We present a model of price discrimination where a monopolist
faces a consumer who is privately informed about the
distribution of his valuation for an indivisible unit of
good but has yet to learn privately the actual valuation.
The monopolist sequentially screens the consumer with a
menu of contracts:
the consumer self-selects once by choosing a contract and
then self-selects again when he learns the actual valuation.
A deterministic sequential mechanism is a menu of refund
contracts, ...
We present a model of price discrimination where a monopolist
faces a consumer who is privately informed about the
distribution of his valuation for an indivisible unit of
good but has yet to learn privately the actual valuation.
The monopolist sequentially screens the consumer with a
menu of contracts:
the consumer self-selects once by choosing a contract and
then self-selects again when he learns the actual valuation.
A deterministic sequential mechanism is a menu of refund
contracts, each consisting of an advance payment and a refund
amount in case of no consumption, but sequential mechanisms
may involve randomization.
We characterize the optimal sequential mechanism when some
consumer types are more eager in the sense of first-order
stochastic dominance, and when some types face greater
valuation uncertainty in the sense of mean-preserving-spread.
We show that it can be optimal to subsidize consumer types
with smaller valuation uncertainty (through low refund, as in
airplane ticket pricing) in order to reduce the rent to those
with greater uncertainty. The size of distortion depends both
on the type distribution and on how informative the consumer's
initial private knowledge is about his valuation, but not
on how much he initially knows about the valuation per se.
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