David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Journal of Logic, Language and Information 15 (4):425-452 (2006)
Understanding the flow of knowledge in multi-agent protocols is essential when proving the correctness or security of such protocols. Current logical approaches, often based on model checking, are well suited for modeling knowledge in systems where agents do not act strategically. Things become more complicated in strategic settings. In this paper we show that such situations can be understood as a special type of game – a knowledge condition game – in which a coalition “wins” if it is able to bring about some epistemic condition. This paper summarizes some results relating to these games. Two proofs are presented for the computational complexity of deciding whether a coalition can win a knowledge condition game with and without opponents (Σ2P-complete and NP-complete respectively). We also consider a variant of knowledge condition games in which agents do not know which strategies are played, and prove that under this assumption, the presence of opponents does not affect the complexity. The decision problem without opponents is still NP-complete, but requires a different proof.
|Keywords||complexity epistemic logic game theory imperfect information knowledge protocol strategy|
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References found in this work BETA
Jaakko Hintikka (1962). Knowledge and Belief. Ithaca, N.Y.,Cornell University Press.
John von Neumann & Oskar Morgenstern (1945). Theory of Games and Economic Behavior. Journal of Philosophy 42 (20):550-554.
Wiebe van der Hoek & Michael Wooldridge (2003). Cooperation, Knowledge, and Time: Alternating-Time Temporal Epistemic Logic and its Applications. Studia Logica 75 (1):125-157.
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