  Personalized pricing is a business strategy to charge different prices to
individual consumers based on their characteristics and behaviors. It has
become common practice in many industries nowadays due to the availability of a
growing amount of high granular consumer data. The discriminatory nature of
personalized pricing has triggered heated debates among policymakers and
academics on how to design regulation policies to balance market efficiency and
equity. In this paper, we propose two sound policy instruments, i.e., capping
the range of the personalized prices or their ratios. We investigate the
optimal pricing strategy of a profit-maximizing monopoly under both regulatory
constraints and the impact of imposing them on consumer surplus, producer
surplus, and social welfare. We theoretically prove that both proposed
constraints can help balance consumer surplus and producer surplus at the
expense of total surplus for common demand distributions, such as uniform,
logistic, and exponential distributions. Experiments on both simulation and
real-world datasets demonstrate the correctness of these theoretical results.
Our findings and insights shed light on regulatory policy design for the
increasingly monopolized business in the digital era.
