Related papers: Eriksson's numbers game and finite Coxeter groups
We introduce and study a class of infinite-horizon non-zero-sum non-cooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics. First we show, in the general case of asymmetric interactions,…
The guarding game is a game in which several cops try to guard a region in a (directed or undirected) graph against Robber. Robber and the cops are placed on the vertices of the graph; they take turns in moving to adjacent vertices (or…
We define a family of vertex colouring games played over a pair of graphs or digraphs $(G,H)$ by players $\forall$ and $\exists$. These games arise from work on a longstanding open problem in algebraic logic. It is conjectured that there is…
We study unique games and estimate some of their values. We prove that if a unique game has a quantum-assisted value close to 1, then it must have a perfect deterministic strategy. We introduce a family of unique games based on groups that…
We start with the well-known game below: Two players hold a sheet of paper to their forehead on which a positive integer is written. The numbers are consecutive and each player can only see the number of the other one. In each time step,…
In this paper we study a variant of the solitaire game Lights-Out, where the player's goal is to turn off a grid of lights. This variant is a two-player impartial game where the goal is to make the final valid move. This version is playable…
Games on graphs provide a natural model for reactive non-terminating systems. In such games, the interaction of two players on an arena results in an infinite path that describes a run of the system. Different settings are used to model…
A tournament is an orientation of a graph. Vertices are players and edges are games, directed away from the winner. Kannan, Tetali and Vempala and McShine showed that tournaments with given score sequence can be rapidly sampled, via simple…
Graph Pebbling is a well-studied single-player game on graphs. We introduce the game of Blocking Pebbles which adapts Graph Pebbling into a two-player strategy game in order to examine it within the context of Combinatorial Game Theory.…
Parity games are games that are played on directed graphs whose vertices are labeled by natural numbers, called priorities. The players push a token along the edges of the digraph. The winner is determined by the parity of the greatest…
Regular games form a well-established class of games for analysis and synthesis of reactive systems. They include coloured Muller games, McNaughton games, Muller games, Rabin games, and Streett games. These games are played on directed…
We introduce a new two-player game on graphs, in which players alternate choosing vertices until the set of chosen vertices forms a dominating set. The last player to choose a vertex is the winner. The game fits into the scheme of several…
Energy games are a well-studied class of 2-player turn-based games on a finite graph where transitions are labeled with integer vectors which represent changes in a multidimensional resource (the energy). One player tries to keep the…
We introduce quantitative reductions, a novel technique for structuring the space of quantitative games and solving them that does not rely on a reduction to qualitative games. We show that such reductions exhibit the same desirable…
A new mathematical model for evolutionary games on graphs is proposed to extend the classical replicator equation to finite populations of players organized on a network with generic topology. Classical results from game theory,…
We begin by reviewing and proving the basic facts of combinatorial game theory. We then consider scoring games (also known as Milnor games or positional games), focusing on the "fixed-length" games for which all sequences of play terminate…
We study the value of unique games as a graph-theoretic parameter. This is obtained by labeling edges with permutations. We describe the classical value of a game as well as give a necessary and sufficient condition for the existence of an…
In this paper we first define a new kind of potential games, called coset weighted potential game, which is a generalized form of weighted potential game. Using semi-tensor product of matrices, an algebraic method is provided to verify…
Simple stochastic games are two-player zero-sum stochastic games with turn-based moves, perfect information, and reachability winning conditions. We present two new algorithms computing the values of simple stochastic games. Both of them…
We consider two-player games over finite graphs in which both players are restricted by fairness constraints on their moves. Given a two player game graph $G=(V,E)$ and a set of fair moves $E_f\subseteq E$ a player is said to play "fair" in…