Reduced Game Properties of Egalitarian Division Rules for TU-Games

CONSISTENCY FOR PROPORTIONAL SOLUTIONS

International Game Theory Review ◽

10.1142/s0219198902000744 ◽

2002 ◽

Vol 04 (03) ◽

pp. 343-356 ◽

Cited By ~ 1

Author(s):

ELENA YANOVSKAYA

Keyword(s):

Cooperative Game ◽

Solution Set ◽

Original Game ◽

Payoff Vector ◽

Tu Games ◽

Reduced Game ◽

Reduced Games ◽

Consistency Property ◽

Finite Set

One of the properties characterizing cooperative game solutions is consistency connecting solution vectors of a cooperative game with finite set of players and its reduced game defined by removing one or more players and by assigning them the payoffs according to some specific principle (e.g., a proposed payoff vector). Consistency of a solution means that any part (defined by a coalition of the original game) of a solution payoff vector belongs to the solution set of the corresponding reduced game. In the paper the proportional solutions for TU-games are defined as those depending only on the proportional excess vectors in the same manner as translation covariant solutions depend on the usual Davis–Maschler excess vectors. The general form of the reduced games defining consistent proportional solutions is given. The efficient, anonymous, proportional TU cooperative game solutions meeting the consistency property with respect to any reduced game are described.

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CONSISTENCY IN VALUES

International Game Theory Review ◽

10.1142/s0219198904000307 ◽

2004 ◽

Vol 06 (04) ◽

pp. 461-473 ◽

Cited By ~ 1

Author(s):

GUILLERMO OWEN

Keyword(s):

Shapley Value ◽

Solution Concept ◽

Tu Games ◽

Ntu Games ◽

Reduced Game ◽

Reduced Games ◽

Shapley Values ◽

Consistent Solution ◽

Person Game ◽

Reasonable Behavior

Given an n-person game (N, v), a reduced game (T, vT) is the game obtained if some subset T of the players assumes reasonable behavior on the part of the remaining players and uses that as a given so as to bargain within T. This "reasonable" behavior on the part of N-T must be defined in terms of some solution concept, ϕ, and so the reduced game depends on ϕ. Then, the solution concept ϕ is said to be consistent if it gives the same result to the reduced games as it does to the original game. It turns out that, given a symmetry condition on two-person games, the Shapley value is the only consistent solution on the space of TU games. Modification of some definitions will instead give the prekernel, the prenucleolus, or the weighted Shapley values. A generalization to NTU games is given. This works well for the class of hyperplane games, but not quite so well for general games.

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On the reduced game property for and the axiomatization of theT-value of TU-games

Top ◽

10.1007/bf02568609 ◽

1996 ◽

Vol 4 (1) ◽

pp. 165-185

Author(s):

Theo S. H. Driessen

Keyword(s):

Tu Games ◽

Reduced Game ◽

Game Property

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An axiomatization of the kernel for TU games through reduced game monotonicity and reduced dominance

Theory and Decision ◽

10.1007/s11238-012-9344-1 ◽

2012 ◽

Vol 74 (1) ◽

pp. 1-12

Author(s):

Theo Driessen ◽

Cheng-Cheng Hu

Keyword(s):

Tu Games ◽

Reduced Game

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Consistency and Potentials in Cooperative TU-Games: Sobolev’s Reduced Game Revived

Chapters in Game Theory - Theory and Decision Library C: ◽

10.1007/0-306-47526-x_5 ◽

2005 ◽

pp. 99-120

Author(s):

Theo Driessen

Keyword(s):

Tu Games ◽

Reduced Game ◽

Cooperative Tu Games

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THE RIVER SHARING PROBLEM: A SURVEY

International Game Theory Review ◽

10.1142/s0219198913400161 ◽

2013 ◽

Vol 15 (03) ◽

pp. 1340016 ◽

Cited By ~ 10

Author(s):

SYLVAIN BEAL ◽

AMANDINE GHINTRAN ◽

ERIC REMILA ◽

PHILIPPE SOLAL

Keyword(s):

Optimal Allocation ◽

Market Mechanism ◽

Tu Game ◽

Tu Games ◽

Cooperative Tu Game ◽

Fair Distribution

The river sharing problem deals with the fair distribution of welfare resulting from the optimal allocation of water among a set of riparian agents. Ambec and Sprumont [Sharing a river, J. Econ. Theor. 107, 453–462] address this problem by modeling it as a cooperative TU-game on the set of riparian agents. Solutions to that problem are reviewed in this article. These solutions are obtained via an axiomatic study on the class of river TU-games or via a market mechanism.

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