

**Bitcoin Mining!**
- Miners use computers to solve computational puzzles
- When a miner solves a puzzle, they are permitted to create a new "block"
- A block is a chunk of data (transactions)
- The miner decides which transactions to include in the block
- In the new block, the miner gives to themselves 6.25 newly created bitcoin
- The miner also gets all the transaction fees in the block
- If the miner cheats (breaks the rules), then the block is rejected by the network, and the miner receives nothing
- Miners are incentivized to cooperate and follow the rules set by the majority of the bitcoin network