Trembling Hand Perfection for Mixed Quantal Response/Nash Equilibria

Posted: 5 Aug 2008

Date Written: July, 31 2008


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.

Keywords: Quantal Response Equilibrium, Trembling Hand Perfection, Non-credible Threats, Entropy

JEL Classification: C70, C72

Suggested Citation

Wolpert, David, Trembling Hand Perfection for Mixed Quantal Response/Nash Equilibria (July, 31 2008). Available at SSRN:

David Wolpert (Contact Author)

Santa Fe Institute ( email )

1399 Hyde Park Road
Santa Fe, NM 897501
United States

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