scholarly journals Owen-stable coalition partitions in games with vector payoffs

2019 ◽  
Vol 10 (3) ◽  
pp. 3-23 ◽  
Author(s):  
Василий Гусев ◽  
Vasily Gusev ◽  
Владимир Мазалов ◽  
Vladimir Mazalov
Keyword(s):  
Characteristic Function ◽  
Cooperative Game ◽  
Cooperative Games ◽  
Owen Value ◽  
Stable Coalition ◽  
Vector Payoffs ◽  
Definition Of ◽  
Games With Vector Payoffs

The paper is devoted to the study of multicriteria cooperative games with vector payoffs and coalition partition. The imputation which is based on the concept of the Owen value is proposed. We use it for the definition of stable coalition partition for bicriteria games. In three person cooperative game with 0-1 characteristic function the conditions under which the coalition partition is stable are found.

DYNAMIC COOPERATIVE GAMES

2000 ◽  
Vol 02 (01) ◽  
pp. 47-65 ◽  
Author(s):  
JERZY A. FILAR ◽  
LEON A. PETROSJAN
Keyword(s):  
Characteristic Function ◽  
Cooperative Game ◽  
Continuous Time ◽  
Cooperative Games ◽  
Solution Concept ◽  
Time Consistency ◽  
Standard Solution ◽  
Instantaneous Characteristic ◽  
Characteristic Function Form ◽  
Over Time

We consider dynamic cooperative games in characteristic function form in the sense that the characteristic function evolves over time in accordance with a difference or differential equation that is influenced not only by the current ("instantaneous") characteristic function but also by the solution concept used to allocate the benefits of cooperation among the players. The latter solution concept can be any one of a number of now standard solution concepts of cooperative game theory but, for demonstration purposes, we focus on the core and the Shapley value. In the process, we introduce some new mechanisms by which players may regard the evolution of cooperative game over time and analyse them with respect to the goal of attaining time consistency either in discrete or in continuous time setting. In discrete time, we illustrate the phenomena that can arise when an allocation according to a given solution concept is used to adapt the values of coalitions at successive time points. In continuous time, we introduce the notion of an "instantaneous" game and its integration over time.

Irrational-Behavior-Proof Conditions Based on Limit Characteristic Functions

2019 ◽  
Vol 7 (1) ◽  
pp. 1-16
Author(s):  
Cui Liu ◽  
Hongwei Gao ◽  
Ovanes Petrosian ◽  
Juan Xue ◽  
Lei Wang
Keyword(s):  
Characteristic Function ◽  
Cooperative Game ◽  
Shapley Value ◽  
Cooperative Games ◽  
Characteristic Functions ◽  
The Core ◽  
The Shapley Value ◽  
Irrational Behavior ◽  
The Individual

Abstract Irrational-behavior-proof (IBP) conditions are important aspects to keep stable cooperation in dynamic cooperative games. In this paper, we focus on the establishment of IBP conditions. Firstly, the relations of three kinds of IBP conditions are described. An example is given to show that they may not hold, which could lead to the fail of cooperation. Then, based on a kind of limit characteristic function, all these conditions are proved to be true along the cooperative trajectory in a transformed cooperative game. It is surprising that these facts depend only upon the individual rationalities of players for the Shapley value and the group rationalities of players for the core. Finally, an illustrative example is given.

CHOQUET EXTENSION OF COOPERATIVE GAMES

2013 ◽  
Vol 30 (04) ◽  
pp. 1350005 ◽  
Author(s):  
CHUNQIAO TAN ◽  
ZHONG-ZHONG JIANG ◽  
XIAOHONG CHEN
Keyword(s):  
Explicit Formula ◽  
Cooperative Game ◽  
Cooperative Games ◽  
Choquet Integral ◽  
Extension Method ◽  
Equivalent Definition ◽  
Multilinear Extension ◽  
Shapley Function ◽  
Definition Of

A multilinear extension of the n-person cooperative game was introduced by Owen in 1972, and a new extension method is proposed in this paper. For n-person cooperative games, any coalition can equivalently be represented by its characteristic vectors. By means of the Choquet integral, a new fuzzy extension, called the Choquet extension, is developed. Furthermore, a Shapley function in this class of fuzzy cooperative games with the Choquet extension form is defined. Axioms of the Shapley function are proposed, and an explicit formula for the Shapley function is given. Finally, an equivalent definition of this Shapley function is discussed.

scholarly journals The Owen Value of Stochastic Cooperative Game

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Cheng-Guo E ◽  
Quan-Lin Li ◽  
Shi-Yong Li
Keyword(s):  
Explicit Expression ◽  
Cooperative Game ◽  
Existence And Uniqueness ◽  
Classical Case ◽  
Owen Value ◽  
Definition Of

We consider stochastic cooperative game and give it the definition of the Owen value, which is obtained by extending the classical case. Then we provide explicit expression for the Owen value of the stochastic cooperative game and discuss its existence and uniqueness.

scholarly journals Attainability in Repeated Games with Vector Payoffs

2015 ◽  
Vol 40 (3) ◽  
pp. 739-755 ◽  
Author(s):  
Dario Bauso ◽  
Ehud Lehrer ◽  
Eilon Solan ◽  
Xavier Venel
Keyword(s):  
Repeated Games ◽  
Vector Payoffs ◽  
Games With Vector Payoffs

LINEAR AND INTEGER PROGRAMMING TECHNIQUES FOR COOPERATIVE GAMES

2002 ◽  
Vol 13 (05) ◽  
pp. 653-666 ◽  
Author(s):  
Qizhi Fang ◽  
Shanfeng Zhu
Keyword(s):  
Integer Programming ◽  
Cooperative Game ◽  
Cooperative Games ◽  
Value Function ◽  
Linear Program ◽  
Grand Coalition ◽  
The Core ◽  
Programming Techniques ◽  
Theoretical Results

Let Γ = (N, v) be a cooperative game with the player set N and value function v : 2N → R. A solution of the game is in the core if no subset of players could gain advantage by breaking away from the grand coalition of all players. This paper surveys theoretical results on the cores for some cooperative game models. These results proved that the linear program duality characterization of the core is a very powerful tool. We will focus on linear and integer programming techniques applied in this area.

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