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

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  • Breitmoser, Yves
  • Tan, Jonathan H.W.
  • Zizzo, Daniel John

Abstract

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.

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  • Breitmoser, Yves & Tan, Jonathan H.W. & Zizzo, Daniel John, 2014. "On the beliefs off the path: Equilibrium refinement due to quantal response and level-k," Games and Economic Behavior, Elsevier, vol. 86(C), pages 102-125.
  • Handle: RePEc:eee:gamebe:v:86:y:2014:i:c:p:102-125
    DOI: 10.1016/j.geb.2014.03.002
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    More about this item

    Keywords

    Incomplete information; Equilibrium refinement; Logit equilibrium; Rationalizability; Quantal response; Level-k; Inequity aversion; Experiment;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
    • D62 - Microeconomics - - Welfare Economics - - - Externalities

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