6.890 Algorithmic Lower Bounds: Fun with Hardness Proofs (Fall '14)

Prof. Erik Demaine     TAs: Sarah Eisenstat, Jayson Lynch


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[+] PPAD (guest lecture by Constantinos Daskalakis). Economic games, Nash equilibrium, Nash's Theorem, Brouwer's Fixed-Point Theorem, Sperner's Lemma, proofs and computational versions. Total search problems (TFNP), directed parity argument, End of the Line, PPAD, Arithmetic Circuit SAT. [Scribe Notes] [src]

This lecture is the first of two guest lectures by Prof. Constantinos Daskalakis about the class PPAD which is intricately related to economic game theory (and a cool idea more generally). Costis is the expert in this area — his PhD thesis, for example, proved that finding Nash equilibria is PPAD-complete.

Specifically, this lecture illustrates beautiful connections (reductions) between Nash's Theorem in economic game theory, Brouwer's Fixed-Point Theorem in topology, and Sperner's Lemma in graph theory. These problems are all PPAD-complete, meaning that they are the hardest search problems that have guaranteed solutions via “directed parity arguments” (formally, a problem called End of the Line). To prove PPAD-hardness (in the next lecture), we introduce an analog of Circuit SAT called Arithmetic Circuit SAT.

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Handwritten notes, page 1/7[previous page][next page][PDF]

Handwritten notes, page 1/7[previous page][next page][PDF]

Slides, page 1/59[previous page][next page][PDF]

Slides, page 1/59[previous page][next page][PDF]

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