  Strategic information is valuable either by remaining private (for instance
if it is sensitive) or, on the other hand, by being used publicly to increase
some utility. These two objectives are antagonistic and leaking this
information might be more rewarding than concealing it. Unlike classical
solutions that focus on the first point, we consider instead agents that
optimize a natural trade-off between both objectives. We formalize this as an
optimization problem where the objective mapping is regularized by the amount
of information revealed to the adversary (measured as a divergence between the
prior and posterior on the private knowledge). Quite surprisingly, when
combined with the entropic regularization, the Sinkhorn loss naturally emerges
in the optimization objective, making it efficiently solvable. We apply these
techniques to preserve some privacy in online repeated auctions.
