How Intractable is the ‘‘Invisible Hand’’:
Polynomial Time Algorithms for
Market Equilibria

Market Equilibrium

Walras, 1874

Arrow-Debreu Theorem, 1954

"Arrow-Debreu Theorem is highly..."

"Arrow-Debreu Theorem is highly..."

"Arrow-Debreu Theorem is highly..."

"Arrow-Debreu Theorem is highly..."

"Arrow-Debreu Theorem is highly..."

Market Equilibrium

History

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History

History

History

Market Equilibrium

Market Equilibrium

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Bang per buck

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"Any goods sold in equality..."

"Any goods sold in equality..."

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Idea of Algorithm

ensuring Invariant initially

How to raise prices?

How to raise prices?

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Termination

Polynomial time

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"Next freezing:"

"Next freezing:"

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Polynomial time

Question

Question

Post-mortem

Primal-Dual Schema

Central Idea Behind
Primal-Dual Schema

Post-mortem

Post-mortem

Post-mortem

Post-mortem

‘‘Primal-Dual-Type’’ Algorithms

Concave utilities

Concave utilities

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 Spending constraint model

"Theorem:"

"Theorem:"

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Devanur &  V.,  2003

Devanur &  V.,  2003

Devanur &  V.,  2003

Devanur &  V.,  2003

Devanur &  V.,  2003

Algorithmic Game Theory

"Q:"

"Global optimality via local improvement"

TCP congestion control

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"Develop an algorithmic theory"

"w.r.t."

"w.r.t."

"w.r.t."

"w.r.t."

"Invariant 1:"

"Invariant 1:"

"Invariant 1:"

"Invariant 1:"

"Invariant 1:"

"Invariant 1:"

"Invariant 1:"

"Maintains both Invariants"

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