15,188 research outputs found
The Complexity of Synthesizing Uniform Strategies
We investigate uniformity properties of strategies. These properties involve
sets of plays in order to express useful constraints on strategies that are not
\mu-calculus definable. Typically, we can state that a strategy is
observation-based. We propose a formal language to specify uniformity
properties, interpreted over two-player turn-based arenas equipped with a
binary relation between plays. This way, we capture e.g. games with winning
conditions expressible in epistemic temporal logic, whose underlying
equivalence relation between plays reflects the observational capabilities of
agents (for example, synchronous perfect recall). Our framework naturally
generalizes many other situations from the literature. We establish that the
problem of synthesizing strategies under uniformity constraints based on
regular binary relations between plays is non-elementary complete.Comment: In Proceedings SR 2013, arXiv:1303.007
Epistemic Analysis of Strategic Games with Arbitrary Strategy Sets
We provide here an epistemic analysis of arbitrary strategic games based on
the possibility correspondences. Such an analysis calls for the use of
transfinite iterations of the corresponding operators. Our approach is based on
Tarski's Fixpoint Theorem and applies both to the notions of rationalizability
and the iterated elimination of strictly dominated strategies.Comment: 8 pages Proc. of the 11th Conference on Theoretical Aspects of
Rationality and Knowledge (TARK XI), 2007. To appea
The Logic of Joint Ability in Two-Player Tacit Games
Logics of joint strategic ability have recently received attention, with arguably the most influential being those in a family that includes Coalition Logic (CL) and Alternating-time Temporal Logic (ATL). Notably, both CL and ATL bypass the epistemic issues that underpin Schelling-type coordination problems, by apparently relying on the meta-level assumption of (perfectly reliable) communication between cooperating rational agents. Yet such epistemic issues arise naturally in settings relevant to ATL and CL: these logics are standardly interpreted on structures where agents move simultaneously, opening the possibility that an agent cannot foresee the concurrent choices of other agents. In this paper we introduce a variant of CL we call Two-Player Strategic Coordination Logic (SCL2). The key novelty of this framework is an operator for capturing coalitional ability when the cooperating agents cannot share strategic information. We identify significant differences in the expressive power and validities of SCL2 and CL2, and present a sound and complete axiomatization for SCL2. We briefly address conceptual challenges when shifting attention to games with more than two players and stronger notions of rationality
The Role of Monotonicity in the Epistemic Analysis of Strategic Games
It is well-known that in finite strategic games true common belief (or common
knowledge) of rationality implies that the players will choose only strategies
that survive the iterated elimination of strictly dominated strategies. We
establish a general theorem that deals with monotonic rationality notions and
arbitrary strategic games and allows to strengthen the above result to
arbitrary games, other rationality notions, and transfinite iterations of the
elimination process. We also clarify what conclusions one can draw for the
customary dominance notions that are not monotonic. The main tool is Tarski's
Fixpoint Theorem.Comment: 20 page
Proof-theoretic Analysis of Rationality for Strategic Games with Arbitrary Strategy Sets
In the context of strategic games, we provide an axiomatic proof of the
statement Common knowledge of rationality implies that the players will choose
only strategies that survive the iterated elimination of strictly dominated
strategies. Rationality here means playing only strategies one believes to be
best responses. This involves looking at two formal languages. One is
first-order, and is used to formalise optimality conditions, like avoiding
strictly dominated strategies, or playing a best response. The other is a modal
fixpoint language with expressions for optimality, rationality and belief.
Fixpoints are used to form expressions for common belief and for iterated
elimination of non-optimal strategies.Comment: 16 pages, Proc. 11th International Workshop on Computational Logic in
Multi-Agent Systems (CLIMA XI). To appea
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