@article{e3dc406445e1436592803ffc73b50c9b,
title = "The context of the game",
abstract = "We study games of incomplete information and argue that it is important to correctly specify the “context” within which hierarchies of beliefs lie. We consider a situation where the players understand more than the analyst: It is transparent to the players—but not to the analyst—that certain hierarchies of beliefs are precluded. In particular, the players{\textquoteright} type structure can be viewed as a strict subset of the analyst{\textquoteright}s type structure. How does this affect a Bayesian equilibrium analysis? One natural conjecture is that this doesn{\textquoteright}t change the analysis—i.e., every equilibrium of the players{\textquoteright} type structure can be associated with an equilibrium of the analyst{\textquoteright}s type structure. We show that this conjecture is wrong. Bayesian equilibrium may fail an Extension Property. This can occur even in the case where the game is finite and the analyst uses the so-called universal structure (to analyze the game)—and, even, if the associated Bayesian game has an equilibrium. We go on to explore specific situations in which the Extension Property is satisfied.",
keywords = "Bayesian games, Context, Hierarchies of beliefs, Robustness, Universal type structure",
author = "Amanda Friedenberg and Martin Meier",
note = "Funding Information: We are indebted to David Ahn, Pierpaolo Battigalli, Adam Brandenburger, John Nachbar, Marciano Siniscalchi, and Satoru Takahashi for many helpful conversations. We also thank Adib Bagh, Tilman B{\"o}rgers, Jeff Ely, Ziv Hellman, George Mailath, Stephen Morris, Antonio Penta, Konrad Podczeck, Kevin Reffett, Pablo Schenone and seminar participants at Arizona State University, Institut f{\"u}r H{\"o}here Studien in Vienna, Rice University, UC Berkeley, UCLA, UC San Diego, University of Pennsylvania, the Third World Congress of the Game Theory Society, the European Econometric Society Conference, and the SAET Conference for important input. Jie Zheng and Diana MacDonald provided excellent research assistance. Parts of this project were completed while Friedenberg was visiting the UC Berkeley Economics Department and while Meier was visiting the Center for Research in Economics and Strategy (CRES) at the Olin Business School. We thank these institutions for their hospitality and CRES for financial support. Friedenberg thanks the Olin Business School and the W.P. Carey School of Business for financial support. Meier was supported by the Spanish Ministerio de Educaci{\'o}n y Ciencia via a Ramon y Cajal Fellowship (IAE-CSIC) and Research Grant (SEJ 2006-02079). Publisher Copyright: {\textcopyright} 2015, Springer-Verlag Berlin Heidelberg.",
year = "2017",
month = feb,
day = "1",
doi = "10.1007/s00199-015-0938-z",
language = "English (US)",
volume = "63",
pages = "347--386",
journal = "Economic Theory",
issn = "0938-2259",
publisher = "Springer New York",
number = "2",
}