Related papers: Equitable Candy Sharing
The garbage disposal game involves a finite set of individuals, each of whom updates their garbage by either receiving from or dumping onto others. We examine the case where only social neighbors, whose garbage levels differ by a given…
We study the mechanism design problem of allocating a set of indivisible items without monetary transfers. Despite the vast literature on this very standard model, it still remains unclear how do truthful mechanisms look like. We focus on…
In the work the fair division problem for two participants in presence of both divisible and indivisible items is considered. The set of all divisions is formally described; it is demonstrated that fair (in terms of Brams and Taylor)…
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…
Consider a 4-player version of Matching Pennies where a team of three players competes against the Devil. Each player simultaneously says "Heads" or "Tails". The team wins if all four choices match; otherwise the Devil wins. If all team…
Necessary and sufficient observable conditions for the nonnegativity of all partial transpositions of multi-mode quantum states are derived. The result is a hierarchy of inequalities for minors in terms of moments of the given state.…
We discuss counterintuitive aspects of probabilities for systems of identical particles obeying quantum statistics. Quantum coins and children (two level systems) and quantum dice (many level systems) are used as examples. It is emphasized…
We indulge in what mathematicians call frivolous activities. In Arithmetic Billiards, a ball is bouncing around in a rectangle. In Parity Checkers we place checkers on a checkerboard under certain parity constraints. Both activities turn…
We define and investigate, via numerical analysis, a one dimensional toy-model of a cloud chamber. An energetic quantum particle, whose initial state is a superposition of two identical wave packets with opposite average momentum, interacts…
Self-stabilizing distributed control is often modeled by token abstractions. A system with a single token may implement mutual exclusion; a system with multiple tokens may ensure that immediate neighbors do not simultaneously enjoy a…
Given a set of $p$ players we consider problems concerning envy-free allocation of collections of $k$ pieces from a given set of goods or chores. We show that if $p\le n$ and each player can choose $k$ pieces out of $n$ pieces of a cake,…
Mechanism design is addressed in the context of fair allocations of indivisible goods with monetary compensation. Motivated by a real-world social choice problem, mechanisms with verification are considered in a setting where (i) agents'…
Group fairness is achieved by equalising prediction distributions between protected sub-populations; individual fairness requires treating similar individuals alike. These two objectives, however, are incompatible when a scoring model is…
We consider the model of the one-dimensional cookie random walk when the initial cookie distribution is spatially uniform and the number of cookies per site is finite. We give a criterion to decide whether the limiting speed of the walk is…
We study quantum walk on a ladder with combination of conventional and split-step protocols. The two components of the walk resulting from periodic boundary conditions can be made to have three kinds of probability distributions. Two of…
A social choice correspondence satisfies balancedness if, for every pair of alternatives, x and y, and every pair of individuals, i and j, whenever a profile has x adjacent to but just above y for individual i while individual j has y…
We consider transferable-utility profit-sharing games that arise from settings in which agents need to jointly choose one of several alternatives, and may use transfers to redistribute the welfare generated by the chosen alternative. One…
General equilibrium equations in economics play the same role with many-body Newtonian equations in physics. Accordingly, each solution of the general equilibrium equations can be regarded as a possible microstate of the economic system.…
In this paper, a new continuous scoring system for soccer is proposed, based on the proportion of time that a team is winning, losing or tied. Several simulations are made applying this technique to complete seasons of different leagues. As…
This work addresses the problem of assigning periodic tasks to workers in a balanced way, i.e., so that each worker performs every task with the same frequency over the long term. The input consists of a list of tasks to be repeated weekly…