We present a general framework for stochastic online maximization problems with
combinatorial feasibility constraints. The framework establishes prophet inequalities by …

The secretary and the prophet inequality problems are central to the field of Stop**
Theory. Recently, there has been a lot of work in generalizing these models to multiple items …

Over the past decade, an exciting connection has developed between the theory of posted-
price mechanisms and the prophet inequality, a result from the theory of optimal stop** …

We consider the classic principal-agent model of contract theory, in which a principal
designs an outcome-dependent compensation scheme to incentivize an agent to take a …

Optimal stop** theory is a powerful tool for analyzing scenarios such as online auctions in
which we generally require optimizing an objective function over the space of stop** rules …

We provide prophet inequality algorithms for online weighted matching in general (non-
bipartite) graphs, under two well-studied arrival models, namely edge arrival and vertex …

A central object in optimal stop** theory is the single-choice prophet inequality for
independent, identically distributed random variables: given a sequence of random …

We study generalizations of the``Prophet Inequality''and``Secretary Problem'', where the
algorithm is restricted to an arbitrary downward-closed set system. For 0, 1 values, we give O …

We survey the main results from [Dütting, Kesselheim, and Lucier 2020]: 1 a simple posted-
price mechanism for subadditive combinatorial auctions with m items that achieves an O (log …

Hill and Kertz studied the prophet inequality on iid distributions [The Annals of Probability
1982]. They proved a theoretical bound of 1-1/e on the approximation factor of their …