Deep and Shallow Thinking in the Long Run

31 Pages Posted: 5 Sep 2020

See all articles by Heinrich H. Nax

Heinrich H. Nax

ETH Zürich; University of Zurich

Jonathan Newton

Kyoto University - Institute of Economic Research

Date Written: July 29, 2020


Humans differ in their strategic reasoning abilities and in beliefs about others’ strategic reasoning abilities. Models of cognitive hierarchies that express these differences have produced new insights regarding equilibrium analysis in economics. This paper investigates the effect of cognitive hierarchies on long run behavior. It is shown that, despite short run behavior being highly sensitive to variation in strategic reasoning abilities, this variation is not replicated in the long run. In particular, when a generalized risk dominant strategy profile exists, it emerges in the long run independently of the strategic reasoning abilities of the players. These abilties may be arbitrarily low or high, may be heterogeneous across players and may evolve over time.

Keywords: bounded rationality, level-k thinking, evolution

JEL Classification: C73, D81, D90

Suggested Citation

Nax, Heinrich H. and Newton, Jonathan, Deep and Shallow Thinking in the Long Run (July 29, 2020). Available at SSRN: or

Heinrich H. Nax

ETH Zürich ( email )

Rämistrasse 101
Zürich, 8092

University of Zurich ( email )

Rämistrasse 71
Zürich, CH-8006

Jonathan Newton (Contact Author)

Kyoto University - Institute of Economic Research ( email )

Kyoto 606-8501

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