Strategy logic Journal Article


Author(s): Chatterjee, Krishnendu; Henzinger, Thomas A; Piterman, Nir
Article Title: Strategy logic
Affiliation IST Austria
Abstract: We introduce strategy logic, a logic that treats strategies in two-player games as explicit first-order objects. The explicit treatment of strategies allows us to specify properties of nonzero-sum games in a simple and natural way. We show that the one-alternation fragment of strategy logic is strong enough to express the existence of Nash equilibria and secure equilibria, and subsumes other logics that were introduced to reason about games, such as ATL, ATL*, and game logic. We show that strategy logic is decidable, by constructing tree automata that recognize sets of strategies. While for the general logic, our decision procedure is nonelementary, for the simple fragment that is used above we show that the complexity is polynomial in the size of the game graph and optimal in the size of the formula (ranging from polynomial to 2EXPTIME depending on the form of the formula).
Keywords: Game theory; Logic; ATL and ATL∗; Nonzero-sum games; Automata theory
Journal Title: Information and Computation
Volume: 208
Issue 6
ISSN: 0890-5401
Publisher: Elsevier  
Date Published: 2010-06-01
Start Page: 677
End Page: 693
Sponsor: This research was supported in part by the Swiss National Science Foundation and by the NSF Grants CCR-0225610 and CCR-0234690.
URL:
DOI: 10.1016/j.ic.2009.07.004
Notes: We thank Lukasz Kaiser for discussions on possible extension of Strategy Logic to partial-information games.
Open access: yes (repository)
IST Austria Authors
  1. Thomas A. Henzinger
    415 Henzinger
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