Related papers: Discussion of Twenty Questions Problem

We exhibit a class of classical or tropical posynomial systems which can be solved by reduction to linear or convex programming problems. This relies on a notion of colorful vectors with respect to a collection of Newton polytopes. This…

Encoding and decoding are the two key steps in information processing. In this work we study the encoding and decoding capabilities of operational theories in the context of information-storability game, where the task is to freely choose a…

In the past three decades, deductive games have become interesting from the algorithmic point of view. Deductive games are two players zero sum games of imperfect information. The first player, called "codemaker", chooses a secret code and…

People regularly make inferences about objects in the world that they cannot see by flexibly integrating information from multiple sources: auditory and visual cues, language, and our prior beliefs and knowledge about the scene. How are we…

In this paper we introduce polytopal stochastic games, an extension of two-player, zero-sum, turn-based stochastic games, in which we may have uncertainty over the transition probabilities. In these games the uncertainty over the…

We consider a card guessing game with complete feedback. An ordered deck of $n$ cards labeled $1$ up to $n$ is riffle-shuffled exactly one time. Given a value $p\in(0{,}1)\setminus\{\frac12\}$, the riffle shuffle is assumed to be…

Main papers on quantum games are written by physicists for physicists, and the inevitable exploitation of physics jargon may create difficulties for mathematicians or economists. Our goal here is to make clear the physical content and to…

Dynamic zero-sum games are an important class of problems with applications ranging from evasion-pursuit and heads-up poker to certain adversarial versions of control problems such as multi-armed bandit and multiclass queuing problems.…

We revisit the game in which each of several players chooses a pattern and then a coin is flipped repeatedly until one of these patterns is generated. In particular, we demonstrate how to compute the probability of any one player winning…

Cooperative games with nonempty core are called balanced, and the set of balanced games is a polyhedron. Given a game with empty core, we look for the closest balanced game, in the sense of the (weighted) Euclidean distance, i.e., the…

Consider the commonly known puzzle, given $k$ glass balls, find an optimal algorithm to determine the lowest floor of a building of $n$ floors from which a thrown glass ball will break. This puzzle was originally posed in its original form…

We consider a two-player search game on a tree $T$. One vertex (unknown to the players) is randomly selected as the target. The players alternately guess vertices. If a guess $v$ is not the target, then both players are informed in which…

Notes on the Spinpossible puzzle game. We give a mathematical description of the game, prove some elementary bounds on the length of optimal solutions, and consider variations of the game which place restrictions on the set of permitted…

We discuss variations of the zero-sum game where Bob selects two distinct numbers, and Alice learns one of them to make a guess which of the numbers is the larger.

This paper is on developing some computer-assisted proof methods involving non-classical inequalities for Shannon entropy. Two areas of the applications of information inequalities are studied: Secret sharing schemes and hat guessing games.…

How often can we expect a Major League Baseball team to score at least 20 runs in a single game? Considered a rare event in baseball, the outcome of scoring at least 20 runs in a game has occurred 224 times during regular season games since…

We present a complete solution to the so-called tennis ball problem, which is equivalent to counting lattice paths in the plane that use North and East steps and lie between certain boundaries. The solution takes the form of explicit…

We introduce an evolutionary game with feedback between perception and reality, which we call the reality game. It is a game of chance in which the probabilities for different objective outcomes (e.g., heads or tails in a coin toss) depend…

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…

Exactly 20 years ago at MFCS, Demaine posed the open problem whether the game of Dots & Boxes is PSPACE-complete. Dots & Boxes has been studied extensively, with for instance a chapter in Berlekamp et al. "Winning Ways for Your Mathematical…