A note on the growth of the dimension in complete simple games

06/09/2020
by   Sascha Kurz, et al.
0

The remoteness from a simple game to a weighted game can be measured by the concept of the dimension or the more general Boolean dimension. It is known that both notions can be exponential in the number of voters. For complete simple games it was only recently shown that the dimension can also be exponential. Here we show that this is also the case for complete simple games with two types of voters and for the Boolean dimension of general complete simple games, which was posed as an open problem.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
05/06/2018

Simple Games versus Weighted Voting Games

A simple game (N,v) is given by a set N of n players and a partition of ...
research
05/06/2021

Dots Boxes is PSPACE-complete

Exactly 20 years ago at MFCS, Demaine posed the open problem whether the...
research
04/17/2014

A Complete Solver for Constraint Games

Game Theory studies situations in which multiple agents having conflicti...
research
03/14/2018

Computational complexity of the avalanche problem on one dimensional Kadanoff sandpiles

In this paper we prove that the general avalanche problem AP is in NC, f...
research
11/20/2019

Node Max-Cut and Computing Equilibria in Linear Weighted Congestion Games

Computing an equilibrium of a game is of central interest in Algorithmic...
research
01/12/2021

On the power of standard information for tractability for L_2-approximation in the average case setting

We study multivariate approximation in the average case setting with the...
research
04/30/2021

Multi-Structural Games and Number of Quantifiers

We study multi-structural games, played on two sets 𝒜 and ℬ of structure...

Please sign up or login with your details

Forgot password? Click here to reset