The Limits of Price Discrimination Under Privacy Constraints
CoRR(2024)
摘要
We consider a producer's problem of selling a product to a continuum of
privacy-conscious consumers, where the producer can implement third-degree
price discrimination, offering different prices to different market segments.
In the absence of privacy constraints, Bergemann, Brooks, and Morris [2015]
characterize the set of all possible consumer-producer utilities, showing that
it is a triangle. We consider a privacy mechanism that provides a degree of
protection by probabilistically masking each market segment, and we establish
that the resultant set of all consumer-producer utilities forms a convex
polygon, characterized explicitly as a linear mapping of a certain
high-dimensional convex polytope into ℝ^2. This characterization
enables us to investigate the impact of the privacy mechanism on both producer
and consumer utilities. In particular, we establish that the privacy constraint
always hurts the producer by reducing both the maximum and minimum utility
achievable. From the consumer's perspective, although the privacy mechanism
ensures an increase in the minimum utility compared to the non-private
scenario, interestingly, it may reduce the maximum utility. Finally, we
demonstrate that increasing the privacy level does not necessarily intensify
these effects. For instance, the maximum utility for the producer or the
minimum utility for the consumer may exhibit nonmonotonic behavior in response
to an increase of the privacy level.
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