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Smoothed Complexity of 2-player Nash Equilibria
[article]

2020
*
arXiv
*
pre-print

Our results therefore separate

arXiv:2007.10857v1
fatcat:i7tgbussgrcwxk3rva6vzwhrwm
*smoothed**complexity*and hardness*of*approximation for*Nash**equilibria*in two-*player*games. ... In contrast to prior work proving PPAD-hardness after*smoothing*by noise*of*magnitude 1/poly(n) [CDT09], our*smoothed**complexity*result is not proved via hardness*of*approximation for*Nash**equilibria*. ... In this work, we resolve the*complexity**of*two-*player**Nash*equilibrium with constant-magnitude*smoothing*, proving that it is PPAD-complete (under randomized reductions). ...##
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Query complexity of approximate nash equilibria

2014
*
Proceedings of the 46th Annual ACM Symposium on Theory of Computing - STOC '14
*

*Nash*

*Equilibria*We prove that the query

*complexity*

*of*end-

*of*-a-simple-path is exp(n).Yakov BabichenkoQuery

*Complexity*

*of*Approximate

*Nash*

*Equilibria*We prove that the query

*complexity*

*of*end-

*of*-a-simple-path ... Yakov Babichenko Query

*Complexity*

*of*Approximate

*Nash*

*Equilibria*The Main Theorem The well supported

*Nash*problem, WSN(n, m, ε): INPUT: n-

*players*, m-actions game. ...

##
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Query Complexity of Approximate Nash Equilibria

2016
*
Journal of the ACM
*

*Nash*

*Equilibria*We prove that the query

*complexity*

*of*end-

*of*-a-simple-path is exp(n).Yakov BabichenkoQuery

*Complexity*

*of*Approximate

*Nash*

*Equilibria*We prove that the query

*complexity*

*of*end-

*of*-a-simple-path ... Yakov Babichenko Query

*Complexity*

*of*Approximate

*Nash*

*Equilibria*The Main Theorem The well supported

*Nash*problem, WSN(n, m, ε): INPUT: n-

*players*, m-actions game. ...

##
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The price of anarchy in games of incomplete information

2012
*
ACM SIGecom Exchanges
*

We outline a recently developed theory for bounding the inefficiency

doi:10.1145/2325713.2325716
fatcat:2jdxa7z2i5ehxpylyorwhfwhyq
*of**equilibria*in games*of*incomplete information, with applications to auctions and routing games. ... outcome*of*the game. (*2*) Invoke the*Nash*equilibrium hypothesis once per*player*, to derive that each*player*i's payoff in the*Nash*equilibrium a is at least as high as if it played a * i instead. ...*equilibria*in congestion games with incomplete information. (5) For Bayes-*Nash**equilibria*in games with correlated*player*preferences, there is no general extension theorem for*smooth*games. ...##
###
The price of anarchy in games of incomplete information

2012
*
Proceedings of the 13th ACM Conference on Electronic Commerce - EC '12
*

We outline a recently developed theory for bounding the inefficiency

doi:10.1145/2229012.2229078
dblp:conf/sigecom/Roughgarden12
fatcat:325pi75qrzfsthmvwh5em6jhqe
*of**equilibria*in games*of*incomplete information, with applications to auctions and routing games. ... outcome*of*the game. (*2*) Invoke the*Nash*equilibrium hypothesis once per*player*, to derive that each*player*i's payoff in the*Nash*equilibrium a is at least as high as if it played a * i instead. ...*equilibria*in congestion games with incomplete information. (5) For Bayes-*Nash**equilibria*in games with correlated*player*preferences, there is no general extension theorem for*smooth*games. ...##
###
The Price of Anarchy in Auctions
[article]

2016
*
arXiv
*
pre-print

This survey outlines a general and modular theory for proving approximation guarantees for

arXiv:1607.07684v1
fatcat:b5t3xgmk75bi7iymdoelblnnl4
*equilibria**of*auctions in*complex*settings. ... We highlight three user-friendly analytical tools:*smoothness*-type inequalities, which immediately yield approximation guarantees for many auction formats*of*interest in the special case*of*complete information ... Bayes-*Nash**equilibria*are relatively well understood.*2*. Bayes-*Nash**equilibria*are fully efficient, with the item always allocated to the bidder with the highest valuation. ...##
###
The Price of Anarchy in Games of Incomplete Information

2015
*
ACM Transactions on Economics and Computation
*

We outline a recently developed theory for bounding the inefficiency

doi:10.1145/2737816
fatcat:jcqvxmvfizhgtmml3g2ve5b4sa
*of**equilibria*in games*of*incomplete information, with applications to auctions and routing games. ... outcome*of*the game. (*2*) Invoke the*Nash*equilibrium hypothesis once per*player*, to derive that each*player*i's payoff in the*Nash*equilibrium a is at least as high as if it played a * i instead. ...*equilibria*in congestion games with incomplete information. (5) For Bayes-*Nash**equilibria*in games with correlated*player*preferences, there is no general extension theorem for*smooth*games. ...##
###
The Price of Anarchy in Auctions

