Query complexity of approximate Nash equilibria

Yakov Babichenko

doi:10.1145/2908734

Query complexity of approximate Nash equilibria

Yakov Babichenko

Data and Decision Sciences

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

We study the query complexity of approximate notions of Nash equilibrium in games with a large number of players n. Our main result states that for n-player binary-action games and for constant ε, the query complexity of an ε-well-supported Nash equilibrium is exponential in n. As a consequence of this result, we get an exponential lower bound on the rate of convergence of adaptive dynamics to approximate Nash equilibria.

Original language	English
Article number	36
Journal	Journal of the ACM
Volume	63
Issue number	4
DOIs	https://doi.org/10.1145/2908734
State	Published - 1 Oct 2016

Keywords

Adaptive dynamics
Approximate Nash equilibrium
Convergence and learning in games
Exact and approximate computation of equilibria
F.2.0 [analysis of algorithms and problem complexity]: general
Query complexity
Rate of convergence

ASJC Scopus subject areas

Software
Control and Systems Engineering
Information Systems
Hardware and Architecture
Artificial Intelligence

Access to Document

10.1145/2908734

Cite this

@article{618d6c8322cc4458a50a1db25a96b4a2,

title = "Query complexity of approximate Nash equilibria",

abstract = "We study the query complexity of approximate notions of Nash equilibrium in games with a large number of players n. Our main result states that for n-player binary-action games and for constant ε, the query complexity of an ε-well-supported Nash equilibrium is exponential in n. As a consequence of this result, we get an exponential lower bound on the rate of convergence of adaptive dynamics to approximate Nash equilibria.",

keywords = "Adaptive dynamics, Approximate Nash equilibrium, Convergence and learning in games, Exact and approximate computation of equilibria, F.2.0 [analysis of algorithms and problem complexity]: general, Query complexity, Rate of convergence",

author = "Yakov Babichenko",

note = "Funding Information: The author gratefully acknowledges support from ISF grant \#2021296. The author wishes to thank Noam Nisan, Sergiu Hart, Paul Goldberg, Yishay Mansour, Stephen Vavasis, Siddharth Barman, and anonymous referees for useful discussions and comments. Publisher Copyright: {\textcopyright} 2016 ACM.",

year = "2016",

month = oct,

day = "1",

doi = "10.1145/2908734",

language = "English",

volume = "63",

journal = "Journal of the ACM",

issn = "0004-5411",

publisher = "Institute of Physics Publishing",

number = "4",

}

TY - JOUR

T1 - Query complexity of approximate Nash equilibria

AU - Babichenko, Yakov

N1 - Funding Information: The author gratefully acknowledges support from ISF grant #2021296. The author wishes to thank Noam Nisan, Sergiu Hart, Paul Goldberg, Yishay Mansour, Stephen Vavasis, Siddharth Barman, and anonymous referees for useful discussions and comments. Publisher Copyright: © 2016 ACM.

PY - 2016/10/1

Y1 - 2016/10/1

N2 - We study the query complexity of approximate notions of Nash equilibrium in games with a large number of players n. Our main result states that for n-player binary-action games and for constant ε, the query complexity of an ε-well-supported Nash equilibrium is exponential in n. As a consequence of this result, we get an exponential lower bound on the rate of convergence of adaptive dynamics to approximate Nash equilibria.

AB - We study the query complexity of approximate notions of Nash equilibrium in games with a large number of players n. Our main result states that for n-player binary-action games and for constant ε, the query complexity of an ε-well-supported Nash equilibrium is exponential in n. As a consequence of this result, we get an exponential lower bound on the rate of convergence of adaptive dynamics to approximate Nash equilibria.

KW - Adaptive dynamics

KW - Approximate Nash equilibrium

KW - Convergence and learning in games

KW - Exact and approximate computation of equilibria

KW - F.2.0 [analysis of algorithms and problem complexity]: general

KW - Query complexity

KW - Rate of convergence

UR - https://www.scopus.com/pages/publications/84991769631

U2 - 10.1145/2908734

DO - 10.1145/2908734

M3 - Article

SN - 0004-5411

VL - 63

JO - Journal of the ACM

JF - Journal of the ACM

IS - 4

M1 - 36

ER -

Query complexity of approximate Nash equilibria

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this