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Robust predictions under finite depth of reasoning

Kota Murayama ()
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Kota Murayama: Northwestern University

The Japanese Economic Review, 2020, vol. 71, issue 1, No 5, 59-84

Abstract: Abstract This paper studies a robustness of solutions in finite depth of reasoning models. The level-k and cognitive hierarchy models often assume that each player has a commonly known anchor behavior (so called a level-0 action) to obtain a sharp prediction. We provide a general framework to examine whether the obtained prediction is robust to small uncertainty about other players’ anchors. Our main result shows that any $$\mathbf p$$p-dominant equilibrium is robust if players put sufficiently small probability (decreasing in $$\mathbf p$$p) on other players’ having high reasoning levels. This result highlights a distinction between the two prominent models: a risk-dominated equilibrium is robust in the cognitive hierarchy model, but not in the level-k model.

Keywords: Robustness; Iterative reasoning; Level-k model; Cognitive hierarchy model; Higher-order belief; Bounded rationality (search for similar items in EconPapers)
JEL-codes: C72 D83 D91 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s42973-019-00005-y

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