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 Maximality in the Farsighted Stable Set

Econometrica ◽  
2019 ◽  
Vol 87 (5) ◽  
pp. 1763-1779 ◽  
Author(s):  
Debraj Ray ◽  
Rajiv Vohra
Keyword(s):  
Stable Set ◽  
Stable Sets ◽  
Von Neumann

Harsanyi (1974) and Ray and Vohra (2015) extended the stable set of von Neumann and Morgenstern to impose farsighted credibility on coalitional deviations. But the resulting farsighted stable set suffers from a conceptual drawback: while coalitional moves improve on existing outcomes, coalitions might do even better by moving elsewhere. Or other coalitions might intervene to impose their favored moves. We show that every farsighted stable set satisfying some reasonable and easily verifiable properties is unaffected by the imposition of these stringent maximality constraints. The properties we describe are satisfied by many, but not all, farsighted stable sets.

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.

VON NEUMANN AND MORGENSTERN STABLE SETS IN A COURNOT MERGER SYSTEM

2000 ◽  
Vol 02 (01) ◽  
pp. 29-45 ◽  
Author(s):  
M. P. ESPINOSA ◽  
E. INARRA
Keyword(s):  
Market Structure ◽  
Structure Determination ◽  
Coalition Formation ◽  
Dominance Relation ◽  
Cournot Oligopoly ◽  
Stable Sets ◽  
Valuation Function ◽  
Abstract System ◽  
Von Neumann ◽  
Oligopoly Markets

We address the problem of endogenous coalition formation in Cournot oligopoly markets. The formation of coalitions is formalised as an abstract system where the elements of the abstract set are derived from a valuation function and the dominance relation specifies the rules of coalition formation. We focus on a particular instance of this approach: Market structure determination under Cournot competition, and in the resulting Cournot merger system we find von Neumann and Morgenstern stable sets.

scholarly journals An existence theorem for abstract stable sets

1991 ◽  
Vol 51 (3) ◽  
pp. 468-472 ◽  
Author(s):  
Chih Chang ◽  
Gerard J. Chang
Keyword(s):  
Existence Theorem ◽  
Dominance Relation ◽  
Stable Set ◽  
Stable Sets

AbstractWe provide an existence theorem for stable sets which is equivalent to Zorn's lemma and study the connections between the unique stable set for majorization and the stable sets for the dominance relation.

scholarly journals VERY WELL-COVERED GRAPHS OF GIRTH AT LEAST FOUR AND LOCAL MAXIMUM STABLE SET GREEDOIDS

2011 ◽  
Vol 03 (02) ◽  
pp. 245-252 ◽  
Author(s):  
VADIM E. LEVIT ◽  
EUGEN MANDRESCU
Keyword(s):  
Perfect Matching ◽  
Local Maximum ◽  
Stable Set ◽  
Stable Sets ◽  
Maximum Cardinality ◽  
Math Program ◽  
The Family ◽  
Maximum Stable Set ◽  
Vertex Set ◽  
Appl Math

A maximum stable set in a graph G is a stable set of maximum cardinality. S is a local maximum stable set of G, and we write S ∈ Ψ(G), if S is a maximum stable set of the subgraph induced by S ∪ N(S), where N(S) is the neighborhood of S. Nemhauser and Trotter Jr. [Vertex packings: structural properties and algorithms, Math. Program.8 (1975) 232–248], proved that any S ∈ Ψ(G) is a subset of a maximum stable set of G. In [Levit and Mandrescu, A new greedoid: the family of local maximum stable sets of a forest, Discrete Appl. Math.124 (2002) 91–101] we have shown that the family Ψ(T) of a forest T forms a greedoid on its vertex set. The cases where G is bipartite, triangle-free, well-covered, while Ψ(G) is a greedoid, were analyzed in [Levit and Mandrescu, Local maximum stable sets in bipartite graphs with uniquely restricted maximum matchings, Discrete Appl. Math.132 (2004) 163–174], [Levit and Mandrescu, Triangle-free graphs with uniquely restricted maximum matchings and their corresponding greedoids, Discrete Appl. Math.155 (2007) 2414–2425], [Levit and Mandrescu, Well-covered graphs and greedoids, Proc. 14th Computing: The Australasian Theory Symp. (CATS2008), Wollongong, NSW, Conferences in Research and Practice in Information Technology, Vol. 77 (2008) 89–94], respectively. In this paper we demonstrate that if G is a very well-covered graph of girth ≥4, then the family Ψ(G) is a greedoid if and only if G has a unique perfect matching.

The von Neumann–Morgenstern stable sets for the mixed extension of 2×2 games

2014 ◽  
Vol 125 (1) ◽  
pp. 70-73
Author(s):  
E. Inarra ◽  
C. Larrea ◽  
A. Saracho
Keyword(s):  
Stable Sets ◽  
Von Neumann

A test of the von Neumann-Morgenstern stable set solution in cooperative non-sidepaymentN-person games

1984 ◽  
Vol 29 (1) ◽  
pp. 13-27 ◽  
Author(s):  
H. Andrew Michener ◽  
Kathryn Potter ◽  
Greg B. Macheel ◽  
Charles G. Depies
Keyword(s):  
Stable Set ◽  
Von Neumann
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