# Tight Revenue Gaps among Simple Mechanisms

@inproceedings{Jin2019TightRG, title={Tight Revenue Gaps among Simple Mechanisms}, author={Yaonan Jin and P. Lu and Z. Tang and Tao Xiao}, booktitle={SODA}, year={2019} }

We consider a fundamental problem in microeconomics: selling a single item to a number of potential buyers, whose values are drawn from known independent and regular (not necessarily identical) distributions. There are four widely-used and widely-studied mechanisms in the literature: {\sf Myerson Auction}~({\sf OPT}), {\sf Sequential Posted-Pricing}~({\sf SPM}), {\sf Second-Price Auction with Anonymous Reserve}~({\sf AR}), and {\sf Anonymous Pricing}~({\sf AP}).
{\sf OPT} is revenue-optimalâ€¦Â Expand

#### 19 Citations

Tight revenue gaps among simple and optimal mechanisms

- Economics, Computer Science
- SECO
- 2020

Some recent developments on establishing tight revenue gaps in Myerson Auction, Sequential Posted Pricing, Second-Price Auction with Anonymous Reserve, and Anonymous Pricing are surveyed. Expand

Tight Revenue Gaps among Multi-Unit Mechanisms

- Computer Science
- EC
- 2021

This paper considers Bayesian revenue maximization in the k-unit setting, where a monopolist seller has k copies of an indivisible item and faces n unit-demand buyers (whose value distributions canâ€¦ Expand

Optimal Pricing For MHR Distributions

- Mathematics, Computer Science
- WINE
- 2018

It is shown that for the natural class of Monotone Hazard Rate (MHR) distributions, offering the same, take-it-or-leave-it price to all bidders can achieve an (asymptotically) optimal revenue. Expand

Tight approximation ratio of anonymous pricing

- Mathematics, Computer Science
- STOC
- 2019

In the single-item setting: the approximation ratio of Second-Price Auction with Anonymous Reserve is improved to 2.62, which breaks the best known upper bound of e â‰ˆ 2.72. Expand

Optimal Pricing For MHR and $\lambda$-Regular Distributions

- Mathematics, Computer Science
- 2018

The authors' anonymous pricing rule now results in an asymptotic approximation ratio that ranges smoothly, with respect to $\lambda, from $1$ (MHR distributions) to $e/(e-1)$ (regular distributions), and explicitly gives a class of continuous distributions that provide matching lower bounds, for every $\lambda$. Expand

Simple posted pricing mechanisms for selling a divisible item

- Mathematics, Computer Science
- ArXiv
- 2020

It is shown that the best linear pricing yields an expected revenue that is at most $O(\kappa^2)$ times smaller than the optimal one, where $\kappa$ is a bound on the curvature of the valuation functions. Expand

Algorithmic Pricing for the Partial Assignment

- Mathematics, Computer Science
- COCOA
- 2019

This paper considers the buyer can be partially satisfied and shows that in this new model, achieving the maximum social welfare is NP-hard and an optimal assignment oracle can be used to achieve themaximum social welfare. Expand

Separation between Second Price Auctions with Personalized Reserves and the Revenue Optimal Auction

- Computer Science, Mathematics
- Oper. Res. Lett.
- 2020

This paper establishes the first separation results for ESP: it is shown that even in the case of distributions drawn i.i.d., but not necessarily satisfying the regularity condition, the ESP cannot achieve more than a $0.778$ fraction of MyeRev in general. Expand

On the Complexity of Sequential Posted Pricing

- Computer Science
- AAMAS
- 2020

It is shown that finding an optimal sequential posted pricing is NP-complete even when the value distributions are of support size three, which is the first result that fully characterizes the computational complexity of sequential posted Pricing family. Expand

G T ] 2 N ov 2 01 8 Tight Approximation Ratio of Anonymous Pricing

- 2018

We consider two canonical Bayesian mechanism design settings. In the single-item setting, we prove tight approximation ratio for anonymous pricing: compared with Myerson Auction, it extracts at leastâ€¦ Expand

#### References

SHOWING 1-10 OF 65 REFERENCES

On the Approximation Ratio of k-Lookahead Auction

- Mathematics, Computer Science
- WINE
- 2011

The k-lookahead auction is revisited and a theoretical implication is that the gap between the revenues of the optimal deterministically truthful and truthful-in-expectation mechanisms is at most a factor of 1+ e, which improves the previous best factor of 5-3 in [2]. Expand

Improved Approximations for Free-Order Prophets and Second-Price Auctions

- Computer Science, Economics
- ArXiv
- 2018

It is shown that for every value of the number of buyers $n$, the eager second price (ESP) auction and sequential posted price mechanisms respectively earn at least $0.6620 and 0.6543 fractions of the optimal revenue, which implies an improved bound for free-order prophet inequalities. Expand

Tight approximation ratio of anonymous pricing

- Mathematics, Computer Science
- STOC
- 2019

In the single-item setting: the approximation ratio of Second-Price Auction with Anonymous Reserve is improved to 2.62, which breaks the best known upper bound of e â‰ˆ 2.72. Expand

Simple Mechanisms for a Subadditive Buyer and Applications to Revenue Monotonicity

- Computer Science, Mathematics
- EC
- 2015

The main result is to derive a bound on how bad this degradation can be (and dub such a bound a proof of approximate revenue monotonicity); it is shown that better bounds on approximatemonotonicity imply a better analysis of the authors' simple mechanisms. Expand

On revenue maximization for selling multiple independently distributed items

- Economics, Medicine
- Proceedings of the National Academy of Sciences
- 2013

It is proved that selling separately guarantees at least fraction of the optimal revenue, whereas for identically distributed items, bundling yields at least a constant fraction ofThe optimal revenue. Expand

Revenue Gaps for Discriminatory and Anonymous Sequential Posted Pricing

- Computer Science, Mathematics
- ArXiv
- 2016

For a class of distributions that includes the uniform and the exponential distribution, the maximization of revenue is shown to be equivalent to the maximizations of welfare with an additional bidder, in the sense that both use the same discriminatory prices. Expand

Randomization Beats Second Price as a Prior-Independent Auction

- Computer Science, Economics
- EC
- 2015

A randomized mechanism strictly outperforms all deterministic mechanisms in terms of worst case guarantee and resolves a question in the design of revenue optimal mechanisms that have access to a single sample from an unknown distribution. Expand

Simple versus optimal mechanisms

- Economics, Computer Science
- EC '09
- 2009

The monopolist's theory of optimal single-item auctions for agents with independent private values can be summarized by two statements. The first is from Myerson [8]: the optimal auction is Vickreyâ€¦ Expand

Simple mechanisms for subadditive buyers via duality

- Computer Science
- SECO
- 2019

It is proved that a simple, deterministic and Dominant Strategy Incentive Compatible (DSIC) mechanism, namely, the sequential posted price with entry fee mechanism, achieves a constant fraction of the optimal revenue among all randomized, Bayesian Incentives Compatible mechanisms, when buyers' valuations are XOS over independent items. Expand

Combinatorial Auctions via Posted Prices

- Economics, Computer Science
- SODA
- 2015

It is shown that when agent preferences are fractionally subadditive (which includes all submodular functions), there always exist prices that, in expectation, obtain at least half of the optimal welfare. Expand