Abstract
We argue that an approach that relies solely on the sequential structure of a game would be useful, and provide an alternative proof of the existence of sequential equilibrium.
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Notes
See paragraph 3 in page 864 in Kreps and Wilson (1982).
See the first paragraph of the concluding remarks in page 885 of Kreps and Wilson (1982).
A game may have multiple roots, in which case a probability distribution on R is specified and interpreted as the distribution of the “states of nature”.
\(B \times M\) is endowed with the relative topology, when viewed as a subset of a (finite-dimensional) Euclidean space, the latter endowed with the standard topology.
This is the behavior strategy profile, associated with the vector of probability distributions \(b^{\epsilon , \star }\), that gives a probability distribution at each of the information sets.
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Acknowledgments
We thank the Editor, Nicholas Yannelis, and an anonymous referee, whose comments significantly improved the paper. We acknowledge comments from participants at the Midwest Theory Conference, Northwestern University, May 2010 and the Gardner Conference, Indiana University, Bloomington, April 2011, and 13th SAET Conference on Current Trends in Economics, MINES Paris Tech, July 2013. We also acknowledge some very useful conversations with the late C. D. Aliprantis on this topic and would also like to thank Michael Baye, Will Geller, Pavlo Prokopovych, and Eric Rasmussen for some very useful questions and comments.
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Chakrabarti, S.K., Topolyan, I. An extensive form-based proof of the existence of sequential equilibrium. Econ Theory Bull 4, 355–365 (2016). https://doi.org/10.1007/s40505-016-0098-8
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DOI: https://doi.org/10.1007/s40505-016-0098-8
Keywords
- Sequential equilibrium
- Perfect Bayesian equilibrium
- Sequential games
- Imperfect information
- Backward induction
- Information sets
- Consistent assessment
- Beliefs