Related papers: Threat, support and dead edges in the Shannon game
We study a generalization of the classical hidden clique problem to graphs with real-valued edge weights. Formally, we define a hypothesis testing problem. Under the null hypothesis, edges of a complete graph on $n$ vertices are associated…
The maintenance of cooperation in the presence of spatial restrictions has been studied extensively. It is well-established that the underlying graph topology can significantly influence the outcome of games on graphs. Maintenance of…
In the game theory literature, there appears to be little research on equilibrium selection for normal-form games with an infinite strategy space and discontinuous utility functions. Moreover, many existing selection methods are not…
Snake is a classic computer game, which has been around for decades. Based on this game, we study the game of Snake on arbitrary undirected graphs. A snake forms a simple path that has to move to an apple while avoiding colliding with…
The game Arc-Kayles is played on an undirected graph with two players taking turns deleting an edge and its endpoints from the graph. We study a generalization of this game, Weighted Arc Kayles (WAK for short), played on graphs with…
There has been a recent surge in transformer-based architectures for learning on graphs, mainly motivated by attention as an effective learning mechanism and the desire to supersede handcrafted operators characteristic of message passing…
The interactive game theoretical approach to the description of perception processes is proposed. The subject is treated formally in terms of a new class of the verbalizable interactive games which are called the perception games. An…
Most networks are not static objects, but instead they change over time. This observation has sparked rigorous research on temporal graphs within the last years. In temporal graphs, we have a fixed set of nodes and the connections between…
Individuals, or organizations, cooperate with or compete against one another in a wide range of practical situations. Such strategic interactions are often modeled as games played on networks, where an individual's payoff depends not only…
We study the m-Eternal Domination problem, which is the following two-player game between a defender and an attacker on a graph: initially, the defender positions k guards on vertices of the graph; the game then proceeds in turns between…
Mobile guards on the vertices of a graph are used to defend it against attacks on either its vertices or its edges. Various models for this problem have been proposed. In this survey we describe a number of these models with particular…
Burning and cooling are diffusion processes on graphs in which burned (or cooled) vertices spread to their neighbors with a new source picked at discrete time steps. In burning, the one tries to burn the graph as fast as possible, while in…
We consider a game for a continuum of non-identical players evolving on a finite state space. Their heterogeneous interactions are represented by a graphon, which can be viewed as the limit of a dense random graph. The player's transition…
A large body of research is currently investigating on the connection between machine learning and game theory. In this work, game theory notions are injected into a preference learning framework. Specifically, a preference learning problem…
We study the parameterized complexity of interdiction problems in graphs. For an optimization problem on graphs, one can formulate an interdiction problem as a game consisting of two players, namely, an interdictor and an evader, who…
The aim of this paper is to solve the "gift exchange" problem: you are one of n players, and there are n wrapped gifts on display; when your turn comes, you can either choose any of the remaining wrapped gifts, or you can "steal" a gift…
The future smart grid is envisioned as a large-scale cyber-physical system encompassing advanced power, communications, control, and computing technologies. In order to accommodate these technologies, it will have to build on solid…
We consider games played on finite graphs, whose goal is to obtain a trace belonging to a given set of winning traces. We focus on those states from which Player 1 cannot force a win. We explore and compare several criteria for establishing…
Cops and robbers is a pursuit-evasion game played on graphs. We completely classify the cop numbers for $n \times n$ knight graphs and queen graphs. This completes the classification of the cop numbers for all $n \times n$ classical chess…
The semi-random graph process is a single player game in which the player is initially presented an empty graph on $n$ vertices. In each round, a vertex $u$ is presented to the player independently and uniformly at random. The player then…