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Query complexity of approximate nash equilibria

Yakov Babichenko
2014 Proceedings of the 46th Annual ACM Symposium on Theory of Computing - STOC '14  
of Approximate 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  ...  Yakov Babichenko Query Complexity of Approximate Nash Equilibria Consequences Computational Complexity This result provides evidence that existence of sub-exponential (in n) algorithm for approximate  ... 
doi:10.1145/2591796.2591829 dblp:conf/stoc/Babichenko14 fatcat:ijnxd5ep35chnbz7tfhntsezji

Query Complexity of Approximate Nash Equilibria [article]

Yakov Babichenko
2014 arXiv   pre-print
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.  ...  Before stating our main result on the query complexity of approximate Nash equilibrium, we introduce the state of the art for the related question on the query complexity of approximate correlated equilibrium  ... 
arXiv:1306.6686v3 fatcat:77wp4dsv3naa7gsusc7komnl3m

Query Complexity of Approximate Nash Equilibria

Yakov Babichenko
2016 Journal of the ACM  
of Approximate 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  ...  Yakov Babichenko Query Complexity of Approximate Nash Equilibria Consequences Computational Complexity This result provides evidence that existence of sub-exponential (in n) algorithm for approximate  ... 
doi:10.1145/2908734 fatcat:s2rshlll5bgx3ivkic6f7q2v6y

Query Complexity of Approximate Equilibria in Anonymous Games [article]

Paul W. Goldberg, Stefano Turchetta
2016 arXiv   pre-print
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.  ...  However, more positive query-complexity bounds are attainable if either further symmetries of the utility functions are assumed or we focus on approximate equilibria.  ...  In the last two years, several researchers obtained bounds for the query complexity for approximate equilibria in different game settings, which we briefly survey.  ... 
arXiv:1412.6455v3 fatcat:za7wr3a4abaljedi4gzktlojw4

Bounds for the query complexity of approximate equilibria

Paul W. Goldberg, Aaron Roth
2014 Proceedings of the fifteenth ACM conference on Economics and computation - EC '14  
For binary-choice games, we show logarithmic upper and lower bounds on the query complexity of approximate correlated equilibrium.  ...  lower bound, thus separating the query complexity of well supported approximate correlated equilibrium from the standard notion of approximate correlated equilibrium.  ...  Finally, we apply Theorem 3.1 to show that small-support approximate CE are harder (in the query complexity sense) to find than are larger-support approximate CE.  ... 
doi:10.1145/2600057.2602845 dblp:conf/sigecom/GoldbergR14 fatcat:h7wplw4vlzhllntngd6t55cpoi

Bounds for the Query Complexity of Approximate Equilibria

Paul W. Goldberg, Aaron Roth
2016 ACM Transactions on Economics and Computation  
For binary-choice games, we show logarithmic upper and lower bounds on the query complexity of approximate correlated equilibrium.  ...  lower bound, thus separating the query complexity of well supported approximate correlated equilibrium from the standard notion of approximate correlated equilibrium.  ...  Finally, we apply Theorem 3.1 to show that small-support approximate CE are harder (in the query complexity sense) to find than are larger-support approximate CE.  ... 
doi:10.1145/2956582 fatcat:efx5k4chcfh2njriookkml735e

Query Complexity of Approximate Equilibria in Anonymous Games [chapter]

Paul W. Goldberg, Stefano Turchetta
2015 Lecture Notes in Computer Science  
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.  ...  Our main result is a new randomized query-efficient algorithm that finds a O(n −1/4 )-approximate Nash equilibrium queryingÕ(n 3/2 ) payoffs and runs in timeÕ(n 3/2 ).  ...  The query complexity of an algorithm is the expected number of single-payoff queries that it needs in the worst case. Hence, an algorithm is query-efficient if its query complexity is o(n 2 ).  ... 
doi:10.1007/978-3-662-48995-6_26 fatcat:7jcyuggwo5bc5lyz2w2v3zc2ou

Metric 1-median selection: Query complexity vs. approximation ratio [article]

Ching-Lueh Chang
2015 arXiv   pre-print
We show that this problem has no deterministic o(n^1+1/(h-1))-query (2h-Ω(1))-approximation algorithms for any constant h∈Z^+∖{1}.  ...  Denote A's query complexity by q(n) = o n 1+1/(h−1) .  ...  The following fact about geometric series is not hard to see. 1 w(P ) is a common and convenient abuse of notation. 3 Query complexity vs. approximation ratio Throughout this section, • n ∈ Z + , • δ ∈  ... 
arXiv:1509.05662v1 fatcat:7rfi5y5ftraehlkg5mwvfdxyiq

