Related papers: F-Saturation Games

In games with a large number of players where players may have overlapping objectives, the analysis of stable outcomes typically depends on player types. A special case is when a large part of the player population consists of imitation…

We provide a self-contained introduction to finite extensive games with perfect information. In these games players proceed in turns having, at each stage, finitely many moves to their disposal, each play always ends, and in each play the…

Let $G$ be a graph and $\mathcal{F}$ be a family of graphs. We say a graph $G$ is $\mathcal{F}$-saturated if $G$ does not contain any member in $\mathcal{F}$ and for any $e\in E(\overline{G})$, $G+e$ creates a copy of some member in $…

Graph games of infinite length are a natural model for open reactive processes: one player represents the controller, trying to ensure a given specification, and the other represents a hostile environment. The evolution of the system…

We study a patrolling game played on a network $Q$, considered as a metric space. The Attacker chooses a point of $Q$ (not necessarily a node) to attack during a chosen time interval of fixed duration. The Patroller chooses a unit speed…

A new class of multi-player competitive stochastic games in discrete-time with an affine specification of the redistribution of payoffs at exercise is proposed and examined. Our games cover as a very special case the classic two-person…

We propose a method to construct finite-state reactive controllers for systems whose interactions with their adversarial environment are modeled by infinite-duration two-player games over (possibly) infinite graphs. The proposed method…

We propose a unifying additive theory for standard conventions in Combinatorial Game Theory, including normal-, mis\`ere- and scoring-play, studied by Berlekamp, Conway, Dorbec, Ettinger, Guy, Larsson, Milley, Neto, Nowakowski, Renault,…

We consider a patrolling game on a graph recently introduced by Alpern et al. (2011) where the Patroller wins if he is at the attacked node while the attack is taking place. This paper studies the periodic patrolling game in the case that…

For an edge-ordered graph $G$, we say that an $n$-vertex edge-ordered graph $H$ is $G$-saturated if it is $G$-free and adding any new edge with any new label to $H$ introduces a copy of $G$. The saturation function describes the minimum…

The domination game on a graph $G$ (introduced by B. Bre\v{s}ar, S. Klav\v{z}ar, D.F. Rall \cite{BKR2010}) consists of two players, Dominator and Staller, who take turns choosing a vertex from $G$ such that whenever a vertex is chosen by…

In 1964, Erd\H{o}s, Hajnal and Moon introduced a saturation version of Tur\'an's classical theorem in extremal graph theory. In particular, they determined the minimum number of edges in a $K_r$-free, $n$-vertex graph with the property that…

We study a generalisation of sabotage games, a model of dynamic network games introduced by van Benthem. The original definition of the game is inherently finite and therefore does not allow one to model infinite processes. We propose an…

We introduce Shortest Connection Game, a two-player game played on a directed graph with edge costs. Given two designated vertices in which they start, the players take turns in choosing edges emanating from the vertex they are currently…

In this paper, we address a pursuit-evasion game involving multiple players by utilizing tools and techniques from reinforcement learning and matrix game theory. In particular, we consider the problem of steering an evader to a goal…

M\"uller games form a well-established class of games for model checking and verification. These games are played on directed graphs $\mathcal G$ where Player 0 and Player 1 play by generating an infinite path through the graph. The winner…

Graph Exploration problems ask a searcher to explore an unknown environment. The environment is modeled as a graph, where the searcher needs to visit each vertex beginning at some vertex. Treasure Hunt problems are a variation of Graph…

An average-time game is played on the infinite graph of configurations of a finite timed automaton. The two players, Min and Max, construct an infinite run of the automaton by taking turns to perform a timed transition. Player Min wants to…

The orienteering problem is a well-studied and fundamental problem in transportation science. In the problem, we are given a graph with prizes on the nodes and lengths on the edges, together with a budget on the overall tour length. The…

Given a graph $F$ and a positive integer $n$, the weak $F$-saturation number $\mathrm{wsat}(K_n,F)$ is the minimum number of edges in a graph $H$ on $n$ vertices such that the edges missing in $H$ can be added, one at a time, so that every…