Sophisticated reasoning, learning, and equilibrium in repeated games with imperfect feedback

Pierpaolo Battigalli () and Davide Bordoli ()
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Pierpaolo Battigalli: Bocconi University and IGIER
Davide Bordoli: Yale University

Economic Theory, 2025, vol. 80, issue 2, No 2, 464 pages

Abstract: Abstract We analyze the infinite repetition with imperfect feedback of a simultaneous or sequential game, assuming that players are strategically sophisticated—but impatient—expected-utility maximizers. Sophisticated strategic reasoning in the repeated game is combined with belief updating to provide a foundation for a refinement of self-confirming equilibrium. In particular, we model strategic sophistication as rationality and common strong belief in rationality. Then, we combine belief updating and sophisticated reasoning to provide sufficient conditions for a kind of learning—that is, the ability, in the limit, to exactly forecast the sequence of future observations—thus showing that impatient agents end up playing a sequence of self-confirming equilibria in strongly rationalizable conjectures of the one-period game.

JEL-codes: C72 C73 D82 D83 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00199-024-01588-3

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