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Knowledge Games and Coalitional Abilities

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Johan van Benthem on Logic and Information Dynamics

Part of the book series: Outstanding Contributions to Logic ((OCTR,volume 5))

Abstract

We present our recent work on the interaction of knowledge and coalitional abilities, on quantifying over information change, and on imperfect information games wherein the actions are public announcements or questions with informative answers. Such case studies should be seen as an implementation of the general programmatic ideas found in Johan van Benthem’s recent books Logical Dynamics of Information and Interaction and Logic in Games.

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Notes

  1. 1.

    We remind the reader that \(G\subseteq N\) typically names a group or coalition of agents, whereas \({\mathbf G}\), i.e. ‘bold-\(G\)’, names a game (\(C\) for coalition clashes with \(C\) for common knowledge).

  2. 2.

    The literature differs in the definition of weakly dominant strategies. Another common definition in addition requires that the strategy is strictly better against at least one combination of actions by the other agents.

  3. 3.

    The notation for coalition operators varies in the literature. In [85], Pauly in fact uses \([G]\) where we use \(\langle G \rangle \). Pauly’s interpretation of the operator uses a \(\exists \forall \) pattern, and since we also will discuss other interpretations of the operator we choose to emphasise its existential nature and use the diamond notation \(\langle G \rangle \).

  4. 4.

    One reason for this is that with perfect recall strategies and imperfect information the model checking problem is assumed to be undecidable [6, 90].

  5. 5.

    The de dicto/de re distinction is well known [88] in logic/language in general and has been known in the area of reasoning about knowledge and action in ai for some time [81].

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Author information

Authors and Affiliations

  1. Department of Information Science and Media Studies, University of Bergen, P.O. Box 7802, 5020, Bergen, Norway

    Thomas Ågotnes

  2. LORIA, CNRS—Université de Lorraine, BP 239, 54506, Vandoeuvre-lès-Nancy, France

    Hans van Ditmarsch

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  1. Thomas Ågotnes
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Correspondence to Hans van Ditmarsch .

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Editors and Affiliations

  1. University of Amsterdam Inst Logic,Language & Computation, Amsterdam, The Netherlands

    Alexandru Baltag

  2. Amsterdam, The Netherlands

    Sonja Smets

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Ågotnes, T., van Ditmarsch, H. (2014). Knowledge Games and Coalitional Abilities. In: Baltag, A., Smets, S. (eds) Johan van Benthem on Logic and Information Dynamics. Outstanding Contributions to Logic, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-06025-5_16

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