IHS Economics Series Working Paper 148
February 2004
Non-implementation of Rational Expectations as a Perfect Bayesian Equilibrium
Dionysius Glycopantis
Allan Muir
Nicholas C. Yannelis
Impressum Author(s):
Dionysius Glycopantis, Allan Muir, Nicholas C. Yannelis
Title:Non-implementation of Rational Expectations as a Perfect Bayesian Equilibrium
ISSN: Unspecified2004 Institut für Höhere Studien - Institute for Advanced Studies (IHS)
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148 Reihe Ökonomie Economics Series
Non-implementation of Rational Expectations as a Perfect Bayesian Equilibrium
Dionysius Glycopantis, Allan Muir, Nicholas C. Yannelis
148 Reihe Ökonomie Economics Series
Non-implementation of Rational Expectations as a Perfect Bayesian Equilibrium
Dionysius Glycopantis, Allan Muir, Nicholas C. Yannelis February 2004
Institut für Höhere Studien (IHS), Wien
Institute for Advanced Studies, Vienna
Contact:
Dionysius Glycopantis Department of Economics City University
Northampton Square
London EC1V 0HB, United Kingdom email: d.glycopantis@city.ac.uk Allan Muir
Department of Mathematics City University
Northampton Square
London EC1V 0HB, United Kingdom email: a.muir@city.ac.uk
Nicholas C. Yannelis Department of Economics
University of Illinois at Urbana-Champaign IL 61820, USA
email: nyanneli@uiuc.edu
Founded in 1963 by two prominent Austrians living in exile – the sociologist Paul F. Lazarsfeld and the economist Oskar Morgenstern – with the financial support from the Ford Foundation, the Austrian Federal Ministry of Education and the City of Vienna, the Institute for Advanced Studies (IHS) is the first institution for postgraduate education and research in economics and the social sciences in Austria.
The Economics Series presents research done at the Department of Economics and Finance and aims to share “work in progress” in a timely way before formal publication. As usual, authors bear full responsibility for the content of their contributions.
Das Institut für Höhere Studien (IHS) wurde im Jahr 1963 von zwei prominenten Exilösterreichern – dem Soziologen Paul F. Lazarsfeld und dem Ökonomen Oskar Morgenstern – mit Hilfe der Ford- Stiftung, des Österreichischen Bundesministeriums für Unterricht und der Stadt Wien gegründet und ist somit die erste nachuniversitäre Lehr- und Forschungsstätte für die Sozial- und Wirtschafts- wissenschaften in Österreich. Die Reihe Ökonomie bietet Einblick in die Forschungsarbeit der Abteilung für Ökonomie und Finanzwirtschaft und verfolgt das Ziel, abteilungsinterne Diskussionsbeiträge einer breiteren fachinternen Öffentlichkeit zugänglich zu machen. Die inhaltliche Verantwortung für die veröffentlichten Beiträge liegt bei den Autoren und Autorinnen.
Abstract
We show that a rational expectations equilibrium need not be incentive compatible, need not be implementable as a perfect Bayesian equilibrium and may not be fully Pareto optimal, unless the utility functions are state independent. A comparison of rational expectations equilibria with core concepts is also provided.
Keywords
Differential information economy, rational expectations equilibrium, coalitional Bayesian incentive compatibility, implementation, game trees, private core, weak fine core, interim weak fine core
JEL Classification
C71, C72, D5, D82
Comments
We wish to thank Dr A. Hadjiprocopis for his invaluable help with the implementation of Latex in a Unix environment.
Contents
1 Introduction 1
2 Differential information economy and REE 2 3 On the incentive compatibility of REE 4 4 Non-implementation of REE allocations as a PBE 7
4.1 Sequential decisions... 7 4.2 Simultaneous decisions ... 12 4.3 Normal form games interpretations ... 17
5 REE and weak fine cores 19
5.1 REE and IWFC ... 19 5.2 REE and WFC ... 22 5.3 A decomposable model; non-revealing REE and WFC... 25
6 REE versus the private core 31
6.1 The Kreps example... 31 6.2 REE and informational asymmetries ... 33
7 Concluding remarks 34
8 References 34
Appendix I: On Nash equilibria and PBEs 36
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