Maximin, minimax, and von Neumann–Morgenstern farsighted stable sets

2015 ◽  
Vol 74 ◽  
pp. 8-12 ◽  
Author(s):  
Ryo Kawasaki
Keyword(s):  
Stable Sets ◽  
Von Neumann

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.

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

scholarly journals Von Neumann-Morgenstern Farsightedly Stable Sets in Two-Sided Matching

2008 ◽  
Author(s):  
Vincent J. Vannetelbosch ◽  
Ana Carmen Mauleon ◽  
Wouter Vergote
Keyword(s):  
Stable Sets ◽  
Von Neumann

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.

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