Related papers: Candy-passing Games on General Graphs, I

A walk of length $n$ in a graph is consistent if there exists an automorphism of the graph that maps the initial $n-1$ vertices to the final $n-1$ vertices of the walk. In this paper we find some sufficient conditions for a consistent walk…

We consider static finite-player network games and their continuum analogs, graphon games. Existence and uniqueness results are provided, as well as convergence of the finite-player network game optimal strategy profiles to their analogs…

Correlated equilibria -- and their generalization $\Phi$-equilibria -- are a fundamental object of study in game theory, offering a more tractable alternative to Nash equilibria in multi-player settings. While computational aspects of…

Monte Carlo simulations and dynamical mean-field approximations are performed to study the phase transitions in rock-scissors-paper game on different host networks. These graphs are originated from lattices by introducing quenched and…

We introduce a new class of network allocation games called graphical distance preservation games. Here, we are given a graph, called a topology, and a set of agents that need to be allocated to its vertices. Moreover, every agent has an…

Semi-supervised learning is a popular class of techniques to learn from labeled and unlabeled data. The paper proposes an application of a recently proposed approach of graph transduction that exploits game theoretic notions to the problem…

We present analytical treatment of quantum walks on a cycle graph. The investigation is based on a realistic physical model of the graph in which decoherence is induced by continuous monitoring of each graph vertex with nearby quantum point…

Motivated by understanding non-strict and strict pure strategy equilibria in network anti-coordination games, we define notions of stable and, respectively, strictly stable colorings in graphs. We characterize the cases when such colorings…

Graphs are closely related to quantum error-correcting codes: every stabilizer code is locally equivalent to a graph code, and every codeword stabilized code can be described by a graph and a classical code. For the construction of good…

This short note establishes positionality of mean-payoff games over infinite game graphs by constructing a well-founded monotone universal graph.

We present, to the best of the authors' knowledge, all known results for the (planar) crossing numbers of specific graphs and graph families. The results are separated into various categories; specifically, results for general graph…

We introduce the concept of a \emph{cycle pattern} for directed graphs as functions from the set of cycles to the set $\{-,0,+\}$. The key example for such a pattern is derived from a weight function, giving rise to the sign of the total…

Admissibility has been studied for games of infinite duration with Boolean objectives. We extend here this study to games of infinite duration with quantitative objectives. First, we show that, un- der the assumption that optimal worst-case…

A Cayley graph $\Ga=\Cay(G,S)$ is said to be normal if $G$ is normal in $\Aut\Ga$. The concept of normal Cayley graphs was first proposed by M.Y.Xu in [Discrete Math. 182, 309-319, 1998] and it plays an important role in determining the…

Graph neural networks (GNNs) are the most widely adopted model in graph-structured data oriented learning and representation. Despite their extraordinary success in real-world applications, understanding their working mechanism by theory is…

We give sufficient conditions for stability of a continuous-time linear switched system consisting of finitely many subsystems. The switching between subsystems is governed by an underlying graph. The results are applicable to switched…

Message-passing graph neural networks (MPNNs) have emerged as the leading approach for machine learning on graphs, attracting significant attention in recent years. While a large set of works explored the expressivity of MPNNs, i.e., their…

In this paper we will be introducing a type of game which as far as this author is aware has never been studied before. These are games where there are two players, one who is trying to get one of his pieces, called a King to a predefined…

We study the existence of quantum state transfer on non-integral circulant graphs. We find that continuous time quantum walks on quantum networks based on certain circulant graphs with $2^k$ $\left(k\in\mathbb{Z}\right)$ vertices exhibit…

We present a linear stability analysis of stationary states (or fixed points) in large dynamical systems defined on random directed graphs with a prescribed distribution of indegrees and outdegrees. We obtain two remarkable results for such…