A simple proof of the sufficiency of Dilmé’s power-sequence test for Kreps-Wilson consistency

Dilmé (Internat J Game Theory 53:673 2024) shows that an assessment is Kreps-Wilson (1982) consistent if and only if it is the limit of a particularly simple kind of sequence of strictly mixed strategies—which Dilmé calls a “power sequence”—and its associated sequence of Bayes-rule induced beliefs. We use Farkas’ lemma to provide a brief and simple proof of Dilmé’s result.