Displaying similar documents to “Three notes on the complexity of model checking fixpoint logic with chop”

Logical consequence and the theory of games

Paul Harrenstein (2004)

Philosophia Scientiae

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Logical notions of consequence have frequently been related to game-theoretical solution concepts. The correspondence between a formula being classically valid and the existence of a winning strategy for a player in a related two-person game, has been most prominent in this context. We propose a conservative extension of the classical notion of consequence that is based on a generalization of the game-theoretical solution concept of Nash equilibrium.

On independence-friendly fixpoint logics

J. C. Bradfield (2004)

Philosophia Scientiae

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We introduce a fixpoint extension of Hintikka and Sandu’s IF (independence-friendly) logic. We obtain some results on its complexity and expressive power. We relate it to parity games of imperfect information, and show its application to defining independence-friendly modal mu-calculi.

On knowledge games.

J. M. Lasry, J. M. Morel, S. Solimini (1989)

Revista Matemática de la Universidad Complutense de Madrid

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We give a formalization of the ?knowledge games? which allows to study their decidability and convergence as a problem of mathematics. Our approach is based on a metalemma analogous to those of Von Neumann and Morgenstern at the beginning of Game Theory. We are led to definitions which characterize the knowledge games as objects is standard set theory. We then study rigorously the most classical knowledge games and, although we also prove that the ?common knowledge? in these games may...

The Give and Take game: Analysis of a resource sharing game

Pedro Mariano, Luís Correia (2015)

International Journal of Applied Mathematics and Computer Science

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We analyse Give and Take, a multi-stage resource sharing game to be played between two players. The payoff is dependent on the possession of an indivisible and durable resource, and in each stage players may either do nothing or, depending on their roles, give the resource or take it. Despite these simple rules, we show that this game has interesting complex dynamics. Unique to Give and Take is the existence of multiple Pareto optimal profiles that can also be Nash equilibria, and a...

Fixpoints, games and the difference hierarchy

Julian C. Bradfield (2003)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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Drawing on an analogy with temporal fixpoint logic, we relate the arithmetic fixpoint definable sets to the winning positions of certain games, namely games whose winning conditions lie in the difference hierarchy over Σ 2 0 . This both provides a simple characterization of the fixpoint hierarchy, and refines existing results on the power of the game quantifier in descriptive set theory. We raise the problem of transfinite fixpoint hierarchies.

An axiomatization of the aspiration core

Hans Keiding (2006)

Banach Center Publications

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The aspiration core of a TU game was introduced by Bennett [1] as a payoff vector which is undominated and achievable in the sense that each player belongs to a coalition which can obtain the specified payoff for its members, and which minimizes the distance to the set of aggregate feasible payoffs among all such payoff vectors. In the paper a set of axioms is proposed which characterize the aspiration core, which may be considered as an extension of the core to a much larger set of...