Related papers: A Doubly Exponentially Crumbled Cake
Austin's moving knife procedure was originally introduced to find a consensus division of an interval/circular cake between two agents, each of whom believes that they receive exactly half of the cake. We generalise this in two ways: we…
We study the problem of fairly allocating a divisible resource, also known as cake cutting, with an additional requirement that the shares that different agents receive should be sufficiently separated from one another. This captures, for…
We consider a simple streaming game between two players Alice and Bob, which we call the mirror game. In this game, Alice and Bob take turns saying numbers belonging to the set $\{1, 2, \dots,2N\}$. A player loses if they repeat a number…
The convex grabbing game is a game where two players, Alice and Bob, alternate taking extremal points from the convex hull of a point set on the plane. Rational weights are given to the points. The goal of each player is to maximize the…
In this article we suggest a model of computation for the cake cutting problem. In this model the mediator can ask the same queries as in the Robertson-Webb model but he or she can only perform algebraic operations as in the Blum-Shub-Smale…
We study a guessing game where Alice holds a discrete random variable $X$, and Bob tries to sequentially guess its value. Before the game begins, Bob can obtain side-information about $X$ by asking an oracle, Carole, any binary question of…
This article deals with the cake cutting problem. In this setting, there exists two notions of fair division: proportional division (when there are n players, each player thinks to get at least 1/n of the cake) and envy-free division (each…
Given a cake in form of a triangle and a box that fits the mirror image of the cake, how to cut the cake into a minimal number of pieces so that it can be put into the box? The cake has an icing, so that we are not allowed to put it into…
In cake-cutting, strategy-proofness is a very costly requirement in terms of fairness: for n=2 it implies a dictatorial allocation, whereas for n > 2 it requires that one agent receives no cake. We show that a weaker version of this…
Cake cutting is a classic model for studying fair division of a heterogeneous, divisible resource among agents with individual preferences. Addressing cake division under a typical requirement that each agent must receive a connected piece…
Suppose Alice has a coin with heads probability $q$ and Bob has one with heads probability $p>q$. Now each of them will toss their coin $n$ times, and Alice will win iff she gets more heads than Bob does. Evidently the game favors Bob, but…
Given a finite set $S$ of points in $\mathbb{R}^d$, which we regard as the locations of voters on a $d$-dimensional political `spectrum', two candidates (Alice and Bob) select one point in $\mathbb{R}^d$ each, in an attempt to get as many…
We consider the problem of envy-free cake cutting, which is the distribution of a continuous heterogeneous resource among self interested players such that nobody prefers what somebody else receives to what they get. Existing work has…
In quantum weak oblivious transfer, Alice sends Bob two bits and Bob can learn one of the bits at his choice. It was found that the security of such a protocol is bounded by $2P_{Alice}^{\ast }+P_{Bob}^{\ast }\geq 2$, where $P_{Alice}^{\ast…
We study the query complexity of cake cutting and give lower and upper bounds for computing approximately envy-free, perfect, and equitable allocations with the minimum number of cuts. The lower bounds are tight for computing connected…
We consider Steinhaus cake dividing game.
The problem of fair division known as "cake cutting" has been the focus of multiple papers spanning several decades. The most prominent problem in this line of work has been to bound the query complexity of computing an envy-free outcome in…
We study the fair allocation of a cake, which serves as a metaphor for a divisible resource, under the requirement that each agent should receive a contiguous piece of the cake. While it is known that no finite envy-free algorithm exists in…
A fair coin is flipped $n$ times, and two finite sequences of heads and tails (words) $A$ and $B$ of the same length are given. Each time the word $A$ appears in the sequence of coin flips, Alice gets a point, and each time the word $B$…
We study the classic cake cutting problem from a mechanism design perspective, in particular focusing on deterministic mechanisms that are strategyproof and fair. We begin by looking at mechanisms that are non-wasteful and primarily show…