Related papers: Non-Stabilizing Parallel Chip-Firing Games

We study chip-firing games on multigraphs whose underlying simple graphs are trees, paths, and stars, denoted as banana trees, paths, and stars respectively. We present a polynomial time algorithm to compute the divisorial gonality of…

We study the complexity of computing equilibria in two classes of network games based on flows - fractional BGP (Border Gateway Protocol) games and fractional BBC (Bounded Budget Connection) games. BGP is the glue that holds the Internet…

We consider for two based graphs $G$ and $H$ the sequence of graphs $G_k$ given by the wedge sum of $G$ and $k$ copies of $H$. These graphs have an action of the symmetric group $\Sigma_k$ by permuting the $H$-summands. We show that the…

Evolutionary prisoner's dilemma games are studied with players located on square lattice and random regular graphs defining four neighbors for each one. The players follow one of the three strategies: tit-for-tat, unconditional cooperation,…

Divisorial gonality and stable divisorial gonality are graph parameters, which have an origin in algebraic geometry. Divisorial gonality of a connected graph $G$ can be defined with help of a chip firing game on $G$. The stable divisorial…

In this paper, we are concerned with the stabilizatbility of Stackelberg game-based systems. In particular, two players are involved in the system where one is the follower to minimize the related cost function and the other is the leader…

We introduce a new family of one-player games, involving the movement of coins from one configuration to another. Moves are restricted so that a coin can be placed only in a position that is adjacent to at least two other coins. The goal of…

The connected domination game is played just as the domination game, with an additional requirement that at each stage of the game the vertices played induce a connected subgraph. The number of moves in a D-game (an S-game, resp.) on a…

This paper provides a friendly introduction to chip-firing games and graph gonality. We use graphs coming from the five Platonic solids to illustrate different tools and techniques for studying these games, including independent sets,…

The stability number of a graph G, denoted by alpha(G), is the cardinality of a maximum stable set, and mu(G) is the cardinality of a maximum matching in G. If alpha(G)+mu(G) equals its order, then G is a Konig-Egervary graph. In this paper…

We study a network extension to the Nash bargaining game, as introduced by Kleinberg and Tardos (STOC'08), where the set of players corresponds to vertices in a graph $G=(V,E)$ and each edge $ij\in E$ represents a possible deal between…

On a filtered probability space $(\Omega,\mathcal{F},P,\mathbb{F}=(\mathcal{F}_t)_{t=0,\dotso,T})$, we consider stopper-stopper games $\overline V:=\inf_{\Rho\in\bT^{ii}}\sup_{\tau\in\T}\E[U(\Rho(\tau),\tau)]$ and $\underline…

This article introduces a quantized chip-firing model with close connections to the theory of rational lattice paths and rational parking functions. Given a graph with a sink and positive integers a,b,c with gcd(a,b)=1, a set S of vertices…

This paper presents a new lower bound for the discrete strategy improvement algorithm for solving parity games due to Voege and Jurdziski. First, we informally show which structures are difficult to solve for the algorithm. Second, we…

Considering the symmetries and self similarity properties of the corresponding labeled graphs, it is shown that the minimal number of moves in the Tower of Hanoi game with $p =4$ pegs and $n \geq p$ disks satisfies the recursive formula $…

Consider a discrete-time process on a graph $G$ where a set $B$ of initial vertices are chosen to be colored blue (the remainder being white) and then a time step consists of every currently blue vertex forcing all of its neighbors to…

A graph $G$ $=$ $(V,E)$ is vertex-pancyclic if for every vertex $u$ and any integer $l$ ranging from $3$ to $|V|$, $G$ contains a cycle $C$ of length $l$ such that $u$ is on $C$. A bipartite graph $G$ $=$ $(V,E)$ is vertex-bipancyclic if…

We give a new proof of the fact that the parallel repetition of the (3-player) GHZ game reduces the value of the game to zero polynomially quickly. That is, we show that the value of the $n$-fold GHZ game is at most $n^{-\Omega(1)}$. This…

Towards characterizing the optimization landscape of games, this paper analyzes the stability of gradient-based dynamics near fixed points of two-player continuous games. We introduce the quadratic numerical range as a method to…

Massively parallel hardware (GPUs) and long sequence data have made parallel algorithms essential for machine learning at scale. Yet dynamical systems, like recurrent neural networks and Markov chain Monte Carlo, were thought to suffer from…