Optimal auctions vs. anonymous pricing

Alaei, Saeed; Hartline, Jason D.; Niazadeh, Rad; Pountourakis, Emmanouil; Yang, Yuan

doi:10.1016/j.geb.2018.08.003

Cited by 51 publications

(104 citation statements)

References 3 publications

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“…Hartline and Roughgarden (2009) show that second-price auction with an anonymous reserve is a 4-approximation to the optimal revenue. Alaei et al (2018) improve this result by showing that anonymous pricing is a tight e-approximation to the optimal ex ante relaxation. Jin et al (2019b) prove that the tight ratio between anonymous pricing and the optimal (discriminatory) sequential post pricing is 2.62, and Jin et al (2019a) show that the same tight ratio holds between anonymous pricing and the optimal mechanism.…”

Section: Introductionmentioning

confidence: 89%

“…Linear utility e-approximation bound. Alaei et al (2018) show that anonymous pricings give a tight e-approximation to ex ante relaxations for agents with regular valuation distributions and linear utility. For regular linear agents, the price-posting revenue curves are concave and equal to the ex ante revenue curves.…”

Section: Ex Ante Relaxationsmentioning

confidence: 99%

“…Moreover, for any non-negative concave function on domain [0, 1], there is a regular value distribution with this function as its revenue curve. Thus, the result of Alaei et al (2018) can be restated as follows.…”

Section: Ex Ante Relaxationsmentioning

confidence: 99%

“…On the other hand, some simple mechanisms (e.g., posting an anonymous price, second-price auction with anonymous reserve) are prevalent broadly. Alaei et al (2018) study the simplest mechanism for asymmetric agents with linear utility, namely, an anonymous pricing where an anonymous price is posted for selling a single good, and the first agent (in an arbitrary order) who values the good at higher price will buy the good. They upper bound the optimal revenue by considering the ex ante relaxation which sell at most one item in expectation over randomness of all agents' values, i.e., the ex post feasibility constraint of selling at most one item is relaxed to that of selling at most one item ex ante.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Auctions vs. Anonymous Pricing

Feng

Hartline

2019

Proceedings of the 2019 ACM Conference on Economics and Computation

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The revenue optimal mechanism for selling a single item to agents with independent but non-identically distributed values is complex for agents with linear utility (Myerson, 1981) and has no closed-form characterization for agents with non-linear utility (cf. Alaei et al., 2012). Nonetheless, for linear utility agents satisfying a natural regularity property, Alaei et al. (2018) showed that simply posting an anonymous price is an eapproximation. We give a parameterization of the regularity property that extends to agents with non-linear utility and show that the approximation bound of anonymous pricing for regular agents approximately extends to agents that satisfy this approximate regularity property. We apply this approximation framework to prove that anonymous pricing is a constant approximation to the revenue optimal single-item auction for agents with public-budget utility, private-budget utility, and (a special case of) riskaverse utility.

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Section: Introductionmentioning

confidence: 89%

Section: Ex Ante Relaxationsmentioning

confidence: 99%

Section: Ex Ante Relaxationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimal Auctions vs. Anonymous Pricing

Feng

Hartline

2019

Proceedings of the 2019 ACM Conference on Economics and Computation

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“…The main technique is to find a worst-case scenario instance. Because the ratio is more complex than in Alaei, Hartline, Niazadeh, Pountourakis, and Yuan (2018), the worst-case scenario instance is no longer triangular. The present paper differs from the aforementioned works in that we consider the problem faced by a monopolist selling to a single buyer whose valuation can come from one of many segments.…”

Section: Related Literaturementioning

confidence: 99%

Third-degree Price Discrimination Versus Uniform Pricing

Bergemann¹,

Castro

Weintraub

2019

SSRN Journal

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We compare the revenue of the optimal third-degree price discrimination policy against a uniform pricing policy. A uniform pricing policy offers the same price to all segments of the market. Our main result establishes that for a broad class of third-degree price discrimination problems with concave revenue functions and common support, a uniform price is guaranteed to achieve one half of the optimal monopoly profits. This revenue bound obtains for any arbitrary number of segments and prices that the seller would use in case he would engage in third-degree price discrimination. We further establish that these conditions are tight, and that a weakening of common support or concavity leads to arbitrarily poor revenue comparisons.

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Optimal Revenue Guarantees for Pricing in Large Markets

Correa

Pizarro

Verdugo

2021

Algorithmic Game Theory

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Posted price mechanisms (PPM) constitute one of the predominant practices to price goods in online marketplaces and their revenue guarantees have been a central object of study in the last decade. We consider a basic setting where the buyers' valuations are independent and identically distributed and there is a single unit on sale. It is well-known that this setting is equivalent to the so-called i.i.d. prophet inequality, for which optimal guarantees are known and evaluate to 0.745 in general (equivalent to a PPM with dynamic prices) and 1 − 1/e ≈ 0.632 in the fixed threshold case (equivalent to a fixed price PPM). In this paper we consider an additional assumption, namely, that the underlying market is very large. This is modeled by first fixing a valuation distribution F and then making the number of buyers grow large, rather than considering the worst distribution for each possible market size. In this setting Kennedy and Kertz [Ann. Probab. 1991] breaks the 0.745 fraction achievable in general with a dynamic threshold policy. We prove that this large market benefit continue to hold when using fixed price PPMs, and show that the guarantee of 0.632 actually improves to 0.712. We then move to study the case of selling k identical units and we prove that the revenue gap of the fixed price PPM approaches 1−1/ √ 2kπ. As this bound is achievable without the large market assumption, we obtain the somewhat surprising result that the large market advantage vanishes as k grows.

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Optimal auctions vs. anonymous pricing

Cited by 51 publications

References 3 publications

Optimal Auctions vs. Anonymous Pricing

Optimal Auctions vs. Anonymous Pricing

Third-degree Price Discrimination Versus Uniform Pricing

Optimal Revenue Guarantees for Pricing in Large Markets

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