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Strategic coalitions in stochastic games

Strategic coalitions in stochastic games
Strategic coalitions in stochastic games
The article compares two different approaches of incorporating probability into coalition logics. One is based on the semantics of games with stochastic transitions and the other on games with the stochastic failures. The work gives an example of a non-trivial property of coalition power for the first approach and a complete axiomatization for the second approach. It turns out that the logical properties of the coalition power modality under the second approach depend on whether the modal language allows the empty coalition. The main technical results for the games with stochastic failures are a strong completeness theorem for the logical system without the empty coalition and an incompleteness theorem which shows that there is no strongly complete logical system in the language with the empty coalition.
axiomatization, completeness, logic, probability, stochastic game
1845
Naumov, Pavel
8b6c40fb-b199-44d5-a8e2-0ebd021566b0
Ros, Kevin
4db1490d-69a7-4c4f-bf00-e239c2f7656e
Naumov, Pavel
8b6c40fb-b199-44d5-a8e2-0ebd021566b0
Ros, Kevin
4db1490d-69a7-4c4f-bf00-e239c2f7656e

Naumov, Pavel and Ros, Kevin (2021) Strategic coalitions in stochastic games. Journal of Logic and Computation, 31 (7), 1845. (doi:10.1093/logcom/exab032).

Record type: Article

Abstract

The article compares two different approaches of incorporating probability into coalition logics. One is based on the semantics of games with stochastic transitions and the other on games with the stochastic failures. The work gives an example of a non-trivial property of coalition power for the first approach and a complete axiomatization for the second approach. It turns out that the logical properties of the coalition power modality under the second approach depend on whether the modal language allows the empty coalition. The main technical results for the games with stochastic failures are a strong completeness theorem for the logical system without the empty coalition and an incompleteness theorem which shows that there is no strongly complete logical system in the language with the empty coalition.

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More information

Published date: 17 May 2021
Keywords: axiomatization, completeness, logic, probability, stochastic game

Identifiers

Local EPrints ID: 451766
URI: http://eprints.soton.ac.uk/id/eprint/451766
PURE UUID: 5e28fb94-71f4-4473-95e7-2ab1d9052389
ORCID for Pavel Naumov: ORCID iD orcid.org/0000-0003-1687-045X

Catalogue record

Date deposited: 26 Oct 2021 16:31
Last modified: 10 Jan 2022 03:24

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Contributors

Author: Pavel Naumov ORCID iD
Author: Kevin Ros

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