相关论文: The Struggles of Chessland

This paper solves a pursuit-evasion problem in which a prince must find a princess who is constrained to move on each day from one vertex of a finite graph to another. Unlike the related and much studied `Cops and Robbers Game', the prince…

We introduce the class of modified Schelling games in which there are different types of agents who occupy the nodes of a location graph; agents of the same type are friends, and agents of different types are enemies. Every agent is…

For any odd integer $n\geq3$ a board (of size $n$) is a square array of $n\times n$ positions with a simple rule of how to move between positions. The goal of the game we introduce is to find a path from the upper left corner of a board to…

"Three is a crowd" is an old proverb that applies as much to social interactions, as it does to frustrated configurations in statistical physics models. Accordingly, social relations within a triangle deserve special attention. With this…

Tumbleweed is a popular two-player perfect-information new territorial game played at the prestigious Mind Sport Olympiad. We define a generalized version of the game, where the board size is arbitrary and so is the possible number of…

A (Euclidean) greedy drawing of a graph is a drawing in which, for any two vertices $s,t$ ($s \neq t$), there is a neighbor vertex of $s$ that is closer to $t$ than to $s$ in the Euclidean distance. Greedy drawings are important in the…

Subject of this letter is the dynamics of a chain obtained performing the continuous limit of a system of links and beads. In particular, the probability distribution of the relative position between two points of the chain averaged over a…

Tessellations are valuable both conceptually and for analysis in the study of the large-scale structure of the universe. They provide a conceptual model for the 'cosmic web,' and are of great use to analyze cosmological data. Here we…

This paper describes a problem arising in sea exploration, where the aim is to schedule the expedition of a ship for collecting information about the resources on the seafloor. The aim is to collect data by probing on a set of carefully…

The aim of this paper is to present a didactical sequence that fosters the development of meanings related to fractions, conceived as numbers that can be placed on the number line. The sequence was carried out in various elementary school…

In this paper we introduce the novel framework of distributionally robust games. These are multi-player games where each player models the state of nature using a worst-case distribution, also called adversarial distribution. Thus each…

In his list of open problems, Martin Erickson described a certain game: "Two players alternately put queens on an n x n chess board so that each new queen is not in range of any queen already on the board (the color of the queens is…

We show that the $n$-round parallel repetition of the Magic Square game of Mermin and Peres is rigid, in the sense that for any entangled strategy succeeding with probability $1 -\varepsilon$, the players' shared state is…

Muller games are played by two players moving a token along a graph; the winner is determined by the set of vertices that occur infinitely often. The central algorithmic problem is to compute the winning regions for the players. Different…

This research considers Bayesian decision-analytic approaches toward the traversal of an uncertain graph. Namely, a traveler progresses over a graph in which rewards are gained upon a node's first visit and costs are incurred for every edge…

Starting from the well-known and elementary problem of inscribing the rectangle of the greatest area in an ellipse, we look at possible, gradually more and more complicated variants of this problem. Our goal is to demonstrate to an average…

Gerrymandering is a practice of manipulating district boundaries and locations in order to achieve a political advantage for a particular party. Lewenberg, Lev, and Rosenschein [AAMAS 2017] initiated the algorithmic study of a…

The Modeling Instruction program at Arizona State University has developed a representational tool, called a system schema, to help students make a first level of abstraction of an actual physical situation [1]. A system schema consists of…

Text-based adventure games provide a platform on which to explore reinforcement learning in the context of a combinatorial action space, such as natural language. We present a deep reinforcement learning architecture that represents the…

Coalition formation over graphs is a well studied class of games whose players are vertices and feasible coalitions must be connected subgraphs. In this setting, the existence and computation of equilibria, under various notions of…