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Published August 1, 2017 | Submitted
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Heterogeneous Quantal Response Equilibrium and Cognitive Hierarchies


We explore an equilibrium model of games where players' choice behavior is given by logit response functions, but their payoff responsiveness is heterogeneous. We extend the definition of quantal response equilibrium to this setting, calling it heterogeneous quantal response equilibrium (HQRE), and prove existence under weak conditions. We generalize HQRE to allow for limited insight, in which players can only imagine others with low responsiveness. We identify a formal connection between this new equilibrium concept, called truncated quantal response equilibrium (TQRE), and the Cognitive Hierarchy (CH) model. We show that CH can be approximated arbitrarily closely by TQRE. We report a series of experiments comparing the performance of QRE, HQRE, TQRE and CH. A surprise is that the fi of the models are quite close across a variety of matrix and dominance-solvable asymmetric information betting games. The key link is that in the QRE approaches, strategies with higher expected payoffs are chosen more often than strategies with lower expected payoff. In CH this property is not built into the model, but generally holds true in the experimental data.

Additional Information

We are grateful to the National Science Foundation grants SES-0079301 and SES-0450712 for supporting this research.

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Submitted - sswp1260.pdf


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