scholarly journals The Cores for Fuzzy Games Represented by the Concave Integral

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Jinhui Pang ◽  
Shujin Li
Keyword(s):  
Cooperative Games ◽  
Characteristic Functions ◽  
Game Model ◽  
Explicit Formulas ◽  
The Core ◽  
Concave Integral ◽  
Fuzzy Games ◽  
Fuzzy Game ◽  
Expected Values ◽  
Fuzzy Core

We propose a new fuzzy game model by the concave integral by assigning subjective expected values to random variables in the interval[0,1]. The explicit formulas of characteristic functions which are determined by coalition variables are discussed in detail. After illustrating some properties of the new game, its fuzzy core is defined; this is a generalization of crisp core. Moreover, we give a further discussion on the core for the new games. Some notions and results from classical games are extended to the model. The nonempty fuzzy core is given in terms of the fuzzy convexity. Our results develop some known fuzzy cooperative games.

scholarly journals The Shapley Values on Fuzzy Coalition Games with Concave Integral Form

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Jinhui Pang ◽  
Xiang Chen ◽  
Shujin Li
Keyword(s):  
Cooperative Game ◽  
Integral Form ◽  
Simple Calculation ◽  
Calculation Formula ◽  
Concave Integral ◽  
Shapley Values ◽  
Linear Aggregation ◽  
Fuzzy Game ◽  
Expected Values

A generalized form of a cooperative game with fuzzy coalition variables is proposed. The character function of the new game is described by the Concave integral, which allows players to assign their preferred expected values only to some coalitions. It is shown that the new game will degenerate into the Tsurumi fuzzy game when it is convex. The Shapley values of the proposed game have been investigated in detail and their simple calculation formula is given by a linear aggregation of the Shapley values on subdecompositions crisp coalitions.

scholarly journals The core and superdifferential of a fuzzy TU-cooperative game

2020 ◽  
Vol 12 (2) ◽  
pp. 20-35
Author(s):  
Валерий Александрович Васильев ◽  
Valery Vasil'ev
Keyword(s):  
Cooperative Game ◽  
Cooperative Games ◽  
Sufficient Conditions ◽  
Subdifferential Calculus ◽  
The Core ◽  
Side Payments ◽  
Weak Homogeneity ◽  
Fuzzy Game

In the paper, we consider conditions providing coincidence of the cores and superdifferentials of fuzzy cooperative games with side payments. It turned out that one of the most simple sufficient conditions consists of weak homogeneity. Moreover, by applying so-called S*-representation of a fuzzy game introduced by the author, we show that for any vwith nonempty core C(v) there exists some game u such that C(v) coincides with the superdifferential of u. By applying subdifferential calculus we describe a structure of the core forboth classic fuzzy extensions of the ordinary cooperative game (e.g., Aubin and Owen extensions) and for some new continuations, like Harsanyi extensions and generalized Airport game.

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.

scholarly journals Integral Representations of Cooperative Game with Fuzzy Coalitions

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Jinhui Pang ◽  
Xiang Chen
Keyword(s):  
Characteristic Function ◽  
Explicit Formula ◽  
Cooperative Game ◽  
Integral Representations ◽  
New Class ◽  
Concave Integral ◽  
Fuzzy Game ◽  
Fuzzy Coalitions ◽  
Expected Values ◽  
Special Case

Classical extensions of fuzzy game models are based on various integrals, such as Butnariu game and Tsurumi game. A new class of symmetric extension of fuzzy game with fuzzy coalition variables is put forward with Concave integral, where players’ expected values are on a partial set of coalitions. Some representations and properties of some limited models are compared in this paper. The explicit formula of characteristic function determined by coalition variables is given. Moreover, a calculation approach of imputations is discussed in detail. The new game could be regarded as a general form of cooperative game. Furthermore, the fuzzy game introduced by Tsurumi is a special case of the proposed game when game is convex.

On the core, nucleolus and bargaining sets of cooperative games with fuzzy payoffs

2019 ◽  
Vol 36 (6) ◽  
pp. 6129-6142 ◽  
Author(s):  
Xia Zhang ◽  
Hao Sun ◽  
Genjiu Xu ◽  
Dongshuang Hou
Keyword(s):  
Cooperative Games ◽  
The Core ◽  
Bargaining Sets

scholarly journals Antagonistic One-To-N Stochastic Duel Game

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1114 ◽  
Author(s):  
Song-Kyoo (Amang) Kim
Keyword(s):  
Real World ◽  
Payoff Function ◽  
Marketing Strategies ◽  
Time Dependent ◽  
Random Time ◽  
Game Model ◽  
Explicit Formulas ◽  
Entry Timing ◽  
The One ◽  
Person Game

This paper is dealing with a multiple person game model under the antagonistic duel type setup. The unique multiple person duel game with the one-shooting-to-kill-all condition is analytically solved and the explicit formulas are obtained to determine the time dependent duel game model by using the first exceed theory. The model could be directly applied into real-world situations and an analogue of the theory in the paper is designed for solving the best shooting time for hitting all other players at once which optimizes the payoff function under random time conditions. It also mathematically explains to build the marketing strategies for the entry timing for both blue and red ocean markets.

A NOTE ON CHARACTERIZING CORE STABILITY WITH FUZZY GAMES

2011 ◽  
Vol 13 (01) ◽  
pp. 105-118 ◽  
Author(s):  
EVAN SHELLSHEAR
Keyword(s):  
Cooperative Game ◽  
Core Stability ◽  
Original Game ◽  
Tu Games ◽  
The Core ◽  
Cooperative Tu Games ◽  
Fuzzy Games ◽  
The Stability

This paper investigates core stability of cooperative (TU) games via a fuzzy extension of the totally balanced cover of a cooperative game. The stability of the core of the fuzzy extension of a game, the concave extension, is shown to reflect the core stability of the original game and vice versa. Stability of the core is then shown to be equivalent to the existence of an equilibrium of a certain correspondence.

scholarly journals Game-Theoretic Principles of Decision Management Modeling Under the Coopetition

2020 ◽  
pp. 2050010
Author(s):  
Iryna Heiets ◽  
Tamara Oleshko ◽  
Oleg Leshchinsky
Keyword(s):  
Infinite Number ◽  
Cooperative Games ◽  
Characteristic Functions ◽  
Optimal Distribution ◽  
Collective Rationality ◽  
Decision Management ◽  
Game Theoretic ◽  
The Individual ◽  
Additional Income

The paper considers the two main game-theoretic models, such as coalition and cooperative. The authors are of the opinion that definitions and notions of cooperative games and coalition games are different, but both games are coopetitive games. Transitivity and superadditivity are presented as the main characteristic functions of coopetitive games. The individual and collective rationality were identified as unconditional requirements for the optimal distribution between players. Furthermore, the additional income added to the guaranteed amount occurs in the event of coopetition. Any substantial coopetitive game has an infinite number of transactions. The authors highlighted that the dominant transaction is the transaction that is better for all coalition numbers without exceptions and it can be reached by the coalition. In addition, the authors propose using Shapley system of axioms to identify coopetitive game results.

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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