Explaining Behavior in the "11-20" Game

We investigate whether subjects’ behavior in the Arad and Rubinstein (2012) "11-20" game could be well explained by the k-level process described by the authors. We replicated their game in our baseline experiment and provided two other variations that retained the same mixed-strategy equilibrium but resulted in different predicted behavior by the k-level process. Our experiments results suggest that k-level process leads to inconsistent predictions. In contrast to the standard k-level process as in Arad and Rubinstein, we allow players to best respond stochastically in our "SK" model and compared the model’s statistical fit against the Quantal Response Equilibrium and Cognitive Hierarchy Model. The SK model and Cognitive Model were able to outperform the QRE in a statistical sense and performed as well as each other. In addition, the Cognitive Hierarchy and to lesser extend the SK model, demonstrate consistent estimates. Our findings suggest that the behavioral assumptions of Arad and Rubinstein k-level process does not fully explain behavior in the "11-20" and better explanations could be obtained when one allows for stochastic best responds as in the SK and Cognitive Hierarchy Models.