STABILITY OF THE CORE IN A CLASS OF NTU GAMES: A CHARACTERIZATION

2002 ◽  
Vol 04 (02) ◽  
pp. 165-172 ◽  
Author(s):  
ANINDYA BHATTACHARYA ◽  
AMIT K. BISWAS
Keyword(s):  
Cooperative Games ◽  
Stable Set ◽  
Regularity Conditions ◽  
Transferable Utility ◽  
Large Core ◽  
Von Neumann ◽  
Ntu Games ◽  
The Core ◽  
Important Solution ◽  
Transferable Utility Games

The core and the stable set are possibly the two most crucially important solution concepts for cooperative games. The relation between the two has been investigated in the context of symmetric transferable utility games and this has been related to the notion of large core. In this paper the relation between the von-Neumann–Morgenstern stability of the core and the largeness of it is investigated in the case of non-transferable utility (NTU) games. The main findings are that under certain regularity conditions, if the core of an NTU game is large then it is a stable set and for symmetric NTU games the core is a stable set if and only if it is large.

scholarly journals Coalition formation and history dependence

2020 ◽  
Vol 15 (1) ◽  
pp. 159-197 ◽  
Author(s):  
Bhaskar Dutta ◽  
Hannu Vartiainen
Keyword(s):  
Coalition Formation ◽  
Stable Set ◽  
Transferable Utility ◽  
Stable Sets ◽  
Solution Concepts ◽  
History Dependence ◽  
Von Neumann ◽  
Finite Games ◽  
A Chain ◽  
Indirect Dominance

Farsighted formulations of coalitional formation, for instance, by Harsanyi and Ray and Vohra, have typically been based on the von Neumann–Morgenstern stable set. These farsighted stable sets use a notion of indirect dominance in which an outcome can be dominated by a chain of coalitional “moves” in which each coalition that is involved in the sequence eventually stands to gain. Dutta and Vohra point out that these solution concepts do not require coalitions to make optimal moves. Hence, these solution concepts can yield unreasonable predictions. Dutta and Vohra restricted coalitions to hold common, history‐independent expectations that incorporate optimality regarding the continuation path. This paper extends the Dutta–Vohra analysis by allowing for history‐dependent expectations. The paper provides characterization results for two solution concepts that correspond to two versions of optimality. It demonstrates the power of history dependence by establishing nonemptyness results for all finite games as well as transferable utility partition function games. The paper also provides partial comparisons of the solution concepts to other solutions.

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.

scholarly journals Hart–Mas-Colell consistency and the core in convex games

2021 ◽  
Author(s):  
Bas Dietzenbacher ◽  
Peter Sudhölter
Keyword(s):  
Shapley Value ◽  
Cooperative Games ◽  
Individual Rationality ◽  
Transferable Utility ◽  
Convex Games ◽  
The Core ◽  
The Shapley Value ◽  
Scale Covariance

AbstractThis paper formally introduces Hart–Mas-Colell consistency for general (possibly multi-valued) solutions for cooperative games with transferable utility. This notion is used to axiomatically characterize the core on the domain of convex games. Moreover, we characterize all nonempty solutions satisfying individual rationality, anonymity, scale covariance, superadditivity, weak Hart–Mas-Colell consistency, and converse Hart–Mas-Colell consistency. This family consists of (a) the Shapley value, (b) all homothetic images of the core with the Shapley value as center of homothety and with positive ratios of homothety not larger than one, and (c) their relative interiors.

Uncoupled Aspiration Adaptation Dynamics Into the Core

2019 ◽  
Vol 20 (2) ◽  
pp. 243-256 ◽  
Author(s):  
Heinrich H. Nax
Keyword(s):  
Finite Time ◽  
Cooperative Games ◽  
Transferable Utility ◽  
The Core ◽  
Best Response ◽  
Dynamic Blocking ◽  
Evolutionary Interpretation ◽  
Require Information ◽  
Empty Core

