Common belief in future and restricted past rationality

Rubén Becerril-Borja () and Andrés Perea ()
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Rubén Becerril-Borja: Universidad Autónoma Metropolitana-Iztapalapa
Andrés Perea: Maastricht University

International Journal of Game Theory, 2020, vol. 49, issue 3, No 4, 747 pages

Abstract: Abstract We introduce the idea that a player believes at every stage of a dynamic game that his opponents will choose rationally in the future and have chosen rationally in a restricted way in the past. This is summarized by the concept of common belief in future and restricted past rationality, which is defined epistemically. Moreover, it is shown that every properly rationalizable strategy of the normal form of a dynamic game can be chosen in the dynamic game under common belief in future and restricted past rationality. We also present an algorithm that uses strict dominance, and show that it selects exactly those strategies that can be chosen under common belief in future and restricted past rationality.

Keywords: Epistemic game theory; Dynamic games; Proper rationalizability; Belief in future rationality; Belief in restricted past rationality (search for similar items in EconPapers)
JEL-codes: C72 C73 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00182-020-00716-2

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