Issue: 2014/Vol.24/No.1, Pages 71-96
PROBABILITIES ON STREAMS AND REFLEXIVE GAMES
Andrew Schumann
Cite as: A. Schumann. Probabilities on streams and reflexive games. Operations Research and Decisions 2014: 24(1), 71-96. DOI 10.5277/ord140105
Abstract
Probability measures on streams (e.g. on hypernumbers and p-adic numbers) have been defined. It was shown that these probabilities can be used for simulations of reflexive games. In particular, it can be proved that Aumann’s agreement theorem does not hold for these probabilities. Instead of this theorem, there is a statement that is called the reflexion disagreement theorem. Based on this theorem, probabilistic and knowledge conditions can be defined for reflexive games at various reflexion levels up to the infinite level.
Keywords: metagame, reflexive game, coinductive probabilities, p-adic probabilities, perlocutionary effect, Aumann’s agreement theorem
Received: Accepted: 7 January 2014