Displaying similar documents to “On the complexity of problems on simple games”

On the complexity of problems on simple games

Josep Freixas, Xavier Molinero, Martin Olsen, Maria Serna (2012)

RAIRO - Operations Research

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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 ...

A class of extensions of Restricted (s,t)-Wythoff’s game

Sanyang Liu, Haiyan Li (2017)

Open Mathematics

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Restricted (s, t)-Wythoff’s game, introduced by Liu et al. in 2014, is an impartial combinatorial game. We define and solve a class of games obtained from Restricted (s, t)-Wythoff’s game by adjoining to it some subsets of its P-positions as additional moves. The results show that under certain conditions they are equivalent to one case in which only one P-position is adjoined as an additional move. Furthermore, two winning strategies of exponential and polynomial are provided for the...

Analysis and improvement attempt of prof. Alan Fowler's negotiation game

Jakub Jan Golik (2018)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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The main goal of the following article is to design an improved version of the negotiation game created by prof. Alan Fowler (Fowler, 1997). I have tried to achieve this by constructing four separate versions of the game which represent different approaches while preserving rules, chosen basic technical assumptions and the simplicity of the base game. Each version of the game is supposed to i.a. make it less obvious, create new negotiation possibilities (including potential cooperation),...

Some values for constant-sum and bilateral cooperative games

Andrzej Młodak (2007)

Applicationes Mathematicae

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We prove new axiomatizations of the Shapley value and the Banzhaf value, defined on the class of nonnegative constant-sum games with nonzero worth of the grand coalition as well as on nonnegative bilateral games with nonzero worth of the grand coalition. A characteristic feature of the latter class of cooperative games is that for such a game any coalition and its complement in the set of all players have the same worth. The axiomatizations are then generalized to the entire class of...

An axiomatization of the aspiration core

Hans Keiding (2006)

Banach Center Publications

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The aspiration core of a TU game was introduced by Bennett [1] as a payoff vector which is undominated and achievable in the sense that each player belongs to a coalition which can obtain the specified payoff for its members, and which minimizes the distance to the set of aggregate feasible payoffs among all such payoff vectors. In the paper a set of axioms is proposed which characterize the aspiration core, which may be considered as an extension of the core to a much larger set of...

Delegation equilibrium payoffs in integer-splitting games

Sylvain Sorin, Cheng Wan (2013)

RAIRO - Operations Research - Recherche Opérationnelle

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This work studies a new strategic game called delegation game. A delegation game is associated to a basic game with a finite number of players where each player has a finite integer weight and her strategy consists in dividing it into several integer parts and assigning each part to one subset of finitely many facilities. In the associated delegation game, a player divides her weight into several integer parts, commits each part to an independent delegate and collects the sum of their...

Permissive strategies: from parity games to safety games

Julien Bernet, David Janin, Igor Walukiewicz (2010)

RAIRO - Theoretical Informatics and Applications

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It is proposed to compare strategies in a parity game by comparing the sets of behaviours they allow. For such a game, there may be no winning strategy that encompasses all the behaviours of all winning strategies. It is shown, however, that there always exists a permissive strategy that encompasses all the behaviours of all memoryless strategies. An algorithm for finding such a permissive strategy is presented. Its complexity matches currently known upper bounds for the simpler...