Related papers: Constrained-Order Prophet Inequalities
Due to numerous applications in retail and (online) advertising the problem of assortment selection has been widely studied under many combinations of discrete choice models and feasibility constraints. In many situations, however, an…
We consider Bayesian online selection problem of a matching in bipartite graphs, i.e., online weighted matching problem with edge arrivals where online algorithm knows distributions of weights, that corresponds to the intersection of two…
Due to their numerous applications, in particular in Mechanism Design, Prophet Inequalities have experienced a surge of interest. They describe competitive ratios for basic stopping time problems where random variables get revealed…
Chances of a gambler are always lower than chances of a casino in the case of an ideal, mathematically perfect roulette, if the capital of the gambler is limited and the minimum and maximum allowed bets are limited by the casino. However, a…
A decision maker observes the evolving state of the world while constantly trying to predict the next state given the history of past states. The ability to benefit from such predictions depends not only on the ability to recognize patters…
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…
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…
Suppose a gambler starts with a fortune in (0,1) and wishes to attain a fortune of 1 by making a sequence of bets. Assume thay whenever the gambler stakes the amount s, the gambler's fortune increases by s with probability w and decreases…
We study the two-agent single-item bilateral trade. Ideally, the trade should happen whenever the buyer's value for the item exceeds the seller's cost. However, the classical result of Myerson and Satterthwaite showed that no mechanism can…
We introduce a "high probability" framework for repeated games with incomplete information. In our non-equilibrium setting, players aim to guarantee a certain payoff with high probability, rather than in expected value. We provide a high…
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…
In \emph{zero-sum two-player hidden stochastic games}, players observe partial information about the state. We address: $(i)$ the existence of the \emph{uniform value}, i.e., a limiting average payoff that both players can guarantee for…
In Bayesian online settings, every element has a value that is drawn from a known underlying distribution, which we refer to as the element's identity. The elements arrive sequentially. Upon the arrival of an element, its value is revealed,…
We study a random game in which two players in turn play a fixed number of moves. For each move, there are two possible choices. To each possible outcome of the game we assign a winner in an i.i.d. fashion with a fixed parameter p. In the…
We introduce a new measure for the performance of online algorithms in Bayesian settings, where the input is drawn from a known prior, but the realizations are revealed one-by-one in an online fashion. Our new measure is called…
We consider the matroid prophet inequality problem. This problem has been extensively studied in the case of adaptive mechanisms. In particular, there is a tight $2$-competitive mechanism for all matroids. However, it is not known what…
Let $X_n,...,X_1$ be i.i.d. random variables with distribution function $F$. A statistician, knowing $F$, observes the $X$ values sequentially and is given two chances to choose $X$'s using stopping rules. The statistician's goal is to stop…
This work studies external regret in sequential prediction games with both positive and negative payoffs. External regret measures the difference between the payoff obtained by the forecasting strategy and the payoff of the best action. In…
We add the assumption that players know their opponents' payoff functions and rationality to a model of non-equilibrium learning in signaling games. Agents are born into player roles and play against random opponents every period.…
In this paper, we investigate the optimal strategies in the Werewolf Game-a widely played strategic social deduction game involving two opposing factions-from a game-theoretic perspective. We consider two scenarios: the game without a…