Related papers: First to reach $n$ game

Let $n, k$ be positive integers. The $(k+1)$-star avoidance game on $K_n$ is played as follows. Two players take it in turn to claim a (previously unclaimed) edge of the complete graph on $n$ vertices. The first player to claim all edges of…

We propose and study a new model for competitions, specifically sports multi-player leagues where the initial strengths of the teams are independent i.i.d. random variables that evolve during different days of the league according to…

We introduce a new setting where a population of agents, each modelled by a finite-state system, are controlled uniformly: the controller applies the same action to every agent. The framework is largely inspired by the control of a…

A general position set of a graph $G$ is a set of vertices $S$ in $G$ such that no three vertices from $S$ lie on a common shortest path. In this paper we introduce and study the general position achievement game. The game is played on a…

In this paper, we study one-player and two-player energy mean-payoff games. Energy mean-payoff games are games of infinite duration played on a finite graph with edges labeled by 2-dimensional weight vectors. The objective of the first…

We study so-called invariant games played with a fixed number $d$ of heaps of matches. A game is described by a finite list $\mathcal{M}$ of integer vectors of length $d$ specifying the legal moves. A move consists in changing the current…

We consider a general round-robin tournament model with equally strong players in which $X_{ij}$ denotes the score of player $i$ against player $j$. We assume that $X_{ij}$ takes values in a countable subset of $[0,1]$ and satisfies…

In two-player games on graphs, the players move a token through a graph to produce an infinite path, which determines the winner of the game. Such games are central in formal methods since they model the interaction between a…

In a zero-sum stochastic game with signals, at each stage, two adversary players take decisions and receive a stage payoff determined by these decisions and a variable called state. The state follows a Markov chain, that is controlled by…

In this paper we study a variant of the Nuel game (a generalization of the duel) which is played in turns by $N$ players. In each turn a single player must fire at one of the other players and has a certain probability of hitting and…

We consider the occupancy problem where balls are thrown independently at infinitely many boxes with fixed positive frequencies. It is well known that the random number of boxes occupied by the first n balls is asymptotically normal if its…

Consider the following process whereby $n$ balls are distributed into $k$ bins. Repeatedly, a ball is removed from a non-empty bin chosen uniformly at random. The process ends when a single non-empty bin remains. Will Ma…

In this paper the results of a simulation of a prisoner's dilemma robin-round tournament are presented. In the tournament each participating strategy plays an iterated prisoner's dilemma against each other strategy (round-robin) and as a…

We extend the classical coupon collector's problem to one in which two collectors are simultaneously and independently seeking collections of $d$ coupons. We find, in finite terms, the probability that the two collectors finish at the same…

In a seminal paper, Meyer [David Meyer, Phys. Rev. Lett. 82, 1052 (1999)] described the advantages of quantum game theory by looking at the classical penny flip game. A player using a quantum strategy can win against a classical player…

We introduce a two-player game in which one and his/her opponent attempt to pack as many ``prisoners'' as possible on the squares of an n-by-n checkerboard; each prisoner has to be ``protected'' by at least as many guards as the number of…

In two-player games on graphs, the players move a token through a graph to produce an infinite path, which determines the winner or payoff of the game. We study {\em bidding games} in which the players bid for the right to move the token.…

This paper concerns two-player alternating play combinatorial games (Conway 1976) in the normal-play convention, i.e. last move wins. Specifically, we study impartial vector subtraction games on tuples of nonnegative integers (Golomb 1966),…

We consider two players, starting with $m$ and $n$ units, respectively. In each round, the winner is decided with probability proportional to each player's fortune, and the opponent loses one unit. We prove an explicit formula for the…

A large class of Positional Games are defined on the complete graph on $n$ vertices. The players, Maker and Breaker, take the edges of the graph in turns, and Maker wins iff his subgraph has a given -- usually monotone -- property. Here we…