Related papers: Nim on hypercubes
We propose a numerical method for stationary Mean Field Games defined on a network. In this framework a correct approximation of the transition conditions at the vertices plays a crucial role. We prove existence, uniqueness and convergence…
We introduce CUT, the class of 2-player partition games. These are NIM type games, played on a finite number of heaps of beans. The rules are given by a set of positive integers, which specifies the number of allowed splits a player can…
Chocolate-bar games are variants of the CHOMP game. A three-dimensional chocolate bar comprises a set of cubic boxes sized 1 X 1 X 1, with a bitter cubic box at the bottom of the column at position (0,0). For non-negative integers u,w such…
We study strategic games on weighted directed graphs, in which the payoff of a player is defined as the sum of the weights on the edges from players who chose the same strategy, augmented by a fixed non-negative integer bonus for picking a…
We study the complexity of computing equilibria in binary public goods games on undirected graphs. In such a game, players correspond to vertices in a graph and face a binary choice of performing an action, or not. Each player's decision…
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,…
Temporal graphs are a popular modelling mechanism for dynamic complex systems that extend ordinary graphs with discrete time. Simply put, time progresses one unit per step and the availability of edges can change with time. We consider the…
Turn-based discounted-sum games are two-player zero-sum games played on finite directed graphs. The vertices of the graph are partitioned between player 1 and player 2. Plays are infinite walks on the graph where the next vertex is decided…
We introduce Multiplicative Modular Nim (MuM), a variant of Nim in which the traditional nim-sum is replaced by heap-size multiplication modulo m. We establish a complete theory for this game, beginning with a direct, Bouton-style analysis…
We encode arbitrary finite impartial combinatorial games in terms of lattice points in rational convex polyhedra. Encodings provided by these \emph{lattice games} can be made particularly efficient for octal games, which we generalize to…
We introduce the notion of universal graphs as a tool for constructing algorithms solving games of infinite duration such as parity games and mean payoff games. In the first part we develop the theory of universal graphs, with two goals:…
We consider the generalized game Lights Out played on a graph and investigate the following question: for a given positive integer $n$, what is the probability that a graph chosen uniformly at random from the set of graphs with $n$ vertices…
We announce misere-play solutions to several previously-unsolved combinatorial games. The solutions are described in terms of misere quotients--commutative monoids that encode the additive structure of specific misere-play games. We also…
For non-monotone single and two-populations time-dependent Mean-Field Game systems we obtain the existence of an infinite number of branches of non-trivial solutions. These non-trivial solutions are in particular shown to exhibit an…
We introduce an impartial combinatorial game on Steiner triple systems called Nofil. Players move alternately, choosing points of the triple system. If a player is forced to fill a block on their turn, they lose. We explore the play of…
We study two impartial games introduced by Anderson and Harary and further developed by Barnes. Both games are played by two players who alternately select previously unselected elements of a finite group. The first player who builds a…
Recently, a standardized framework was proposed for introducing quantum-inspired moves in mathematical games with perfect information and no chance. The beauty of quantum games-succinct in representation, rich in structures, explosive in…
Combinatorial Game Theory is a branch of mathematics and theoretical computer science that studies sequential 2-player games with perfect information. Normal play is the convention where a player who cannot move loses. Here, we generalize…
A natural partial ordering exists on the set of all weighted games and, more broadly, on all linear games. We describe several properties of the partially ordered sets formed by these games and utilize this perspective to enumerate proper…
We introduce a new class of population games that we call monotropic; these are games characterized by the presence of a unique globally neutrally stable Nash equilibrium. Monotropic games generalize strictly concave potential games and…