Possibilistic beliefs and higher-level rationality
We consider rationality and rationalizability for normal-form games of incomplete information in which the players have possibilistic beliefs about their opponents. In this setting, we prove that the strategies compatible with the players being level-k rational coincide with the strategies surviving...
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| Format: | Working Paper |
| Language: | en_US |
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© Massachusetts Institute of Technology
2022
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| Online Access: | https://hdl.handle.net/1721.1/141763 |
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| author | Chen, Jing Micali, Silvio Pass, Rafael |
| author_facet | Chen, Jing Micali, Silvio Pass, Rafael |
| author_sort | Chen, Jing |
| collection | MIT |
| description | We consider rationality and rationalizability for normal-form games of incomplete information in which the players have possibilistic beliefs about their opponents. In this setting, we prove that the strategies compatible with the players being level-k rational coincide with the strategies surviving a natural k-step iterated elimination procedure. We view the latter strategies as the (level-k) rationalizable ones in our possibilistic setting.
Rationalizability was defined by Pearce [23] and Bernheim [12] for complete-information settings. Our iterated elimination procedure is similar to that proposed by Dekel, Fuden- berg, and Morris [14] in a Bayesian setting. For other iterated elimination procedures and corresponding notions of rationalizability in Bayesian settings, see Brandenburger and Dekel [9], Tan and Werlang [24], Battigalli and Siniscalchi [8], Ely and Peski [15], Weinstein and Yildiz [25], and Halpern and Pass [19]. |
| first_indexed | 2024-09-23T10:45:00Z |
| format | Working Paper |
| id | mit-1721.1/141763 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:45:00Z |
| publishDate | 2022 |
| publisher | © Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1417632022-04-08T03:28:43Z Possibilistic beliefs and higher-level rationality Chen, Jing Micali, Silvio Pass, Rafael We consider rationality and rationalizability for normal-form games of incomplete information in which the players have possibilistic beliefs about their opponents. In this setting, we prove that the strategies compatible with the players being level-k rational coincide with the strategies surviving a natural k-step iterated elimination procedure. We view the latter strategies as the (level-k) rationalizable ones in our possibilistic setting. Rationalizability was defined by Pearce [23] and Bernheim [12] for complete-information settings. Our iterated elimination procedure is similar to that proposed by Dekel, Fuden- berg, and Morris [14] in a Bayesian setting. For other iterated elimination procedures and corresponding notions of rationalizability in Bayesian settings, see Brandenburger and Dekel [9], Tan and Werlang [24], Battigalli and Siniscalchi [8], Ely and Peski [15], Weinstein and Yildiz [25], and Halpern and Pass [19]. This material is based on work supported by the U.S. Office of Naval Research, Grant No. N00014-09-1-0597. Any opinions, findings, conclusions or recommendations therein are those of the author(s) and do not necessarily reflect the views of the Office of Naval Research. 2022-04-07T18:06:11Z 2022-04-07T18:06:11Z 2014-06-09 Working Paper https://hdl.handle.net/1721.1/141763 Chen, J., Micali, S., & Pass, R. (2014). Possibilistic beliefs and higher-level rationality (ECIR Working Paper No. 2014-1). MIT Political Science Department. en_US ECIR Working Paper No. 2014-1 Attribution-NonCommercial-NoDerivs 3.0 United States http://creativecommons.org/licenses/by-nc-nd/3.0/us/ application/pdf © Massachusetts Institute of Technology |
| spellingShingle | Chen, Jing Micali, Silvio Pass, Rafael Possibilistic beliefs and higher-level rationality |
| title | Possibilistic beliefs and higher-level rationality |
| title_full | Possibilistic beliefs and higher-level rationality |
| title_fullStr | Possibilistic beliefs and higher-level rationality |
| title_full_unstemmed | Possibilistic beliefs and higher-level rationality |
| title_short | Possibilistic beliefs and higher-level rationality |
| title_sort | possibilistic beliefs and higher level rationality |
| url | https://hdl.handle.net/1721.1/141763 |
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