A new epistemic model
AbstractMeier (2012) gave a "mathematical logic foundation" of the purely measurable universal type space (Heifetz and Samet, 1998). The mathematical logic foundation, however, discloses an inconsistency in the type space literature: a finitary language is used for the belief hierarchies and an infinitary language is used for the beliefs. In this paper we propose an epistemic model to fix the inconsistency above. We show that in this new model the universal knowledgebelief space exists, is complete and encompasses all belief hierarchies. Moreover, by examples we demonstrate that in this model the players can agree to disagree Aumann (1976)'s result does not hold, and Aumann and Brandenburger (1995)'s conditions are not sufficient for Nash equilibrium. However, we show that if we substitute selfevidence (Osborne and Rubinstein, 1994) for common knowledge, then we get at that both Aumann (1976)'s and Aumann and Brandenburger (1995)'s results hold.
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Bibliographic InfoPaper provided by Corvinus University of Budapest in its series Corvinus Economics Working Papers (CEWP) with number 1530.
Date of creation: 18 Apr 2014
Date of revision:
Incomplete information game; Agreeing to disagree; Nash equilibrium; Epistemic game theory; Knowledge-belief space; Belief hierarchy; Common knowledge; Self-evidence; Nash equilibrium;
Find related papers by JEL classification:
- C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
- D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
- D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information
This paper has been announced in the following NEP Reports:
- NEP-ALL-2014-05-04 (All new papers)
- NEP-CTA-2014-05-04 (Contract Theory & Applications)
- NEP-GTH-2014-05-04 (Game Theory)
- NEP-HPE-2014-05-04 (History & Philosophy of Economics)
- NEP-MIC-2014-05-04 (Microeconomics)
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