Adam Brandenburger, Amanda Friedenberg, and Terri Kneeland's "Two Approaches to Iterated Reasoning in Games"

December 18, 2020

Level-k analysis and epistemic game theory are two different ways of investigating iterative reasoning in games. This paper explores the relationship between these two approaches. An important difference between them is that level-k analysis begins with an exogenous anchor on the players’ beliefs, while epistemic analysis begins with arbitrary epistemic types (hierarchies of beliefs). To close the gap, we develop the concept of a level-k epistemic type structure, that incorporates the exogenous anchor. We also define a complete level-k type structure where the exogenous anchor is the only restriction on hierarchies of beliefs. One might conjecture that, in a complete structure, the strategies that can be played under rationality and (m − 1)th-order belief of rationality are precisely those strategies played by a level-k player, for any k ≥ m. In fact, we prove that the strategies that can be played are the m-rationalizable strategies (i.e., the strategies that survive m rounds of elimination of strongly dominated strategies). This surprising result says that level-k analysis and epistemic game theory are two genuinely different approaches, with different implications for inferring the players’ reasoning about rationality from their observed behavior.

Adam Brandenburger is the J.P. Valles Professor of Business Economics and Strategy at NYU Stern.
Read the full paper here.