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Information and beliefs in a repeated normal-form game

Published online by Cambridge University Press:  14 March 2025

David N. Danz ,
Dietmar Fehr  and
Dorothea Kübler
David N. Danz*
Affiliation:
Wissenschaftszentrum Berlin, Berlin, Germany
Dietmar Fehr*
Affiliation:
Wissenschaftszentrum Berlin, Berlin, Germany
Dorothea Kübler*
Affiliation:
Wissenschaftszentrum Berlin, Berlin, Germany Technische Universität Berlin, Berlin, Germany
*
[email protected]
[email protected]
[email protected]
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Abstract

We study beliefs and actions in a repeated normal-form game. Using a level-k model of limited strategic reasoning and allowing for other-regarding preferences, we classify action and belief choices with regard to their strategic sophistication and study their development over time. In addition to a baseline treatment with common knowledge of the game structure, feedback about actions in the previous period and random matching, we run treatments (i) with fixed matching, (ii) without information about the other player’s payoffs, and (iii) without feedback about previous play. In all treatments with feedback, we observe more strategic play (increasing by 15 percent) and higher-level beliefs (increasing by 18 percent) over time. Without feedback, neither beliefs nor actions reach significantly higher levels of reasoning (with increases of 2 percentage points for actions and 6 percentage points for beliefs). The levels of reasoning reflected in actions and beliefs are highly consistent, but less so for types with lower levels of reasoning.

Keywords

BeliefsLevel-k modelLearning

JEL classification

D84: Expectations • Speculations C92: Laboratory, Group Behavior D83: Search • Learning • Information and Knowledge • Communication • Belief • Unawareness C72: Noncooperative Games
Type
Research Article
Information
Experimental Economics , Volume 15 , Issue 4 , December 2012 , pp. 622 - 640
Copyright
Copyright © 2012 Economic Science Association

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Footnotes

Electronic Supplementary Material The online version of this article (doi:https://doi.org/10.1007/s10683-012-9317-9) contains supplementary material, which is available to authorized users.

We are grateful for valuable comments of the editor, Jacob Goeree, and two anonymous referees whose critical comments helped us to improve the paper. We also wish to thank Britt Grosskopf, Kyle Hyndman, Rajiv Sarin, Roberto Weber, Georg Weizsäcker, Axel Werwatz and seminar participants at the Humboldt-Universität zu Berlin, EUI Florence, CRC 649 Workshop 2007, ESA World Meeting 2007, IMEBE 2008, VfS Annual Meeting 2008 and Econometric Society Meetings 2009 for valuable comments. We are indebted to Jana Stöver and Susanne Thiel for their help with running the experiments. Financial support from the Deutsche Forschungsgemeinschaft via CRC 649 Economic Risk is gratefully acknowledged.

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