Adam Brandenburger, Alexander Danieli, and Amanda Friedenberg's "The Implications of Finite-Order Reasoning," forthcoming in Theoretical EconomicsDecember 18, 2020
The epistemic conditions of rationality and mth-order strong belief of rationality (RmSBR, Battigalli and Siniscalchi, 2002) formalize the idea that players engage in contextualized forward-induction reasoning. This paper characterizes the behavior consistent with RmSBR across all type structures. In particular, in a class of generic games, R(m −1)SBR is characterized by a new solution concept we call an m-best response sequence (m-BRS). Such sequences are an iterative version of extensive-form best response sets (Battigalli and Friedenberg, 2012). The strategies that survive m rounds of extensiveform rationalizability are consistent with an m-BRS, but there are m-BRS’s which are disjoint from the former set. As such, there is behavior that is consistent with R(m − 1)SBR but inconsistent with m rounds of extensive-form rationalizability. We use our characterization to draw implications for the interpretation of experimental data. Specifically, we show that the implications are non-trivial in the 3-repeated Prisoner’s Dilemma and Centipede games.
Adam Brandenburger is the J.P. Valles Professor of Business Economics and Strategy at NYU Stern.
Read the full paper here.