Privacy Can Arise Endogenously in an Economic System with Learning Agents

Nivasini Ananthakrishnan, Tiffany Ding, Mariel Werner, Sai Praneeth Karimireddy, Michael I. Jordan

Abstract:

We study price-discrimination games between buyers and a seller where privacy arises endogenously—
that is, utility maximization yields equilibrium strategies where privacy occurs naturally. In this game,
buyers with a high valuation for a good have an incentive to keep their valuation private, lest the
seller charge them a higher price. This yields an equilibrium where some buyers will send a signal that
misrepresents their type with some probability; we refer to this as buyer-induced privacy. When the seller
is able to publicly commit to providing a certain privacy level, we find that their equilibrium response is to
commit to ignore buyers’ signals with some positive probability; we refer to this as seller-induced privacy.
We then turn our attention to a repeated interaction setting where the game parameters are unknown
and the seller cannot credibly commit to a level of seller-induced privacy. In this setting, players must
learn strategies based on information revealed in past rounds. We find that, even without commitment
ability, seller-induced privacy arises as a result of reputation building. We characterize the resulting
seller-induced privacy and seller’s utility under no-regret and no-policy-regret learning algorithms and
verify these results through simulations