On Knowledge Games
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We give a formalization of the “knowledge games” which allows to study their decidability and convergence as a problem of mathematics. Our approach is based on a metalemma analogous to those of Von Neumann and Morgenstern at the beginning of Game Theory. We are led to definitions which characterize the knowledge games as objects is standard set theory. We then study rigorously the most classical knowledge games and, although we also prove that the “common knowledge” in these games may be incomputable, show their decidability in a simple way.
1980 Mathematics Subject Classification (1985 revision): 90D12, 03B25, 68M10.