On the existence and efficiency of the von Neumann-Morgenstern stable set in a n-player prisoners' dilemma

2001 ◽  
Vol 30 (2) ◽  
pp. 291-307 ◽  
Author(s):  
Noritsugu Nakanishi
Keyword(s):  
Stable Set ◽  
Von Neumann ◽  
Prisoners Dilemma

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.

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

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.

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