# Prophet Secretary for Combinatorial Auctions and Matroids

@inproceedings{Ehsani2017ProphetSF, title={Prophet Secretary for Combinatorial Auctions and Matroids}, author={Soheil Ehsani and Mohammad Taghi Hajiaghayi and Thomas Kesselheim and Sahil Singla}, booktitle={ACM-SIAM Symposium on Discrete Algorithms}, year={2017} }

The secretary and the prophet inequality problems are central to the field of Stopping Theory. Recently, there has been a lot of work in generalizing these models to multiple items because of their applications in mechanism design. The most important of these generalizations are to matroids and to combinatorial auctions (extends bipartite matching). Kleinberg-Weinberg \cite{KW-STOC12} and Feldman et al. \cite{feldman2015combinatorial} show that for adversarial arrival order of random variables…

## 95 Citations

### Single-Sample Prophet Inequalities via Greedy-Ordered Selection

- MathematicsSODA
- 2022

This work develops an intuitive and versatile greedy-based technique that yields SSPIs directly rather than through the reduction to OOSs, and analyzes the power and limitations of different SSPI approaches by providing a partial converse to the reduction from S SPI to O OS given by Azar et al.

### Single-Sample Prophet Inequalities Revisited

- Mathematics, Computer ScienceArXiv
- 2021

A framework for analyzing policies against a greedy-like prophet solution is developed, and the first SSPI for general (non-bipartite) matching environments is obtained, as well as improved competitive ratios for transversal and truncated partition matroids.

### An O(log log m) Prophet Inequality for Subadditive Combinatorial Auctions

- Computer Science2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)
- 2020

A simple and incentive compatible mechanism based on posted prices that achieves an O(log log m) approximation to the optimal revenue for subadditive valuations under an item-independence assumption is constructed.

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

- EconomicsArXiv
- 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.

### Optimal Online Contention Resolution Schemes via Ex-Ante Prophet Inequalities

- MathematicsESA
- 2018

The first optimal $1/2$-OCRS for matroids is designed by reducing the problem to designing a matroid prophet inequality where it is compared to the stronger benchmark of an ex-ante relaxation.

### An Improved Lower Bound for Matroid Intersection Prophet Inequalities

- MathematicsArXiv
- 2022

We consider prophet inequalities subject to feasibility constraints that are the intersection of q matroids. The best-known algorithms achieve a Θ( q )-approximation, even when restricted to…

### On Submodular Prophet Inequalities and Correlation Gap

- Mathematics, Computer ScienceSAGT
- 2021

Improved constant factor combinatorial prophet inequalities for both monotone and non-monotone submodular functions over any constraint that admits an Online Contention Resolution Scheme are obtained and efficient polynomial-time algorithms are described that achieve these bounds.

### Improved Truthful Mechanisms for Combinatorial Auctions with Submodular Bidders

- Computer Science2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)
- 2019

This work presents a computationally-efficient truthful mechanism with approximation ratio that improves upon the state-of-the-art by an exponential factor and achieves an O((log logm)^3) -approximation in expectation, uses only O(n) demand queries, and has universal truthfulness guarantee.

### Prophet secretary through blind strategies

- Computer Science, MathematicsSODA
- 2019

A new type of multi-threshold strategy, called blind strategy, that sets a nonincreasing sequence of thresholds that depends only on the distribution of the maximum of the random variables, and the gambler stops the first time a sample surpasses the threshold of the stage is introduced.

### Query Efficient Prophet Inequality with Unknown I.I.D. Distributions

- Computer ScienceArXiv
- 2022

A new model is proposed in which the algorithm has access to an oracle that answers quantile queries about the distribution and the extent to which it can use a small number of queries to achieve good competitive ratios is studied.

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