Knowledge condition games

Abstract
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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DOI 10.1007/s10849-006-9014-1
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References found in this work BETA
Reasoning About Knowledge.Ronald Fagin (ed.) - 2003 - MIT Press.
Knowledge and Belief.Jaakko Hintikka - 1962 - Ithaca: Cornell University Press.
Theory of Games and Economic Behavior.John von Neumann & Oskar Morgenstern - 1945 - Journal of Philosophy 42 (20):550-554.
The Strategy of Conflict.Thomas Schelling - 1960 - Harvard University Press.

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