scholarly journals The core of a cooperative game without side payments

1961 ◽  
Vol 98 (3) ◽  
pp. 539-539 ◽  
Author(s):  
Robert J. Aumann
Keyword(s):  
Cooperative Game ◽  
The Core ◽  
Side Payments

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.

The core of a cooperative game without side payments

1987 ◽  
Vol 54 (2) ◽  
pp. 273-288 ◽  
Author(s):  
H. Keiding ◽  
L. Thorlund-Petersen
Keyword(s):  
Cooperative Game ◽  
The Core ◽  
Side Payments

scholarly journals THE POSITIVE PREKERNEL OF A COOPERATIVE GAME

2000 ◽  
Vol 02 (04) ◽  
pp. 287-305 ◽  
Author(s):  
PETER SUDHÖLTER ◽  
BEZALEL PELEG
Keyword(s):  
Cooperative Game ◽  
Weak Version ◽  
Transferable Utility ◽  
Bargaining Set ◽  
The Core ◽  
Reduced Game ◽  
Positive Kernel ◽  
Game Property ◽  
Transferable Utility Games

The positive prekernel, a solution of cooperative transferable utility games, is introduced. We show that this solution inherits many properties of the prekernel and of the core, which are both sub-solutions. It coincides with its individually rational variant, the positive kernel, when applied to any zero-monotonic game. The positive (pre)kernel is a sub-solution of the reactive (pre)bargaining set. We prove that the positive prekernel on the set of games with players belonging to a universe of at least three possible members can be axiomatized by non-emptiness, anonymity, reasonableness, the weak reduced game property, the converse reduced game property, and a weak version of unanimity for two-person games.

The Coase Theorem, the Nonempty Core, and the Legal Neutrality Principle

2019 ◽  
Vol 16 (1) ◽  
Author(s):  
Bertrand Crettez
Keyword(s):  
Resource Allocation ◽  
Transaction Costs ◽  
Cooperative Game ◽  
Coase Theorem ◽  
Pareto Optimal ◽  
Liability Rules ◽  
The Core ◽  
Optimal Allocations ◽  
Legal Position ◽  
Person Game

Abstract The Coase theorem states that where there are externalities and no transaction costs resource allocation is Pareto-optimal and independent of the stakeholders’ legal position. This result has been challenged many times. In the cooperative game approach to resource allocation, the refutation is made by constructing a three-person game which has an empty core under one set of liability rules—which implies that optimal allocations are coalitionally unstable–and a nonempty core under another set. In this example, however, the probability that the core is non-empty is rather high (5/6). Yet, even if coalitionally stable Pareto-optimal arrangements are likely, to establish the plain validity of the Coase theorem it must be shown that the legal neutrality statement also holds. We show that for the three-person cooperative game example mentioned above, the probability that the two assertions of the Coase theorem hold can be as low as 3/8.

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.

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.

An axiomatization of the core of a cooperative game

1986 ◽  
Vol 20 (2) ◽  
pp. 111-115 ◽  
Author(s):  
Hans Keiding
Keyword(s):  
Cooperative Game ◽  
The Core

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.

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