2017
*
The Journal of Artificial Intelligence Research
*

This survey outlines a general and modular theory for proving approximation guarantees for

doi:10.1613/jair.5272
fatcat:7gcmpshgivh2vj4xu2enqe3nue
*equilibria**of*auctions in*complex*settings. ... We highlight three user-friendly analytical tools:*smoothness*-type inequalities, which immediately yield approximation guarantees for many auction formats*of*interest in the special case*of*complete information ... Bayes-*Nash**equilibria*are relatively well understood.*2*. Bayes-*Nash**equilibria*are fully efficient, with the item always allocated to the bidder with the highest valuation. ...##
###
On the Approximation and Smoothed Complexity of Leontief Market Equilibria
[article]

2006
*
arXiv
*
pre-print

We show that the problem

arXiv:cs/0602090v1
fatcat:3ghfwx53lnhilmsqv5rl7mqkha
*of*finding an \epsilon-approximate*Nash*equilibrium*of*an n by n two-person games can be reduced to the computation*of*an (\epsilon/n)^*2*-approximate market equilibrium*of*a Leontief ... PPAD is not in RP, that the*smoothed**complexity**of*the Scarf's general fixed-point approximation algorithm (when applying to solve the approximate Leontief market exchange problem) or*of*any algorithm ... To relate the*complexity**of*finding an approximate*Nash*equilibrium*of*two-person games with the*smoothed**complexity**of*Leontief economies, we examine the*equilibria**of*perturbations*of*the reduction presented ...##
###
Settling the Complexity of Computing Two-Player Nash Equilibria
[article]

2007
*
arXiv
*
pre-print

This is the first

arXiv:0704.1678v1
fatcat:bv5kllzvurg7fjlt2gq7d6nolu
*of*a series*of*results concerning the*complexity**of**Nash**equilibria*. ... We prove that Bimatrix, the problem*of*finding a*Nash*equilibrium in a two-*player*game, is complete for the*complexity*class PPAD Polynomial Parity Argument, Directed version) introduced by Papadimitriou ... We would like to thank everyone who asked about the*smoothed**complexity**of*the Lemke-Howson algorithm, especially John Reif for being the first*player*to ask us this question. ...##
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Local Nash Equilibria are Isolated, Strict Local Nash Equilibria in `Almost All' Zero-Sum Continuous Games
[article]

2020
*
arXiv
*
pre-print

That is, there exists an open-dense subset

arXiv:2002.01007v1
fatcat:spoeiiv4jvd5lezooq2wcpj32y
*of*zero-sum games for which local*Nash**equilibria*are non-degenerate differential*Nash**equilibria*. ... We further show that differential*Nash**equilibria**of*zero-sum games are structurally stable. ... Proof: Consider a two-*player*, zero-sum game (f, −f ) for some generic sufficiently*smooth*f ∈ C r (X, R). Then, by Theorem*2*, a local*Nash**equilibria*x is a differential*Nash**equilibria*. ...##
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Settling the complexity of computing two-player Nash equilibria

2009
*
Journal of the ACM
*

It also serves as a starting point for a series

doi:10.1145/1516512.1516516
fatcat:4csizuhga5h4jnbkrickxw6d2y
*of*results concerning the*complexity**of*two-*player**Nash**equilibria*. ... Our result, building upon the work*of*Daskalakis, Goldberg, and Papadimitriou on the*complexity**of*four-*player**Nash**equilibria*[21], settles a long standing open problem in algorithmic game theory. ... The*Smoothed**Complexity**of**Nash**Equilibria*The proof*of*Theorem 1.4 is then the simplest part*of*the paper. ...##
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On the complexity of constrained Nash equilibria in graphical games

2009
*
Theoretical Computer Science
*

Based on this framework, the

doi:10.1016/j.tcs.2009.05.030
fatcat:e5fwu7ypxrgpnb7d3umyagi7zm
*complexity**of*deciding the existence and*of*computing constrained*equilibria*is then investigated, in the light*of*evidencing how the intrinsic difficulty*of*these tasks is ... A widely accepted rational behavior for non-cooperative*players*is based on the notion*of**Nash*equilibrium. ... on the*complexity*issues related to*Nash**equilibria*by considering the various classes*of*games defined in Section*2*. ...##
###
Query Complexity of Approximate Equilibria in Anonymous Games
[chapter]

2015
*
Lecture Notes in Computer Science
*

We also give an example

doi:10.1007/978-3-662-48995-6_26
fatcat:7jcyuggwo5bc5lyz2w2v3zc2ou
*of*a*2*-strategy, 3-*player*anonymous game that does not have any exact*Nash*equilibrium in rational numbers. ... The general topic we consider is query*complexity*, that is, how many queries are necessary or sufficient to compute an exact or approximate*Nash*equilibrium. ... Related Work In the last decade, there has been interest in the*complexity**of*computing approximate*Nash**equilibria*. ...##
###
Intrinsic Robustness of the Price of Anarchy

2015
*
Journal of the ACM
*

First, we identify a "canonical sufficient condition" for an upper bound

doi:10.1145/2806883
fatcat:lx6nlwhv5jd2vdry57jigwnql4
*of*the POA for pure*Nash**equilibria*, which we call a*smoothness*argument. ... This measure implicitly assumes that*players*successfully reach some*Nash*equilibrium. ... )*Nash**equilibria*[*2*, 8, 9] . ...
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