Strategy logic

  • Authors:

  • Krishnendu Chatterjee;Thomas A. Henzinger;Nir Piterman

  • Affiliations:

  • IST Austria (Institute of Science and Technology Austria), Am Campus 1, IST Austria, Klosterneuburg 3400, Austria;IST Austria (Institute of Science and Technology Austria), Am Campus 1, IST Austria, Klosterneuburg 3400, Austria and EPFL, BC 350, EPFL Station 14, CH-1015 Lausanne, Switzerland;Imperial College London, Huxley 359, South Kensington Campus, London, SW7 2AZ, UK

  • Venue:
  • Information and Computation
  • Year:
  • 2010

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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).