Displaying similar documents to “A game of fair division with continuum of players”

Large games with only small players and strategy sets in Euclidean spaces

Andrzej Wieczorek (2005)

Applicationes Mathematicae

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The games of type considered in the present paper (LSE-games) extend the concept of LSF-games studied by Wieczorek in [2004], both types of games being related to games with a continuum of players. LSE-games can be seen as anonymous games with finitely many types of players, their action sets included in Euclidean spaces and payoffs depending on a player's own action and finitely many integral characteristics of distributions of the players' (of all types) actions. We prove the existence...

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...

Separability by semivalues modified for games with coalition structure

Rafael Amer, José Miguel Giménez (2009)

RAIRO - Operations Research

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Two games are inseparable by semivalues if both games obtain the same allocation whatever semivalue is considered. The problem of separability by semivalues reduces to separability from the null game. For four or more players, the vector subspace of games inseparable from the null game by semivalues contains games different to zero-game. Now, for five or more players, the consideration of a priori coalition blocks in the player set allows us to reduce in a significant way the dimension...