Related papers: How to Cut a Cake Fairly: A Generalization to Grou…

In this paper, we consider a generalization of cooperative games to the case where a coalition can distribute the earned utility not only among its members but also to other players. In particular, we consider an example where coalitions…

Knockout tournaments constitute a popular format for organizing sports competitions. While prior results have shown that it is often possible to manipulate a knockout tournament by fixing the bracket, these results ignore the prevalent…

The MandM Game involves two players who begin with I1 and I2 MandM's. During each round, each player tosses a fair coin: if the coin lands heads, that player eats one MandM, and if it lands tails, the player does not eat. If, at the end of…

Shake slice generalizes the notion of a slice link, naturally extending the notion of shake slice knots to links. There is also a relative version, shake concordance, that generalizes link concordance. We show that if two links are shake…

In this note we study how to share a good between n players in a simple and equitable way. We give a short proof for the existence of such fair divisions.

We consider the classic cake cutting problem in the Robertson-Webb model, with the objective of proportional fairness. We show that any randomized algorithm must use $\Omega(n \log n)$ queries.

The game of war is one of the most popular international children's card games. In the beginning of the game, the pack is split into two parts, then on each move the players reveal their top cards. The player having the highest card…

We study the cutoff phenomenon for generalized riffle shuffles where, at each step, the deck of cards is cut into a random number of packs of multinomial sizes which are then riffled together.

In Fair AI literature, the practice of maliciously creating unfair models that nevertheless satisfy fairness constraints is known as "cherry-picking". A cherry-picking model is a model that makes mistakes on purpose, selecting bad…

We consider the classic cake-cutting problem of producing envy-free allocations, restricted to the case of four agents. The problem asks for a partition of the cake to four agents, so that every agent finds her piece at least as valuable as…

In cooperative games, the core is the most popular solution concept, and its properties are well known. In the classical setting of cooperative games, it is generally assumed that all coalitions can form, i.e., they are all feasible. In…

The problem of dividing resources fairly occurs in many practical situations and is therefore an important topic of study in economics. In this paper, we investigate envy-free divisions in the setting where there are multiple players in…

We prove that all cubulated groups are semistable at infinity. In doing so we prove two further results about cubulations of groups. The first of these states that any one-ended cubulated group has a cubulation for which all halfspaces are…

We study the problem of fairly allocating indivisible items and a desirable heterogeneous divisible good (i.e., cake) to agents with additive utilities. In our paper, each indivisible item can be a good that yields non-negative utilities to…

We present a canonical way to decompose finite graphs into highly connected local parts. The decomposition depends only on an integer parameter whose choice sets the intended degree of locality. The global structure of the graph, as…

Bob cuts a pizza into slices of not necessarily equal size and shares it with Alice by alternately taking turns. One slice is taken in each turn. The first turn is Alice's. She may choose any of the slices. In all other turns only those…

In this paper, we study the classic problem of fairly allocating indivisible items with the extra feature that the items lie on a line. Our goal is to find a fair allocation that is contiguous, meaning that the bundle of each agent forms a…

We propose an abstract approach to coalition formation that focuses on simple merge and split rules transforming partitions of a group of players. We identify conditions under which every iteration of these rules yields a unique partition.…

This paper deals with a problem in which two players share a previously sliced pizza and try to eat as much amount of pizza as they can. It takes time to eat each piece of pizza and both players eat pizza at the same rate. One is allowed to…

Ann likes oranges much more than apples; Bob likes apples much more than oranges. Tomorrow they will receive one fruit that will be an orange or an apple with equal probability. Giving one half to each agent is fair for each realization of…