CPS 590.4: Computational Microeconomics: Game Theory, Social Choice, and Mechanism Design
Game Theory and Mechanism Design
Transcript of Game Theory and Mechanism Design
Game Theory Mechanism Design
Game Theory and Mechanism Design
Jeff Jacobs
Stanford University
November 2, 2013
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Game Theory Mechanism Design
Sad (and happy!) introduction
Invented by von Neumann and Morgenstern in 1945
Not related to video games
:(
Can be used to analyze video games!
:)
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Game Theory Mechanism Design
Sad (and happy!) introduction
Invented by von Neumann and Morgenstern in 1945
Not related to video games
:(
Can be used to analyze video games!
:)
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Game Theory Mechanism Design
Sad (and happy!) introduction
Invented by von Neumann and Morgenstern in 1945
Not related to video games
:(
Can be used to analyze video games!
:)
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Game Theory Mechanism Design
Sad (and happy!) introduction
Invented by von Neumann and Morgenstern in 1945
Not related to video games
:(
Can be used to analyze video games!
:)
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Game Theory Mechanism Design
Sad (and happy!) introduction
Invented by von Neumann and Morgenstern in 1945
Not related to video games
:(
Can be used to analyze video games!
:)
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Game Theory Mechanism Design
Your First Game: Rock, Paper, Scissors
Rock Paper Scissors
Rock 0, 0 −1, 1 1,−1
Paper 1,−1 0, 0 −1, 1
Scissors −1, 1 1,−1 0, 0
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Game Theory Mechanism Design
Nash Equilibrium: Prisoners’ Dilemma
Stay Silent Confess
Stay Silent −1,−1 −10, 0
Confess 0,−10 −3,−3
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Game Theory Mechanism Design
Nash Equilibrium: Prisoners’ Dilemma
Stay Silent Confess
Stay Silent −1,−1 −10, 0
Confess 0,−10 −3,−3
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Game Theory Mechanism Design
Nash Equilibrium: Prisoners’ Dilemma
Stay Silent Confess
Stay Silent −1,−1 −10, 0
Confess 0,−10 −3,−3
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Game Theory Mechanism Design
Nash Equilibrium: Prisoners’ Dilemma
Stay Silent ConfessStay Silent −1,−1 −10, 0
Confess 0,−10 −3,−3
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Game Theory Mechanism Design
Nash Equilibrium: Prisoners’ Dilemma
Stay Silent ConfessStay Silent −1,−1 −10, 0
Confess 0,−10 −3,−3
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Game Theory Mechanism Design
Nash Equilibrium: Prisoners’ Dilemma
Stay Silent Confess
Stay Silent −1,−1 −10, 0
Confess 0,−10 −3,−3
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Game Theory Mechanism Design
Nash Equilibrium: Prisoners’ Dilemma
Stay Silent Confess
Stay Silent −1,−1 −10, 0Confess 0,−10 −3,−3
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Game Theory Mechanism Design
Nash Equilibrium: Prisoners’ Dilemma
Stay Silent Confess
Stay Silent −1,−1 −10, 0Confess 0,−10 −3,−3
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Game Theory Mechanism Design
Nash Equilibrium: Prisoners’ Dilemma
Stay Silent Confess
Stay Silent −1,−1 −10, 0Confess 0,−10 −3,−3
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Game Theory Mechanism Design
Nash Equilibrium: Prisoners’ Dilemma
Stay Silent Confess
Stay Silent −1,−1 −10, 0Confess 0,−10 −3,−3
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Game Theory Mechanism Design
Nash Equilibrium: Prisoners’ Dilemma
Stay Silent ConfessStay Silent −1,−1 −10, 0Confess 0,−10 −3,−3
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Game Theory Mechanism Design
Why is Nash Equilibria Important?
Nash’s Theorem (Nash, 1951)
Every game with a finite number of players and actions has at leastone Nash equilibrium.
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Game Theory Mechanism Design
What is Mechanism Design?
We get to design a game
We want the game to have a certain outcome
Let’s design it so that the outcome we want is a Nashequilibrium!
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Game Theory Mechanism Design
Auctions
We have a good g that we want to sell
We have n bidders, each of whom has a valuation vi for thegood
They submit their bids bi in sealed envelopes
Who do we give the item to?
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Game Theory Mechanism Design
The Vickrey Auction
Instead of giving to the highest bidder for their bid, give tothe highest bidder for the second highest bid.
Claim: Vickrey auction induces an honest bidding Nashequilibrium.
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Game Theory Mechanism Design
The Vickrey Auction
Thought Experiment 1: What happens if I bid lower than myvalue?
Thought Experiment 2: What happens if I bid higher than myvalue?
Conclusion: Honest bidding is a Nash equilibrium!
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Game Theory Mechanism Design
The Vickrey Auction
Thought Experiment 1: What happens if I bid lower than myvalue?
Thought Experiment 2: What happens if I bid higher than myvalue?
Conclusion: Honest bidding is a Nash equilibrium!
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Game Theory Mechanism Design
The Vickrey Auction
Thought Experiment 1: What happens if I bid lower than myvalue?
Thought Experiment 2: What happens if I bid higher than myvalue?
Conclusion: Honest bidding is a Nash equilibrium!
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Game Theory Mechanism Design
The End
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