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Temperature is a deceptively simple concept that still raises deep questions at the forefront of quantum physics research. The observation of thermalisation in completely isolated quantum systems, such as cold-atom quantum simulators,…

Positional games are a well-studied class of combinatorial game. In their usual form, two players take turns to play moves in a set (`the board'), and certain subsets are designated as `winning': the first person to occupy such a set wins…

Modern software systems may exhibit a nondeterministic behavior due to many unpredictable factors. In this work, we propose the node coverage game, a two player turn-based game played on a finite game graph, as a formalization of the…

We introduce a topological combinatorial game called the Region Smoothing Swap Game. The game is played on a game board derived from the connected shadow of a link diagram on a (possibly non-orientable) surface by smoothing at crossings.…

Combinatorial game theory (CGT), as introduced by Berlekamp, Conway and Guy, involves two players who move alternately in a perfect information, zero-sum game, and there are no chance devices. Also the games have the finite descent property…

We study a variant of the chip-firing game called the diffusion game. In the diffusion game, we begin with some integer labelling of the vertices of a graph, interpreted as a number of chips on each vertex, and then for each subsequent step…

We study the behavior of a simple string bit model at finite temperature. We use thermal perturbation theory to analyze the high temperature regime. But at low temperatures we rely on the large $N$ limit of the dynamics, for which the exact…

The minority game is a simple congestion game in which the players' main goal is to choose among two options the one that is adopted by the smallest number of players. We characterize the set of Nash equilibria and the limiting behavior of…

A network model based on players' aspirations is proposed and analyzed theoretically and numerically within the framework of evolutionary game theory. In this model, players decide whether to cooperate or defect by comparing their payoffs…

Energy parity games are infinite two-player turn-based games played on weighted graphs. The objective of the game combines a (qualitative) parity condition with the (quantitative) requirement that the sum of the weights (i.e., the level of…

In this paper we will discuss scoring play games. We will give the basic definitions for scoring play games, and show that they form a well defined set, with clear and distinct outcome classes under these definitions. We will also show that…

n infinite two-player zero-sum game with a Borel winning set, in which the opponent's actions are monitored eventually but not necessarily immediately after they are played, is determined. The proof relies on a representation of the game as…

An instantaneous temperature path of a point particle in the space - temperature manifold can be represented as a string of length L=1/kT (thermostring). The thermostring swepts a surface in the space-time-temperature manyfold at its…

Determining whether Global Average Temperature (GAT) is an integrated process of order 1, I(1), or is a stationary process around a trend function is crucial for detection, attribution, impact and forecasting studies of climate change. In…

We study the combinatorial two-player game Tron. We answer the extremal question on general graphs and also consider smaller graph classes. Bodlaender and Kloks conjectured in [2] PSPACE- completeness. We proof this conjecture.

We are used to measure temperature with a thermometer and we know from everyday life that different types of thermometers measure the same temperature. This experience can be based on equilibrium thermodynamics, which explains the…

In this paper we experiment with a 2-player strategy board game where playing models are evolved using reinforcement learning and neural networks. The models are evolved to speed up automatic game development based on human involvement at…

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…

We study a combinatorial game derived from a problem in the German National Mathematics Competition. In this game, two players take turns removing numbers from a finite set of natural numbers, aiming to satisfy a certain divisibility…

Motivated by the success of domination games and by a variation of the coloring game called the indicated coloring game, we introduce a version of domination games called the indicated domination game. It is played on an arbitrary graph $G$…