Related papers: A Doubly Exponentially Crumbled Cake

Let $n, k$ be positive integers. The $(k+1)$-star avoidance game on $K_n$ is played as follows. Two players take it in turn to claim a (previously unclaimed) edge of the complete graph on $n$ vertices. The first player to claim all edges of…

Alice communicates with words drawn uniformly amongst $\{\ket{j}\}_{j=1..n}$, the canonical orthonormal basis. Sometimes however Alice interleaves quantum decoys $\{\frac{\ket{j}+i\ket{k}}{\sqrt{2}}\}$ between her messages. Such pairwise…

We examine the history of cake cutting mechanisms and discuss the efficiency of their allocations. In the case of piecewise uniform preferences, we define a game that in the presence of strategic agents has equilibria that are not dominated…

In this paper, we study algorithms for special cases of energy games, a class of turn-based games on graphs that show up in the quantitative analysis of reactive systems. In an energy game, the vertices of a weighted directed graph belong…

Given a graph $G$ and $k \in \mathbb{N}$, we introduce the following game played in $G$. Each round, Alice colours an uncoloured vertex of $G$ red, and then Bob colours one blue (if any remain). Once every vertex is coloured, Alice wins if…

The following problem is considered. Two players are each required to allocate a quota of~$n$ counters among~$k$ boxes labelled~$1,2,\ldots,k$. At times $t=1,2,3,\ldots$ a random box is identified; the probability of choosing box~$i$…

We study the classic problem of \emph{fairly} dividing a heterogeneous and divisible resource -- modeled as a line segment $[0,1]$ and typically called as a \emph{cake} -- among $n$ agents. This work considers an interesting variant of the…

An incidence of a graph $G$ is a pair $(v,e)$ where $v$ is a vertex of $G$ and $e$ an edge incident to $v$. Two incidences $(v,e)$ and $(w,f)$ are adjacent whenever $v = w$, or $e = f$, or $vw = e$ or $f$. The incidence coloring game [S.D.…

Unconditionally secure non-relativistic bit commitment is known to be impossible in both the classical and the quantum world. However, when committing to a string of n bits at once, how far can we stretch the quantum limits? In this letter,…

Subset take-away is a two-player game involving a fixed finite set A. Players alternate choosing a proper, non-empty subset of A, with the condition that one may not name a set containing a set that was named earlier. A player unable to…

In this work, we consider "decision" variants of a monogamy-of-entanglement game by Tomamichel, Fehr, Kaniewski, and Wehner [New Journal of Physics '13]. In its original "search" variant, Alice prepares a (possibly entangled) state on…

In a Maker-Breaker game on a graph $G$, Breaker and Maker alternately claim edges of $G$. Maker wins if, after all edges have been claimed, the graph induced by his edges has some desired property. We consider four Maker-Breaker games…

Let $P$ be a partially ordered set. We prove that if $n$ is sufficiently large, then there exists a packing $\mathcal{P}$ of copies of $P$ in the Boolean lattice $(2^{[n]},\subset)$ that covers almost every element of $2^{[n]}$:…

In contrast to the classical cake-cutting problem (how to fairly divide a desirable object), "chore division" is the problem of how to divide an undesirable object. We develop the first explicit algorithm for envy-free chore division among…

Imagine that Alice and Bob, unable to communicate, are both given a 16-bit string such that the strings are either equal, or they differ in exactly 8 positions. Both parties are then supposed to output a 4-bit string in such a way that…

Let $P$ be a set of $n$ points in general position in the plane. Let $R$ be a set of $n$ points disjoint from $P$ such that for every $x,y \in P$ the line through $x$ and $y$ contains a point in $R$ outside of the segment delimited by $x$…

The $[X,Y]$-edge colouring game is played with a set of $k$ colours on a graph $G$ with initially uncoloured edges by two players, Alice (A) and Bob (B). The players move alternately. Player $X\in\{A,B\}$ has the first move.…

We expand the theory of pebbling to graphs with weighted edges. In a weighted pebbling game, one player distributes a set amount of weight on the edges of a graph and his opponent chooses a target vertex and places a configuration of…

The angel-devil game is played on an infinite two-dimensional ``chessboard''. The squares of the board are all white at the beginning. The players called angel and devil take turns in their steps. When it is the devil's turn, he can turn a…

Here, we present a variant of the sliding coins game. Two coins are placed on distinct squares of a semi-infinite linear board with squares numbered $0, 1, 2, dots, $. Two players take turns and move a coin to a lower unoccupied square.…