Equilibrium coalitional behavior

Kimya, Mert

doi:10.3982/te3055

Cited by 26 publications

(21 citation statements)

References 49 publications

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“… There is now a sizable literature that studies farsighted stability in coalitional games. This includes Aumann and Myerson (), Chwe (), Xue (), Diamantoudi and Xue (), Herings, Mauleon, and Vannetelbosch (, ), Jordan (), Ray (), Page and Wooders (), Mauleon, Vannetelbosch, and Vergote (), Kimya (), Ray and Vohra (), Bloch and van den Nouweland (), Dutta and Vohra (), and Dutta and Vartiainen (). …”

mentioning

confidence: 99%

Maximality in the Farsighted Stable Set

Ray

Vohra

2019

ECTA

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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.

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confidence: 99%

Maximality in the Farsighted Stable Set

Ray

Vohra

2019

ECTA

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“…The next couple of simple examples, adapted from Xue (), Herings et al (), and Kimya () illustrate some drawbacks of these solution concepts.…”

Section: Related Solution Conceptsmentioning

confidence: 99%

“…One way to interpret Examples and is that maximality imposes the type of logic inherent in backward induction or, more generally, subgame perfection. In a recent interesting paper, Kimya () also formulates two solution concepts that integrate coalitional analysis with noncooperative logic. Kimya too focuses on paths with elements being triples of the form

false(x, y, S false)

with

S \in E false(x, y false)

and

x, y \in X

.…”

Section: Related Solution Conceptsmentioning

confidence: 99%

“… See, for instance, Chwe (), Bloch (), Ray and Vohra (, , ), Xue (), Diamantoudi and Xue (), Konishi and Ray (), Herings et al (, ), Anesi (), Mauleon et al (), Vartiainen (), Anesi and Seidmann (), Chander (), Kimya (), and Dutta and Vohra (). Aumann and Myerson () also modeled farsighted behavior, but from a different perspective.…”

mentioning

confidence: 99%

“… Path‐based coalitional solutions include Xue (), Mariotti (), and Kimya (). However, as discussed in Section , they are based on assumptions that are, in general, not compatible with HREFS and, hence, not directly comparable to coherence. …”

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confidence: 99%

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Coalition formation and history dependence

Dutta

Vartiainen

2020

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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.

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