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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
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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