Related papers: Prophet Inequalities: Separating Random Order from…
The prophet inequality is one of the cornerstone problems in optimal stopping theory and has become a crucial tool for designing sequential algorithms in Bayesian settings. In the i.i.d. $k$-selection prophet inequality problem, we…
We study a pricing problem where a seller has $k$ identical copies of a product, buyers arrive sequentially, and the seller prices the items aiming to maximize social welfare. When $k=1$, this is the so called "prophet inequality" problem…
The online ordered Ramsey game is played between two players, Builder and Painter, on an infinite sequence of vertices with ordered graphs $(G_1,G_2)$, which have linear orderings on their vertices. On each turn, Builder first selects an…
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…
In the Submodular Welfare Maximization (SWM) problem, the input consists of a set of $n$ items, each of which must be allocated to one of $m$ agents. Each agent $\ell$ has a valuation function $v_\ell$, where $v_\ell(S)$ denotes the welfare…
We study game-theoretically secure protocols for the classical ordinal assignment problem (aka matching with one-sided preference), in which each player has a total preference order on items. To achieve the fairness notion of equal…
We study the repeated optimal stopping problem, in which the same optimal stopping instance with an unknown distribution is solved repeatedly over $T$ rounds. We aim to simultaneously achieve strong per-round performance guarantees relative…
We study the problem of computing maximin share guarantees, a recently introduced fairness notion. Given a set of $n$ agents and a set of goods, the maximin share of a single agent is the best that she can guarantee to herself, if she would…
We consider the fundamental scenario where a single item is to be sold to one of two agents. Both agents draw their valuation for the item from the same probability distribution. However, only one of them submits a bid to the mechanism. The…
We revisit the problem of selecting an item from $n$ choices that appear before us in random sequential order so as to minimize the expected rank of the item selected. In particular, we examine the stopping rule where we reject the first…
We consider the classical online bipartite matching problem in the probe-commit model. In this problem, when an online vertex arrives, its edges must be probed to determine if they exist, based on known edge probabilities. A probing…
In the online (time-series) search problem, a player is presented with a sequence of prices which are revealed in an online manner. In the standard definition of the problem, for each revealed price, the player must decide irrevocably…
In the prophet secretary problem, $n$ values are drawn independently from known distributions, and presented in a uniformly random order. A decision-maker must accept or reject each value when it is presented, and may accept at most $k$…
We investigate brokerage between traders from an online learning perspective. At any round $t$, two traders arrive with their private valuations, and the broker proposes a trading price. Unlike other bilateral trade problems already studied…
A decision maker typically (i) incorporates training data to learn about the relative effectiveness of treatments, and (ii) chooses an implementation mechanism that implies an ``optimal'' predicted outcome distribution according to some…
We study a fair division problem with indivisible items, namely the computation of maximin share allocations. Given a set of $n$ players, the maximin share of a single player is the best she can guarantee to herself, if she would partition…
We consider a matching system with random arrivals of items of different types. The items wait in queues -- one per each item type -- until they are "matched." Each matching requires certain quantities of items of different types; after a…
In online combinatorial allocations/auctions, n bidders sequentially arrive, each with a combinatorial valuation (such as submodular/XOS) over subsets of m indivisible items. The aim is to immediately allocate a subset of the remaining…
Hill and Kertz studied the prophet inequality on iid distributions [The Annals of Probability 1982]. They proved a theoretical bound of $1-\frac{1}{e}$ on the approximation factor of their algorithm. They conjectured that the best…
Over the past two decades, significant strides have been made in stochastic problems such as revenue-optimal auction design and prophet inequalities, traditionally modeled with $n$ independent random variables to represent the values of $n$…