Reinvestigating [formula omitted] behavior in ring games

Abstract

Kneeland (2015) separates different orders of belief in rationality with a new identifying assumption that a lower-order player does not respond to the changes in higher-order opponents’ payoffs. This paper points out two features in the games used by Kneeland (2015) that could potentially obfuscate the empirical validity of the identifying assumption, and reports the experimental results using two new sets of games with these features removed. The deviation rates from the theoretical prediction are higher in this experiment, and a larger fraction of subjects cannot be confidently assigned to a type. The deviations also lead to underestimation of reasoning levels in one set of the data, which could be partially corrected by a model of imprecise response and non-degenerate beliefs. The findings suggest that the empirical validity of the identification strategy in Kneeland (2015) is subject to the payoff structure and that the payoff numbers should be carefully chosen depending on the purpose of the research.