# On the complexity of problems on simple games

Josep Freixas; Xavier Molinero; Martin Olsen; Maria Serna

RAIRO - Operations Research (2012)

- Volume: 45, Issue: 4, page 295-314
- ISSN: 0399-0559

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topFreixas, Josep, et al. "On the complexity of problems on simple games." RAIRO - Operations Research 45.4 (2012): 295-314. <http://eudml.org/doc/222510>.

@article{Freixas2012,

abstract = {Simple games cover voting systems in which a single alternative, such as a bill or an
amendment, is pitted against the status quo. A simple game or a yes-no voting system is a
set of rules that specifies exactly which collections of “yea” votes yield passage of the
issue at hand. Each of these collections of “yea” voters forms a winning coalition. We are
interested in performing a complexity analysis on problems defined on such families of
games. This analysis as usual depends on the game representation used as input. We
consider four natural explicit representations: winning, losing, minimal winning, and
maximal losing. We first analyze the complexity of testing whether a game is simple and
testing whether a game is weighted. We show that, for the four types of representations,
both problems can be solved in polynomial time. Finally, we provide results on the
complexity of testing whether a simple game or a weighted game is of a special type. We
analyze strongness, properness, weightedness, homogeneousness, decisiveness and
majorityness, which are desirable properties to be fulfilled for a simple game. Finally,
we consider the possibility of representing a game in a more succinct and natural way and
show that the corresponding recognition problem is hard.},

author = {Freixas, Josep, Molinero, Xavier, Olsen, Martin, Serna, Maria},

journal = {RAIRO - Operations Research},

keywords = {Simple; weighted; majority games; NP-completeness; simple},

language = {eng},

month = {1},

number = {4},

pages = {295-314},

publisher = {EDP Sciences},

title = {On the complexity of problems on simple games},

url = {http://eudml.org/doc/222510},

volume = {45},

year = {2012},

}

TY - JOUR

AU - Freixas, Josep

AU - Molinero, Xavier

AU - Olsen, Martin

AU - Serna, Maria

TI - On the complexity of problems on simple games

JO - RAIRO - Operations Research

DA - 2012/1//

PB - EDP Sciences

VL - 45

IS - 4

SP - 295

EP - 314

AB - Simple games cover voting systems in which a single alternative, such as a bill or an
amendment, is pitted against the status quo. A simple game or a yes-no voting system is a
set of rules that specifies exactly which collections of “yea” votes yield passage of the
issue at hand. Each of these collections of “yea” voters forms a winning coalition. We are
interested in performing a complexity analysis on problems defined on such families of
games. This analysis as usual depends on the game representation used as input. We
consider four natural explicit representations: winning, losing, minimal winning, and
maximal losing. We first analyze the complexity of testing whether a game is simple and
testing whether a game is weighted. We show that, for the four types of representations,
both problems can be solved in polynomial time. Finally, we provide results on the
complexity of testing whether a simple game or a weighted game is of a special type. We
analyze strongness, properness, weightedness, homogeneousness, decisiveness and
majorityness, which are desirable properties to be fulfilled for a simple game. Finally,
we consider the possibility of representing a game in a more succinct and natural way and
show that the corresponding recognition problem is hard.

LA - eng

KW - Simple; weighted; majority games; NP-completeness; simple

UR - http://eudml.org/doc/222510

ER -

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