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International Conference on Agents and Artificial Intelligence

ICAART 2013: Agents and Artificial Intelligence pp 131–148Cite as

Epistemic and Probabilistic ATL with Quantification and Explicit Strategies

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 449))

Abstract

We introduce QAPI (quantified ATL with probabilism and incomplete information), which extends epistemic and probabilistic ATL with quantification of strategies and a flexible mechanism to reason about strategies in the object language. This allows QAPI to express complex strategic properties such as equilibria and to treat the behavior of the “counter-coalition” in a very flexible way. We provide bisimulation relations, model checking results, and study the issues arising from the interplay between quantifiers and both epistemic and temporal operators.

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Notes

  1. 1.

    A probability distribution \(\mathrm {\text {Pr}}\) on \(Q\) is discrete, if there is a countable set \(Q'\subseteq Q\) such that \(\sum _{q\in Q'} \mathrm {\text {Pr}} \left( q\right) =1\).

  2. 2.

    I.e., if \(\mathrm {S}_i\) is an \(A\)-strategy choice variable for some coalition \(A\), then \(\mathsf {S}_i\) is a strategy choice for \(A\).

  3. 3.

    It is not sufficient to rely on the uniformity of strategy choices (the same strategy must be chosen in \(A\)-indistinguishable states), since there must be a single strategy that is successful in all \(\varGamma \)-indistinguishable states, and \(\varGamma \) might have less information than \(A\).

  4. 4.

    To express this as a variable, the CGS needs to record the last move of each player in the state in the obvious way.

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Author information

Authors and Affiliations

  1. Institut für Informatik, Christian-Albrechts-Universität zu Kiel, 24098, Kiel, Germany

    Henning Schnoor

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  1. Henning Schnoor
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Correspondence to Henning Schnoor .

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Editors and Affiliations

  1. INSTICC, Setúbal, Portugal

    Joaquim Filipe

  2. Instituto de Telecomunicações, Lisbon, Portugal

    Ana Fred

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Schnoor, H. (2014). Epistemic and Probabilistic ATL with Quantification and Explicit Strategies. In: Filipe, J., Fred, A. (eds) Agents and Artificial Intelligence. ICAART 2013. Communications in Computer and Information Science, vol 449. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44440-5_8

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  • DOI: https://doi.org/10.1007/978-3-662-44440-5_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44439-9

  • Online ISBN: 978-3-662-44440-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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