Robust Predictions under Finite Depth of Reasoning
29 Pages Posted: 29 Jun 2014 Last revised: 1 May 2019
Date Written: April 29, 2019
Abstract
This paper studies a robustness of solutions in finite depth of reasoning models. The level-k and cognitive hierarchy models conventionally assume that each player has a commonly known anchor behavior 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 p-dominant equilibrium is robust if players put sufficiently small probability (decreasing in 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
JEL Classification: C72, C92, D82
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