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The recent popularity of Wordle has revived interest in guessing games. We develop a general method for finding optimal strategies for guessing games while avoiding an exhaustive search. Our main contributions are several theorems that…
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…
We study a variation of the game of best choice (also known as the secretary problem or game of googol) under an additional assumption that the ranks of interview candidates are restricted using permutation pattern-avoidance. We describe…
Mafia (also called Werewolf) is a party game. The participants are divided into two competing groups: citizens and a mafia. The objective is to eliminate the opponent group. The game consists of two consecutive phases (day and night) and a…
The classical Prophet Inequality arises from a fundamental problem in optimal-stopping theory. In this problem, a gambler sees a finite sequence of independent, non-negative random variables. If he stops the sequence at any time, he…
The growing popularity of social deduction games has created an increasing need for intelligent frameworks where humans can collaborate with AI agents, particularly in post-pandemic contexts with heightened psychological and social…
Fantasy football leagues involve strategic player trades to optimize team performance. However, identifying optimal trades is complex due to varying player projections, positional needs, and league-specific scoring. Existing approaches…
In this work, we study the single-choice prophet inequality problem, where a gambler faces a sequence of~$n$ online i.i.d. random variables drawn from an unknown distribution. When a variable reveals its value, the gambler needs to decide…
Consider a gambler who observes a sequence of independent, non-negative random numbers and is allowed to stop the sequence at any time, claiming a reward equal to the most recent observation. The famous prophet inequality of Krengel,…
Prophet inequality concerns a basic optimal stopping problem and states that simple threshold stopping policies -- i.e., accepting the first reward larger than a certain threshold -- can achieve tight $\frac{1}{2}$-approximation to the…
This paper focuses on the emergence of communication to support cooperation in environments modeled as social deduction games (SDG), that are games where players communicate freely to deduce each others' hidden intentions. We first state…
In the classical prophet inequality settings, a gambler is given a sequence of $n$ random variables $X_1, \dots, X_n$, taken from known distributions, observes their values in this (potentially adversarial) order, and select one of them,…
We present solutions to a continuous patrolling game played on network. In this zero-sum game, an Attacker chooses a time and place to attack a network for a fixed amount of time. A Patroller patrols the network with the aim of intercepting…
We introduce a model of competing agents in a prophet setting, where rewards arrive online, and decisions are made immediately and irrevocably. The rewards are unknown from the outset, but they are drawn from a known probability…
Mafia can be described as an experiment in human psychology and mass hysteria, or as a game between informed minority and uninformed majority. Focus on a very restricted setting, Mossel et al. [to appear in Ann. Appl. Probab. Volume 18,…
This paper studies a two-player game with a quantitative surveillance requirement on an adversarial target moving in a discrete state space and a secondary objective to maximize short-term visibility of the environment. We impose the…
In this paper, we introduce an over-time variant of the well-known prophet inequality with i.i.d. random variables. Instead of stopping with one realized value at some point in the process, we decide for each step how long we select the…
The Traitors is a social deduction game in which an informed minority of Traitors face an uninformed majority of Faithful, and the recurring question facing the Faithful is how to vote. Random voting is known to be optimal for the…
We study the interaction between a network designer and an adversary over a dynamical network. The network consists of nodes performing continuous-time distributed averaging. The adversary strategically disconnects a set of links to prevent…
Two-player zero-sum repeated games are well understood. Computing the value of such a game is straightforward. Additionally, if the payoffs are dependent on a random state of the game known to one, both, or neither of the players, the…