Trembling Hand Perfection for Mixed Quantal Response/Nash Equilibria

The Quantal Response Equilibrium (QRE) is a powerful alternative to full rationality equilibrium concepts. Under the QRE all joint strategies have non-zero probability, so non-credible threats cannot arise. However in mixed scenarios, where some players use quantal response and some use best response, non-credible threats are possible. To address this I first show how to reformulate the QRE as a best response equilibrium where expected utilities are replaced by more general objective functions. I then show that under this reformulation one definition of trembling hand perfection cannot be used to remove non-credible threats in mixed scenarios, while another definition can