Characterizing permissibility, proper rationalizability, and iterated admissibility by incomplete information
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Characterizing permissibility, proper rationalizability, and iterated admissibility by incomplete information Shuige Liu1,2 Accepted: 11 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract We characterize three interrelated solution concepts in epistemic game theory: permissibility, proper rationalizability, and iterated admissibility. We define the lexicographic epistemic model in a framework with incomplete information. Based on it, we give two groups of conditions; one characterizes permissibility and proper rationalizability, the other characterizes permissibility in an alternative way and iterated admissibility. In each group, the conditions for the latter are stronger than those for the former, which corresponds to the fact that proper rationalizability and iterated admissibility are incomparable but compatible refinements of permissibility within the complete information framework. The essential difference between the two groups is whether a full belief of rationality is needed. Keywords Epistemic game theory · Incomplete information · Lexicographic belief · Permissibility · Proper rationalizability · Iterated admissibility
The author is grateful to the editors and the anonymous reviewer for their comments and advice. She owes a debt of gratitude to Andrés Perea for his thorough reading of the early versions of this paper and his numerous valuable comments and suggestions. She is grateful to Christian Bach, János Flesch, Dmitriy Kvasov, Zsombor Z. Méder, Abraham Neyman, Funaki Yukihiko for their valuable discussions and encouragements. She thanks all teachers and students in the 4th Epicenter Spring Course on Epistemic Game Theory in Maastricht University for their inspiring teaching and stimulating discussions. She gratefully acknowledge the support of Grant-in-Aids for Young Scientists (B) of JSPS No. 17K13707, Grants for Special Research Project No. 2017K-016, and No. 2020C-018 of Waseda University.
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Shuige Liu [email protected]
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Faculty of Political Science and Economics, Waseda University, 1-6-1 Nishi-Waseda, Shinjuku-ku, Tokyo 169-8050, Japan
2
EPICENTER, Maastricht University, 6200 MD Maastricht, The Netherlands
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S. Liu
1 Introduction Non-cooperative game theory studies an individual’s decision-making in an interactive situation. Since one’s payoff there is not entirely determined by her own choice, decision-making requires her to form a belief about every other participant’s choice, about every other participant’s belief about every other’s choice, and so on. Investigating properties of hierarchical belief structures and their behavioral consequences opened up a field called epistemic game theory. See Battigalli and Bonanno (1999), Perea (2012), and Dekel and Siniscalchi (2015) for surveys on this field. In epistemic game theory, various concepts have been developed to describe specific belief structures. One is lexicographic belief (Blume et al. 1991a, b). A lexicographic belief describes a player’s conjecture about the opponents’ behavior by a
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