When the Punishment Must Fit the Crime: Remarks on the Failure of Simple Penal
Codes in Extensive-Form Games

by George J. Mailath, Volker Nocke and Lucy White

October 14, 2004, revised March 28, 2006

In repeated normal-form games, simple penal codes (Abreu 1986, 1988) permit an elegant characterization of the set of subgame-perfect outcomes. We show that the logic of simple penal codes fails in repeated extensive-form games. We provide two examples illustrating that a subgame-perfect outcome may be supported \emph{only} by a profile with the property that the continuation play after a deviation is tailored not only to the identity of the deviator, but also to the nature of the deviation. Keywords: Simple Penal Code, Subgame Perfect Equilibrium, Repeated Extensive Game, Optimal Punishment. JEL Classifiication Codes: C70, C72, C73.

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Updated July 26, 2006 .