A New Game Equivalence and its Modal Logic

Johan van Benthem
(ILLC University of Amsterdam)
Nick Bezhanishvili
(ILLC University of Amsterdam)
Sebastian Enqvist
(Department of Philosophy Stockholm University)

We revisit the crucial issue of natural game equivalences, and semantics of game logics based on these. We present reasons for investigating finer concepts of game equivalence than equality of standard powers, though staying short of modal bisimulation. Concretely, we propose a more finegrained notion of equality of "basic powers" which record what players can force plus what they leave to others to do, a crucial feature of interaction. This notion is closer to game-theoretic strategic form, as we explain in detail, while remaining amenable to logical analysis. We determine the properties of basic powers via a new representation theorem, find a matching "instantial neighborhood game logic", and show how our analysis can be extended to a new game algebra and dynamic game logic.

In Jérôme Lang: Proceedings Sixteenth Conference on Theoretical Aspects of Rationality and Knowledge (TARK 2017), Liverpool, UK, 24-26 July 2017, Electronic Proceedings in Theoretical Computer Science 251, pp. 57–74.
Published: 25th July 2017.

ArXived at: http://dx.doi.org/10.4204/EPTCS.251.5 bibtex PDF
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