- 397 Downloads
We show that if an agent reasons according to standard inference rules, the truth and introspection axioms extend from the set of non-epistemic propositions to the whole set of propositions. This implies that the usual axiomatization of partitional possibility correspondences is redundant, and provides a justification for truth and introspection that is partly based on reasoning.
KeywordsKnowledge Introspection Truth axiom Partitional information structures Epistemic game theory
JEL ClassificationD80 D83 D89
We are indebted to Geir Asheim, Giacomo Bonanno, Amanda Friedenberg, Willemien Kets, Friederike Mengel, Andrés Perea, Philippe Mongin, Mark Voorneveld, and Jörgen Weibull for fruitful discussions and useful comments. We would also like to thank the audiences of the Epistemic Game Theory Workshop (Stony Brook), Game Theory Conference (Stony Book), ESEM (Barcelona), SAET (Ischia), CRETE (Tinos), Bocconi University, LSE, Santa Fe Institute, Paris Game Theory Seminar, IHPST (Paris), Stockholm School of Economics, University of Warwick, HEC Lausanne, and Göteborg University. The financial support from the Marie Curie Intra-European Fellowship is gratefully acknowledged (PIEF-GA-2009-237614).
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
- Fagin R., Halpern J. Y., Moses Y., Vardi M. Y. (1995) Reasoning about knowledge. MIT press, CambridgeGoogle Scholar
- Geanakoplos, J. (1989). Game theory without partitions, and applications to speculation and consensus. Cowles Foundation Discussion Paper No. 914.Google Scholar
- Harsanyi, J. (1967–1968). Games with incomplete information played by Bayesian players, I–III. Management Science, 14, 159–182, 320–334, 486–502.Google Scholar
- Hughes G. E., Cresswell M. J. (1968) An introduction to modal logic. Methuen, LondonGoogle Scholar