8.6 Price Differentiation Under Incomplete Information

In Sections 8.3–8.5, we discuss various pricing schemes with different implementational complexity level under complete information, the revenues of which can be viewed as the benchmark of practical pricing designs. In this section, we further study the incomplete information scenario, where the service provider does not know the group association of each user. The challenge for pricing in this case is that the service provider needs to provide the right incentive so that a group i user does not want to pretend to be a user in a different group. It is clear that the CP scheme in Section 8.3 and the PP scheme in Section 8.5 cannot be directly applied here. The SP scheme in Section 8.4 is a special case, because it does not require the user-group association information in the first place and thus can be applied in the incomplete information scenario directly. On the other hand, we know that the SP scheme may suffer a considerable revenue loss compared with the CP scheme. Thus it is natural to ask whether it is possible to design an incentive-compatible differentiation scheme under incomplete information. In this section, we design a quantity-based price menu to incentivize users to make the right self-selection and to achieve the same maximum revenue of the CP scheme under complete information with proper technical conditions. We name it the incentive-compatible complete price (ICCP) differentiation scheme.

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