perverse adventures in game theory

Part I

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

hare

10, 10

0, 5

5, 5

5, 0

PRISONER'S DILEMMA

C

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.