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Cognitive Hierarchies in Extensive Form Games

Lin, Po-Hsuan and Palfrey, Thomas R. (2022) Cognitive Hierarchies in Extensive Form Games. Social Science Working Paper, 1460. California Institute of Technology , Pasadena, CA. (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20220207-233838741

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Abstract

The cognitive hierarchy (CH) approach posits that players in a game are heterogeneous with respect to levels of strategic sophistication. A level-k player believes all other players in the game have lower levels of sophistication distributed from 0 to k-1, and these beliefs correspond to the truncated distribution of a "true" distribution of levels. We extend the CH framework to extensive form games, where these initial beliefs over lower levels are updated as the history of play in the game unfolds, providing information to players about other players' levels of sophistication. For a class of centipede games with a linearly increasing pie, we fully characterize the dynamic CH solution and show that it leads to the game terminating earlier than in the static CH solution for the centipede game in reduced normal form.


Item Type:Report or Paper (Working Paper)
ORCID:
AuthorORCID
Lin, Po-Hsuan0000-0003-3437-1734
Palfrey, Thomas R.0000-0003-0769-8109
Additional Information:We thank Colin F. Camerer, Jean-Laurent Rosenthal, Joseph Tao-yi Wang and audiences at the 2021 ESA North American Conference and the 2022 SAET Conference for their valuable comments.
Group:Social Science Working Papers
Subject Keywords:Cognitive Hierarchy, Extensive Form Games, Learning, Centipede Game
Series Name:Social Science Working Paper
Issue or Number:1460
Classification Code:JEL Classification Numbers: C72
Record Number:CaltechAUTHORS:20220207-233838741
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20220207-233838741
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:113326
Collection:CaltechAUTHORS
Deposited By: Mary Martin
Deposited On:08 Feb 2022 17:33
Last Modified:15 Aug 2022 16:26

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