Hiding the classifier and letting agents best respond to a discounted average of past classifiers multiplies the deterministic worst-case mistake bound by about 1/(1-gamma) or by the maximum in-degree of the manipulation graph.
This induces a false positive mistake
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Should Decision-Makers Reveal Classifiers in Online Strategic Classification?
Hiding the classifier and letting agents best respond to a discounted average of past classifiers multiplies the deterministic worst-case mistake bound by about 1/(1-gamma) or by the maximum in-degree of the manipulation graph.