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Game Theory

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by

Adam Galambos

on 10 September 2013

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Transcript of Game Theory

Game Theory
The science of strategy
Studies strategic situations: the payoff to a participant in the interaction depends not only on his/her/its own actions, but also on the actions of others.
History
Simultaneous move games
Sequential move games
Repeated games
What is a game?
Players: who are the participants in the interaction?
Strategies: what are the choices of the players?
Payoffs: what are the consequences of various combinations of choices?
Alice
Bob
Mum
Rat
Mum
Rat
-1
-1
-5
-5
-10
0
0
-10
Prisoner's Dilemma
Bob
10
Stay
-10
Alice
10
Swerve
Swerve
Stay
Chicken
-10
-2
-2
Alice
Battle of the sexes
Bob
3
0
10
0
Game
3
Game
Show
Show
6
0
1
0
Penalty kick
Left
Left
Right
1
Right
1
0
Kicker
Goalie
0
0
6
10
1
0
HEX
Alice
Bob
enter
stay out
fight
acquiesce
1
5
0
0
2
2
fight
2
Alice
acquiesce
2
0
Bob
0
enter
5
1
stay out
2
5
fight
0
1
2
enter
stay out
Alice
0
Bob
acquiesce
acquiesce
1
enter
Bob
0
2
0
Alice
5
fight
2
stay out
Subgame perfect equilibrium
Start at the end: analyze the endgame first
"Roll back" the optimal actions from there
Rules out incredible threats
Commitment
How can you change the game to make your threat credible?
Scuttle your ships
Reduce your options
Biblical times: GT in the Bible
1838: Cournot
1913: Zermelo: in chess, either white can force a win, or black can force a win, or both sides can force a draw.
1928: Von Neumann’s minimax theorem
1944: Von Neumann and Morgenstern
1950-53: Nash
1952: John Charles C. McKinsey, Introduction to the Theory of Games
1972: International Journal of Game Theory was founded by Oskar Morgenstern
1990: The first graduate level microeconomics textbook to fully integrate game theory into the standard microeconomic material was David M. Krep’s A Course in Microeconomic Theory
1994: Nash, Harsanyi, Selten Nobel
2005: Aumann, Schelling Nobel
2007: Hurwicz, Maskin, Myerson Nobel
GT is central to economics, becoming important in political science, bi- ology, psychology, sociology, has applications in philosophy, pure mathematics, business!
Mechanism Design
Rat
Mum
-10
-1
-5
Mum
0
0
-1
Bob
-10
Rat
Alice
-5
Prisoner's Dilemma
Play the same game repeatedly
Total payoff: Sum or average of stage payoffs
Or, the discounted sum of payoffs
In repeated games,
Outcomes that are not sustainable in the stage game could be equilibrium outcomes
Cooperation is much easier to sustain
Change the perspective:
Instead of analyzing a game with given rules, design the rules to achieve desirable outcomes
Not the same as "central planning!"
Successful applications: auction design, matching (medical residencies, school choice, course registration)
http://www.slate.com/id/2108640/
Campaign strategy:
Business:
http://www.newyorker.com/arts/critics/books/2010/07/26/100726crbo_books_gottlieb
Voting systems:
Basic intro:
Adam Galambos, Lawrence University
Ken Binmore: Game Theory
A Very Short Introduction
Full transcript