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Tight bound for separate pricing revenue with two items

Determine the exact tight worst-case approximation factor c for a two-item monopolist such that optimally pricing each item separately always yields at least a c fraction of the optimal revenue achievable by any mechanism.

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Background

As an analogy to approximation-style results, the paper cites revenue-approximation guarantees for simple mechanisms in monopoly pricing with two items: a 50% guarantee for separate pricing, later improved to about 62%.

The authors note that the tight value of this guarantee remains unknown, explicitly flagging it as an open problem in the literature.

References

For example (for approximately optimizing a monopolist's revenue rather than an aggregate, social welfare function), prove that for a two-item monopolist, optimally pricing each item separately guarantees at least 50% of the optimal revenue, a guarantee that was later improved to ∼62% by , with a tight bound on this guarantee still remaining an open problem.

— Quantifying Inefficiency (2412.11984 - Gonczarowski et al., 16 Dec 2024) in Discussion (Section 6), footnote