Abstract Dynamics for play of transferable-utility cooperative games are proposed that require information regarding own payoff experiences and other players’ past actions, but not regarding other players’ payoffs. The proposed dynamics provide an evolutionary interpretation of the proto-dynamic ‘blocking argument’ (Edgeworth, 1881) based on the behavioral principles of ‘aspiration adaptation’ (Sauermann and Selten, 1962) instead of best response. If the game has a non-empty core, the dynamics are absorbed into the core in finite time with probability one. If the core is empty, the dynamics cycle infinitely through all coalitions.

scholarly journals On extensions of the core and the anticore of transferable utility games

2013 ◽  
Vol 43 (1) ◽  
pp. 37-63 ◽  
Author(s):  
Jean Derks ◽  
Hans Peters ◽  
Peter Sudhölter
Keyword(s):  
Transferable Utility ◽  
The Core ◽  
Transferable Utility Games

THE EGALITARIAN NON-k-AVERAGED CONTRIBUTION (ENkAC-) VALUE FOR TU-GAMES

1999 ◽  
Vol 01 (01) ◽  
pp. 45-61 ◽  
Author(s):  
TSUNEYUKI NAMEKATA ◽  
THEO S. H. DRIESSEN
Keyword(s):  
Solution Concept ◽  
Sufficient Condition ◽  
Individual Contribution ◽  
Transferable Utility ◽  
Tu Games ◽  
The Core ◽  
Centre Of Gravity ◽  
Transferable Utility Game ◽  
Individual Contributions ◽  
Transferable Utility Games

This paper deals in a unified way with the solution concepts for transferable utility games known as the Centre of the Imputation Set value (CIS-value), the Egalitarian Non-Pairwise-Averaged Contribution value (ENPAC-value) and the Egalitarian Non-Separable Contribution value (ENSC-value). These solutions are regarded as the egalitarian division of the surplus of the overall profits after each participant is conceded to get his individual contribution specified in a respective manner. We offer two interesting individual contributions (lower- and upper-k-averaged contribution) based on coalitions of size k(k ∈ {1,…,n-1}) and introduce a new solution concept called the Egalitarian Non-k-Averaged Contribution value ( EN k AC -value). CIS-, ENPAC- and ENSC-value are the same as EN 1 AC -, EN n-2 AC - and EN n-1 AC -value respectively. It turns out that the lower- and the upper-k-averaged contribution form a lower- and an upper-bound of the Core respectively. The Shapley value is the centre of gravity of n-1 points; EN 1 AC -,…, EN n-1 AC -value. EN k AC -value of the dual game is equal to EN n-k AC -value of the original game. We provide a sufficient condition on the transferable utility game to guarantee that the EN k AC -value coincides with the well-known solution called prenucleolus. The condition requires that the largest excesses at the EN k AC -value are attained at the k-person coalitions, whereas the excesses of k-person coalitions at the EN k AC -value do not differ.

Consistent extensions and subsolutions of the core for the multichoice transferable-utility games

Optimization ◽  
2013 ◽  
Vol 64 (4) ◽  
pp. 913-928 ◽  
Author(s):  
Yan-An Hwang ◽  
Yu-Hsien Liao ◽  
Chun-Hsien Yeh
Keyword(s):  
Transferable Utility ◽  
The Core ◽  
Transferable Utility Games

scholarly journals Maximizing the Minimal Satisfaction—Characterizations of Two Proportional Values

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1129
Author(s):  
Wenzhong Li ◽  
Genjiu Xu ◽  
Hao Sun
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Cooperative Games ◽  
Transferable Utility ◽  
Payoff Vector ◽  
The Core ◽  
Proportional Allocation ◽  
Consistency Property ◽  
Associated Consistency

A class of solutions are introduced by lexicographically minimizing the complaint of coalitions for cooperative games with transferable utility. Among them, the nucleolus is an important representative. From the perspective of measuring the satisfaction of coalitions with respect to a payoff vector, we define a family of optimal satisfaction values in this paper. The proportional division value and the proportional allocation of non-separable contribution value are then obtained by lexicographically maximizing two types of satisfaction criteria, respectively, which are defined by the lower bound and the upper bound of the core from the viewpoint of optimism and pessimism respectively. Correspondingly, we characterize these two proportional values by introducing the equal minimal satisfaction property and the associated consistency property. Furthermore, we analyze the duality of these axioms and propose more approaches to characterize these two values on basis of the dual axioms.

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