On the beliefs off the path: Equilibrium refinement due to quantal response and level-k

• Published in: Games and economic behavior Vol. 86; pp. 102 - 125
• Main Authors: Breitmoser, Yves, Tan, Jonathan H.W., Zizzo, Daniel John
• Format: Journal Article
• Language: English
• Published: Duluth Elsevier Inc 01.07.2014; Academic Press
• Subjects: Belief & doubt; Beliefs; Cognitive models; Convergence; Economic behaviour; Equilibrium; Equilibrium refinement; Experiment; Forecasts; Game theory; Incomplete information; Inequity aversion; Learning; Level-k; Logit equilibrium; Markov analysis; Markovian processes; Quantal response; Rationalizability; Studies; D62; Inequity aversion; Logit equilibrium; Level-k; Equilibrium refinement; Experiment; Rationalizability; C91; Incomplete information; C72; Quantal response
• ISSN: 0899-8256; 1090-2473
• DOI: 10.1016/j.geb.2014.03.002

The extensive form game we study has multiple perfect equilibria, but it has a unique limiting logit equilibrium (QRE) and a unique level-k prediction as k approaches infinity. The convergence paths of QRE and level-k are different, but they converge to the same limit point. We analyze whether subjects adapt beliefs when gaining experience, and if so whether they take the QRE or the level-k learning path. We estimate transitions between level-k and QRE belief rules using Markov-switching rule learning models. The analysis reveals that subjects take the level-k learning path and that they advance gradually, switching from level 1 to 2, from level 2 to equilibrium, and reverting to level 1 after observing opponents deviating from equilibrium. The steady state therefore contains a mixture of behavioral rules: levels 0, 1, 2, and equilibrium with weights of 2.9%, 16.6%, 37.9%, and 42.6%, respectively.