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Approximating the Minmax Value of Three-Player Games within a Constant is as Hard as Detecting Planted Cliques [chapter]

Kord Eickmeyer, Kristoffer Arnstfelt Hansen, Elad Verbin
2012 Lecture Notes in Computer Science  
For any constant > 0 it is NP hard to approximate the minmax value of an n × n × n game with 0-1 payoffs within additive error 1/n .  ...  Our Results We show a relationship between the task of approximating the minmax value in a 3-player game and the planted clique detection problem.  ...  A. Proof of Lemma 4 In this section we give a proof of Lemma 4. Here we do not attempt to optimize parameters. We let p = η/2e, and let c 1 be a constant to be specified later.  ... 
doi:10.1007/978-3-642-33996-7_9 fatcat:h47kxitsenhdjelujzbd2r4mmi

Reducibility and Computational Lower Bounds for Problems with Planted Sparse Structure [article]

Matthew Brennan, Guy Bresler, Wasim Huleihel
2019 arXiv   pre-print
In this work we introduce several new techniques to give a web of average-case reductions showing strong computational lower bounds based on the planted clique conjecture using natural problems as intermediates  ...  These include tight lower bounds for Planted Independent Set, Planted Dense Subgraph, Sparse Spiked Wigner, Sparse PCA, a subgraph variant of the Stochastic Block Model and a biased variant of Sparse PCA  ...  This work was supported in part by the grants ONR N00014-17-1-2147 and NSF CCF-1565516.  ... 
arXiv:1806.07508v2 fatcat:opmqaaweyzhrnjjgqdacdocc54

New Models and Methods for Formation and Analysis of Social Networks [article]

Swapnil Dhamal
2017 arXiv   pre-print
This doctoral work focuses on three main problems related to social networks: (1) Orchestrating Network Formation: We consider the problem of orchestrating formation of a social network having a certain  ...  individuals to be targeted for initiating the diffusion process. (3) Scalable Preference Aggregation: It is extremely useful to determine a small number of representatives of a social network such that  ...  Assuming O(n) permutations for approximate computation of Shapley value [75] (since exact computation is #P-hard), the algorithm's time complexity is approximately O(nT).  ... 
arXiv:1706.09310v1 fatcat:gd2jxhuqzfdotmiq5anoon4vm4

Randomness in complexity theory and logics [article]

Kord Eickmeyer, Humboldt-Universität Zu Berlin, Humboldt-Universität Zu Berlin
and we give a reduction from a problem concerning bipartite graphs to the problem of computing the minmax-value in three-player games.  ...  This thesis is comprised of two main parts whose common theme is the question of how powerful randomness as a computational resource is.  ...  For any constant > 0 it is NP hard to approximate the minmax value of an n × n × n game with 0-1 payoffs within additive error 1/n .  ... 
doi:10.18452/16364 fatcat:zsyigi6ko5dyhghmgntszjcsfi

Abstracts of Working Papers in Economics

1990 Abstracts of Working Papers in Economics  
AB The aim of the paper is to look at the pricing of European type options under the assumption of a stochastic interest rate in a discrete time context.  ...  In expected utility, and as it turns out, in the case of smooth Frechet differentiability of the representation functional, derivation of pi(0) = 0.  ...  The new interpretation is suggested by the fact that games typically have a large number of Nash solutions, and players are not indifferent as to which occurs.  ... 
doi:10.1017/s0951007900001534 fatcat:ctxzhimskrcllg5cpy7s6dbvdy

Abstracts of Working Papers in Economics

2000 Abstracts of Working Papers in Economics  
The authors model the problem as an incomplete information, simultaneous-move game between PRP's.  ...  as is government revenue.  ...  w is the maximum clique size in G.  ... 
doi:10.1017/s0951007900004915 fatcat:62y3byrmc5ag5czgxtoyqmhhdm

Gambling and society : interdisciplinary studies on the subject of gambling [article]

William R. Eadington, University Of Calgary, University Of Calgary
Profitability and Behavior of the Gaming Industry Relative to the Stock Market - James J. Noel and Stuart E. Curtis Part Three: THE SOCIOLOGY OF GAMBLING 11.  ...  This book is an attempt to provide better information on which to base future decisions on the role of gambling in society.  ...  For example, if the player has a soft total k 10 and draws a card with face value, i, then if k i is more than the resulting hard sum is k i, and V is the expected value of the resulting hand if the optimal  ... 
doi:10.11575/prism/9556 fatcat:z3sji342kfe2xjxvv33vidtofa