decision THEORY

• Game Theory properly a subset of Decision Theory
• Making choices under uncertainty
• Definitions of 'uncertainty' is a rabbit hole - Knightian Uncertainty and unknown unknowns
• Perfectly frictionless spheres are OK too

GAME THEORY

"the study of mathematical models of conflict and cooperation between intelligent rational decision-makers" - aka interactive decision theory

• Originally built out by John von Neumann, whom you may have heard of
• Found applications in biology, economics, politics, CS
• "players", "information", "available actions", and "payoffs per action" defined formally

GAME THEORY (con't)

• cooperative / non-cooperative (can players make binding commitments?)
• symmetric / asymmetric (do action payoffs depend on player identity?)
• zero-sum / nonzero-sum
• simultaneous / sequential
• perfect / imperfect information

Coordination game

stag

stag

hare

hare

10, 10

0, 5

5, 5

5, 0

PRISONER'S DILEMMA

C

C

D

D

8, 8

0, 10

5, 5

10, 0

equilibriA & Pareto dominance

Each player improves their own situation by switching from "cooperating" to "defecting", given knowledge that the other player's best decision is to "defect".

• Nash Equilibria - points at which no player can improve their outcome by changing their strategy while other players maintain the same strategy
• Pareto Efficiency - impossible to make any one individual better off without making at least one individual worse off
• Stag Hunt has two stable equilibria, one of which pareto-dominates the other
• Prisoner's Dilemma has only one Nash equilibrium, which is not pareto-efficient

iterated games

• In nature and in human practise agents avoid game-theoretic traps

• Iterated Prisoner's Dilemma

• (Axelrod, 1984) In a tournament, simplest program won - "cooperate at first, then do whatever other player did last, except cooperate 5% of the time you'd normally defect"

an even more fun game...

nonzero-sum, sequential, perfect information

Simple rules: I'm selling a dollar on auction, starting at 5 cents; bid raises in increments of 0.05

Winner takes the dollar; second-highest bidder also pays the amount that they bid.

GO