Axiomatising Nash-Consistent Coalition Logic

Hansen, Helle Hvid; Pauly, Marc

doi:10.1007/3-540-45757-7_33

Cited by 4 publications

(5 citation statements)

References 7 publications

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“…is a filtration in the sense of Definition 12 is proved in [8] for the coalitional modalities. We have added to that a minimal filtration for modality O .…”

Section: Filtrationsmentioning

confidence: 96%

“…Filtrations of coalition models are introduced, e.g., in [8] for the purpose of axiomatizing Nashconsistent Coalition Logic. Here we only add the filtration for the relation corresponding to the modality O .…”

Section: Filtrationsmentioning

confidence: 99%

“…So M F Σ(δ) is a filtration in the sense of Definition 12. In [8] it is also shown that playability is preserved by that filtration and that every subset of W F Σ(δ) is definable by a formula of Σ(δ) as follows. First, for every state |w| ∈ |W | we define…”

Section: Filtrationsmentioning

confidence: 99%

“…The conditions above are needed to ensure the Filtration Lemma, as showed in [8] for the neighbourhood relations and e.g., in [5] for the binary relation.…”

Section: Definition 12 (Filtrationmentioning

confidence: 99%

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Strategic games and truly playable effectivity functions

Goranko

Jamroga

Turrini

2012

Auton Agent Multi-Agent Syst

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A well known (and often used) result by Marc Pauly states that for every playable effectivity function E there exists a strategic game that assigns to coalitions exactly the same power as E, and vice versa. While the latter direction of the correspondence is correct, we show that the former does not always hold in the case of infinite game models. We point out where the proof of correspondence goes wrong, and we present examples of playable effectivity functions in infinite models for which no equivalent strategic game exists. Then, we characterize the class of truly playable effectivity functions, that does correspond to strategic games. Moreover, we discuss a construction that transforms any playable effectivity function into a truly playable one while preserving the power of most (but not all) coalitions. We also show that Coalition Logic is not expressive enough to distinguish between playable and truly playable effectivity functions, and we extend it to a logic that can make this distinction while enjoying finite axiomatization and finite model property.

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“…is a filtration in the sense of Definition 12 is proved in [8] for the coalitional modalities. We have added to that a minimal filtration for modality O .…”

Section: Filtrationsmentioning

confidence: 96%

Section: Filtrationsmentioning

confidence: 99%

Section: Filtrationsmentioning

confidence: 99%

“…The conditions above are needed to ensure the Filtration Lemma, as showed in [8] for the neighbourhood relations and e.g., in [5] for the binary relation.…”

Section: Definition 12 (Filtrationmentioning

confidence: 99%

See 2 more Smart Citations

Strategic games and truly playable effectivity functions

Goranko

Jamroga

Turrini

2012

Auton Agent Multi-Agent Syst

View full text Add to dashboard Cite

show abstract

“…Another source of inspiration for further logical analysis here may be the work on so-called 'Nashconsistent powers' in game theory,[22], and in coalition logic,[16].…”

mentioning

confidence: 99%