Related papers: On Hats and other Covers
We investigate the packing and covering densities of linear and nonlinear binary codes, and establish a number of duality relationships between the packing and covering problems. Specifically, we prove that if almost all codes (in the class…
For a topological space $X$ and a point $x \in X$, consider the following game -- related to the property of $X$ being countably tight at $x$. In each inning $n\in\omega$, the first player chooses a set $A_n$ that clusters at $x$, and then…
Quantum entanglement is known to provide a strong advantage in many two-party distributed tasks. We investigate the question of how much entanglement is needed to reach optimal performance. For the first time we show that there exists a…
This paper investigates the strategic concealment of environment representations used by players in competitive games. We consider a defense scenario in which one player (the Defender) seeks to infer and exploit the representation used by…
There are many papers written on the Two Envelopes Problem that usually study some of its variations. In this paper we will study and compare the most significant variations of the problem. We will see the correct decisions for each player…
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…
Consider the following two-player game on the edges of $K_n$, the complete graph with $n$ vertices: Starting with an empty graph $G$ on the vertex set of $K_n$, in each round the first player chooses $b \in \mathbb{N}$ edges from $K_n$…
While many games were designed for steganography and robust watermarking, few focused on reversible watermarking. We present a two-encoder game related to the rate-distortion optimization of content-adaptive reversible watermarking. In the…
A two-player one-round binary game consists of two cooperative players who each replies by one bit to a message that he receives privately; they win the game if both questions and answers satisfy some predetermined property. A game is…
We study the complexity of solving two-player infinite duration games played on a fixed finite graph, where the control of a node is not predetermined but rather assigned randomly. In classic random-turn games, control of each node is…
In some scenarios ("anti-coordination games"), individuals are better off choosing different actions than their neighbors while in other scenarios ("coordination games"), it is beneficial for individuals to choose the same strategy as their…
We consider the graph coloring game, a game in which two players take turns properly coloring the vertices of a graph, with one player attempting to complete a proper coloring, and the other player attempting to prevent a proper coloring.…
Consider the following probability puzzle: A fair coin is flipped n times. For each HT in the resulting sequence, Bob gets a point, and for each HH Alice gets a point. Who is more likely to win? We provide a proof that Bob wins more often…
We study a combinatorial coloring game between two players, Spoiler and Algorithm, who alternate turns. First, Spoiler places a new token at a vertex in $G$, and Algorithm responds by assigning a color to the new token. Algorithm must…
An extensive literature in economics and social science addresses contests, in which players compete to outperform each other on some measurable criterion, often referred to as a player's score, or output. Players incur costs that are an…
Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we…
We consider 2-player games played on a finite state space for infinite rounds. The games are concurrent: in each round, the two players choose their moves simultaneously; the current state and the moves determine the successor. We consider…
We introduce a quantum cloning game in which $k$ separate collaborative parties receive a classical input, determining which of them has to share a maximally entangled state with an additional party (referee). We provide the optimal winning…
We consider the problem of a particular kind of quantum correlation that arises in some two-party games. In these games, one player is presented with a question they must answer, yielding an outcome of either 'win' or 'lose'. Molina and…
Mastermind game is a two players zero sum game of imperfect information. The first player, called codemaker, chooses a secret code and the second player, called codebreaker, tries to break the secret code by making as few guesses as…