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Electronic Colloquium on Computational Complexity

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Reports tagged with PPAD:
TR06-012 | 17th January 2006
Bruno Codenotti, Mauro Leoncini, Giovanni Resta

Efficient Computation of Nash Equilibria for Very Sparse Win-Lose Games

It is known that finding a Nash equilibrium for win-lose bimatrix
games, i.e., two-player games where the players' payoffs are zero
and one, is complete for the class PPAD.

We describe a linear time algorithm which computes a Nash
equilibrium for win-lose bimatrix games where the number of winning
positions ... more >>>

TR07-082 | 27th July 2007
Christian Borgs, Jennifer Chayes, Nicole Immorlica, Adam Kalai, Vahab Mirrokni, Christos H. Papadimitriou

The Myth of the Folk Theorem

The folk theorem suggests that finding Nash Equilibria
in repeated games should be easier than in one-shot games. In
contrast, we show that the problem of finding any (epsilon) Nash
equilibrium for a three-player infinitely-repeated game is
computationally intractable (even when all payoffs are in
{-1,0,-1}), unless all of PPAD ... more >>>

TR11-103 | 31st July 2011
Yang Li


We initiate the study of the relationship between two complexity classes, BQP
(Bounded-Error Quantum Polynomial-Time) and PPAD (Polynomial Parity Argument,
Directed). We first give a conjecture that PPAD is contained in BQP, and show
a necessary and sufficient condition for the conjecture to hold. Then we prove
that the conjecture ... more >>>

TR15-001 | 2nd January 2015
Nir Bitansky, Omer Paneth, Alon Rosen

On the Cryptographic Hardness of Finding a Nash Equilibrium

Revisions: 1

We prove that finding a Nash equilibrium of a game is hard, assuming the existence of indistinguishability obfuscation and injective one-way functions with sub-exponential hardness. We do so by showing how these cryptographic primitives give rise to a hard computational problem that lies in the complexity class PPAD, for which ... more >>>

TR15-153 | 21st September 2015
Tim Roughgarden

Computing Equilibria: A Computational Complexity Perspective

Computational complexity is the subfield of computer science that rigorously studies the intrinsic difficulty of computational problems. This survey explains how complexity theory defines “hard problems”; applies these concepts to several equilibrium computation problems; and discusses implications for computation, games, and behavior. We assume minimal prior background in computer science.

... more >>>

TR16-063 | 18th April 2016
Pavel Hubacek, Eylon Yogev

Hardness of Continuous Local Search: Query Complexity and Cryptographic Lower Bounds

Revisions: 1

Local search proved to be an extremely useful tool when facing hard optimization problems (e.g. via the simplex algorithm, simulated annealing, or genetic algorithms). Although powerful, it has its limitations: there are functions for which exponentially many queries are needed to find a local optimum. In many contexts the optimization ... more >>>

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