Hierarchies of beliefs for compact possibility models |
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| Institution: | 1. Université de Toulouse I, CNRS-GREMAQ, and IDEI, 21 Allée de Brienne, 31000 Toulouse, France;2. Department of Economics, London School of Economics and Political Science, Houghton Street, WC2A 2AE London, UK;3. Université Catholique de Louvain CORE, 34 Voie du Roman Pays, B-1348 Louvain-la-Neuve, Belgium;1. Department of Economics and Risk Management Institute, National University of Singapore, Singapore;2. Faculty of Economics, University of Tokyo, Japan;3. Department of Economics, National University of Singapore, Singapore;4. Department of Economics, University of California, Riverside, United States of America |
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| Abstract: | In this paper, we construct a universal type space for a class of possibility models by imposing topological restrictions on the players’ beliefs. Along the lines of Mertens and Zamir International Journal of Game Theory, 14 (1985) 1] or Brandenburger and Dekel Journal of Economic Theory 59 (1993) 189], we show that the space of all hierarchies of compact beliefs that satisfy common knowledge of coherency (types) is canonically homeomorphic to the space of compact beliefs over the state of nature and the types of the other players. The resulting type space is universal, in the sense that any compact and continuous possibility structure can be uniquely represented within it. We show how to extend our construction to conditional systems of compact beliefs. |
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