Complexity of Approximate Query Answering under Inconsistency in Datalog+/-

Thomas Lukasiewicz, Enrico Malizia, Cristian Molinaro
2018 Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence  
In this paper, we analyze the complexity of conjunctive query answering under these two semantics for a wide range of Datalog+/- languages.  ...  Several semantics have been proposed to query inconsistent ontological knowledge bases, including the intersection of repairs and the intersection of closed repairs as two approximate inconsistency-tolerant  ...  We analyze the complexity of approximate inconsistency-tolerant query answering for a wide range of Datalog ± languages and for several different complexity measures; in particular: We consider different  ... 
doi:10.24963/ijcai.2018/265 dblp:conf/ijcai/LukasiewiczMM18 fatcat:4bry7ip7b5gj3olcnq34easrkm

Submodular Maximization with Nearly Optimal Approximation, Adaptivity and Query Complexity [article]

Matthew Fahrbach, Vahab Mirrokni, Morteza Zadimoghaddam
2018 arXiv   pre-print
The approximation guarantee and query complexity are optimal, and the adaptivity is nearly optimal. Moreover, the number of queries is substantially less than in previous works.  ...  Motivated by these applications, we study the adaptivity and query complexity of adaptive submodular optimization.  ...  The adaptivity complexity of this subroutine is O(log(n)) and its query complexity is O(n).  ... 
arXiv:1807.07889v2 fatcat:szcpe6gvhfaozjpcmuunnzfr2e

The quantum query complexity of approximating the median and related statistics [article]

Ashwin Nayak, Felix Wu
1998 arXiv   pre-print
We consider the quantum query complexity of computing an ϵ-approximate median, given the sequence X as an oracle.  ...  We prove a lower bound of Ω(1/ϵ,n) queries for any quantum algorithm that computes an ϵ-approximate median with any constant probability greater than 1/2.  ...  Corollary 1.12 The quantum query complexity of the ǫ-approximate mean problem is Ω( 1 ǫ ). Brassard et al.  ... 
arXiv:quant-ph/9804066v2 fatcat:sjur2nsdhjccbcdkgh6abaqd6e

Polylogarithmic Approximation for Edit Distance and the Asymmetric Query Complexity [article]

Alexandr Andoni, Robert Krauthgamer, Krzysztof Onak
2010 arXiv   pre-print
compute a (log n)^O(1/epsilon) approximation in n^(1+epsilon) time.  ...  This result arises naturally in the study of a new asymmetric query model.  ...  Query Complexity Lower Bound.  ... 
arXiv:1005.4033v1 fatcat:znduu5pc5vgxng4nuk27lyciku

Polylogarithmic Approximation for Edit Distance and the Asymmetric Query Complexity

Alexandr Andoni, Robert Krauthgamer, Krzysztof Onak
2010 2010 IEEE 51st Annual Symposium on Foundations of Computer Science  
This result arises naturally in the study of a new asymmetric query model.  ...  Indeed, we obtain our main result by designing an algorithm that makes a small number of queries in this model. We then provide a nearly-matching lower bound on the number of queries.  ...  Both exhibit a smooth tradeoff between the approximation factor and the query complexity.  ... 
doi:10.1109/focs.2010.43 dblp:conf/focs/AndoniKO10 fatcat:nh2z4zwl5zfdxe3sgmdevv6y3u

Logarithmic Query Complexity for Approximate Nash Computation in Large Games [article]

Paul W. Goldberg, Francisco J. Marmolejo-Cossío, Zhiwei Steven Wu
2016 arXiv   pre-print
O( n) rounds/queries are required. We also show how to obtain a slight improvement over 1/8, by introducing a small amount of communication between the players.  ...  We study algorithms having query access to the game's payoff function, aiming to find ϵ-Nash equilibria. We seek algorithms that obtain ϵ as small as possible, in time polynomial in n.  ...  With randomised algorithms, the query complexity of approximate correlated equilibrium is Θ(log n) for any positive ε [10] .  ... 
arXiv:1610.08906v1 fatcat:yidnqargqzhczor6e4gwjy75ly

Logarithmic Query Complexity for Approximate Nash Computation in Large Games

Paul W. Goldberg, Francisco J. Marmolejo-Cossío, Zhiwei Steven Wu
2018 Theory of Computing Systems  
O(log n) rounds/queries are required. We also show how to obtain a slight improvement over 1 8 , by introducing a small amount of communication between the players.  ...  We study algorithms having query access to the game's payoff function, aiming to find ε-Nash equilibria. We seek algorithms that obtain ε as small as possible, in time polynomial in n.  ...  With randomised algorithms, the query complexity of approximate correlated equilibrium is (log n) for any positive ε [10] .  ... 
doi:10.1007/s00224-018-9851-8 fatcat:anx73rllrvcwzfktqs5csqf3li
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