Game Theory and Mechanism Design - Stanford University … · 2013. 11. 2. · Game Theory...
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Game Theory Mechanism Design Game Theory and Mechanism Design Jeff Jacobs Stanford University [email protected] November 2, 2013 1 / 26
Transcript of Game Theory and Mechanism Design - Stanford University … · 2013. 11. 2. · Game Theory...
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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