Adam Brandenburger, Alexander Danieli, and Amanda Friedenberg's "The Implications of Finite-Order Reasoning," forthcoming in Theoretical Economics
December 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.
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.