Related papers: The one-round Voronoi game replayed

In the planar one-round discrete Voronoi game, two players $\mathcal{P}$ and $\mathcal{Q}$ compete over a set $V$ of $n$ voters represented by points in $\mathbb{R}^2$. First, $\mathcal{P}$ places a set $P$ of $k$ points, then $\mathcal{Q}$…

Let $V$ be a multiset of $n$ points in $\mathbb{R}^d$, which we call voters, and let $k\geq 1$ and $\ell\geq 1$ be two given constants. We consider the following game, where two players $\mathcal{P}$ and $\mathcal{Q}$ compete over the…

We study the discrete Voronoi game, where two players alternately claim vertices of a graph for t rounds. In the end, the remaining vertices are divided such that each player receives the vertices that are closer to his or her claimed…

We study competitive location problems in a continuous setting, in which facilities have to be placed in a rectangular domain $R$ of normalized dimensions of $1$ and $\rho\geq 1$, and distances are measured according to the Manhattan…

We study novel variations of Voronoi games and associated random processes that we call Voronoi choice games. These games provide a rich framework for studying questions regarding the power of small numbers of choices in multi-player,…

The one-round discrete Voronoi game, with respect to a $n$-point user set $U$, consists of two players Player 1 ($\mathcal{P}_1$) and Player 2 ($\mathcal{P}_2$). At first, $\mathcal{P}_1$ chooses a set of facilities $F_1$ following which…

\textit{Voronoi game} is a geometric model of competitive facility location problem played between two players. Users are generally modeled as points uniformly distributed on a given underlying space. Each player chooses a set of points in…

Following the solution to the One-Round Voronoi Game in arXiv:2011.13275, we naturally may want to consider similar games based upon the competitive locating of points and subsequent dividing of territories. In order to appease the tears of…

Consider a stream of $n$ random points (say, from the unit square) arriving one by one, where a player has to make an irreversible immediate decision for each arriving point whether to pick it. The player has to pick a single point, and the…

Spiro, Surya and Zeng (Electron. J. Combin. 2023; arXiv:2207.11272) recently studied a semi-restricted variant of the well-known game Rock, Paper, Scissors; in this variant the game is played for $3n$ rounds, but one of the two players is…

We consider a four-player game on the discrete hypercube $Q_n = \{0,1\}^n$, where each of the four players has chosen a single vertex of the hypercube. Such a position is called a profile. Imagine there is a voter at every vertex, and each…

Consider the following variant of Rock, Paper, Scissors (RPS) played by two players Rei and Norman. The game consists of $3n$ rounds of RPS, with the twist being that Rei (the restricted player) must use each of Rock, Paper, and Scissors…

At some places (see the references) Martin Erickson describes a certain game: "Two players alternately write O's (first player) and X's (second player) in the unoccupied cells of an n x n grid. The first player (if any) to occupy four cells…

There are $n$ independent Bernoulli random variables with parameters $p_i$ that are observed sequentially. Two players, A and B, act in turns starting with player A. Each player has the possibility on his turn, when $I_k=1$, to choose…

We consider a game with two players, consisting of a number of rounds, where the first player to win $n$ rounds becomes the overall winner. Who wins each individual round is governed by a certain urn having two types of balls (type 1 and…

A common format for sports contests involves pairwise matches between two teams, with the #1 player of team A matched against the #1 player of team B, the #2 player of team A against the #2 player of team B, and so on. This paper addresses…

In a classical chess round-robin tournament, each of $n$ players wins, draws, or loses a game against each of the other $n-1$ players. A win rewards a player with 1 points, a draw with 1/2 point, and a loss with 0 points. We are interested…

Nora and Wanda are two players who choose coefficients of a degree $d$ polynomial from some fixed unital commutative ring $R$. Wanda is declared the winner if the polynomial has a root in the ring of fractions of $R$ and Nora is declared…

This paper is concerned with asymptotic behaviour of a repeated game of "odds and evens", with strategies of both players represented by finite automata. It is proved that, for every $n$, there is an automaton with $2^n \cdot…

We give conditions for equilibria in the following Voronoi game on the discrete hypercube. Two players position themselves in $\{0,1\}^d$ and each receives payoff equal to the measure (under some probability distribution) of their Voronoi…