Essay about Game Theory Introduction

1229 Words Jan 17th, 2015 5 Pages
Game Theory Background An Illustrative Example Course Structure

Introduction to Game Theory
Econ 414
Jeff Borowitz

Summer I 2010

Jeff Borowitz

Introduction to Game Theory

1 / 18

Game Theory Background An Illustrative Example Course Structure

Rational Choice

What is Game Theory?

Game Theory is really “Multi-Party Decision Theory” Outside of game theory, we think of just one actor (firms maximizing profits, workers deciding how much to work, etc.) Decisions involving many parties are very relevant to economics
Oligopoly Public Goods Working together on a team project

Jeff Borowitz

Introduction to Game Theory

2 / 18

Game Theory Background An Illustrative Example Course Structure

Rational Choice
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Player 1 gets a payoff that depends on her action and the actions of the other players, 2, 3, . . . , n. Define individual i ’s utility over the outcomes that arise when every other player takes a particular action. Call player 1’s payoff u1 . If each player plays strategy Si , the payoff can be written: u1 (S1 , S2 , . . . , Sn ) Or generally the payoff that i gets when players all play S1 , S2 , . . . , Sn is ui (S1 , S2 , . . . , Sn ) Sometimes for convenience, I will abuse notation and write this as: ui (Si , S−i ) where S−i denotes the strategies of each player except i
Jeff Borowitz Introduction to Game Theory 7 / 18

Game Theory Background An Illustrative Example Course Structure

The Simplified Prisoner’s Dilemma

A single person decision
Bob is arrested and charged with a crime. He is thinking about what to do when he is interrogated If he confesses to the crime, he goes to jail for 4 years If he remains silent, there’s only enough evidence to send him to jail for 1 year.

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