Related papers: Static pricing for multi-unit prophet inequalities
A prophet inequality states, for some $\alpha\in[0,1]$, that the expected value achievable by a gambler who sequentially observes random variables $X_1,\dots,X_n$ and selects one of them is at least an $\alpha$ fraction of the maximum value…
We continue the study of the performance for fixed-price mechanisms in the bilateral trade problem, and improve approximation ratios of welfare-optimal mechanisms in several settings. Specifically, in the case where only the buyer…
In this paper, we survey literature on prophet inequalities for subadditive combinatorial auctions. We give an overview of the previous best $O(\log \log m)$ prophet inequality as well as the preceding $O(\log m)$ prophet inequality. Then,…
Prophet inequalities consist of many beautiful statements that establish tight performance ratios between online and offline allocation algorithms. Typically, tightness is established by constructing an algorithmic guarantee and a…
In the classic prophet inequality, samples from independent random variables arrive online. A gambler that knows the distributions must decide at each point in time whether to stop and pick the current sample or to continue and lose that…
Time or money? That is a question! In this paper, we consider this dilemma in the pricing regime, in which we try to find the optimal pricing scheme for identical items with heterogenous time-sensitive buyers. We characterize the…
In a classical online decision problem, a decision-maker who is trying to maximize her value inspects a sequence of arriving items to learn their values (drawn from known distributions), and decides when to stop the process by taking the…
We consider the classical mathematical economics problem of {\em Bayesian optimal mechanism design} where a principal aims to optimize expected revenue when allocating resources to self-interested agents with preferences drawn from a known…
We consider a monopolist seller with $n$ heterogeneous items, facing a single buyer. The buyer has a value for each item drawn independently according to (non-identical) distributions, and her value for a set of items is additive. The…
The prophet and secretary problems demonstrate online scenarios involving the optimal stopping theory. In a typical prophet or secretary problem, selection decisions are assumed to be immediate and irrevocable. However, many online settings…
We study revenue maximization through sequential posted-price (SPP) mechanisms in single-dimensional settings with $n$ buyers and independent but not necessarily identical value distributions. We construct the SPP mechanisms by considering…
We consider the problem of pricing a reusable resource service system. Potential customers arrive according to a Poisson process and purchase the service if their valuation exceeds the current price. If no units are available, customers…
Prophet inequalities are fundamental optimal stopping problems, where a decision-maker observes sequentially items with values sampled independently from known distributions, and must decide at each new observation to either stop and gain…
We introduce the \textit{prophet inequality with uncertain acceptance} model, in which a decision maker sequentially observes a sequence of independent options, each characterized by a value $x_i$ and an acceptance probability $p_i$, both…
Prophet inequalities bound the expected reward that can be obtained in a stopping problem by the optimal reward of its corresponding off-line version. We propose a systematic technique for deriving prophet inequalities for stopping problems…
We consider prophet inequalities in a setting where agents correspond to both elements in a matroid and vertices in a graph. A set of agents is feasible if they form both an independent set in the matroid and an independent set in the…
This paper considers a finite horizon optimal stopping problem for a sequence of independent and identically distributed random variables, where the objective is to design stopping rules that attempt to select the random variable with the…
Consider a trade market with one seller and multiple buyers. The seller aims to sell an indivisible item and maximize their revenue. This paper focuses on a simple and popular mechanism--the fixed-price mechanism. Unlike the standard…
In the adaptive ProbeMax problem, given a collection of mutually-independent random variables $X_1, \ldots, X_n$, our goal is to design an adaptive probing policy for sequentially sampling at most $k$ of these variables, with the objective…
We study a natural combinatorial pricing problem for sequentially arriving buyers with equal budgets. Each buyer is interested in exactly one pair of items and purchases this pair if and only if, upon arrival, both items are still available…