Related papers: Combinatorial Games with a Pass: A dynamical syste…
In this paper, we study a colorful, impartial combinatorial game played on a two-dimensional grid, Transverse Wave. We are drawn to this game because of its apparent simplicity, contrasting intractability, and intrinsic connection to two…
Maybe an event can't be modeled completely through on game but there is more chance with several games. With emphasis on players' rationality, we present new properties of strategic games, which result in production of other games. Here, a…
Game theory has been widely applied to many areas including economics, biology and social sciences. However, it is still challenging to quantify the global stability and global dynamics of the game theory. We developed a landscape and flux…
Quantum mechanics courses focus mostly on its computational aspects. This alone does not provide the same depth of understanding as most physicists have of classical mechanics. The understanding of classical mechanics is significantly…
The dynamics by iteration of a function on a compact metric space, sometimes called a cascade, can be extended to the dynamics of a closed relation on such a space. Here we apply this relation dynamics to study semiflows (and their relation…
In soccer, passing is the most frequent interaction between players and plays a significant role in creating scoring chances. Experts are interested in analyzing players' passing behavior to learn passing tactics, i.e., how players build up…
In Parrondo's games, the apparently paradoxical situation occurs where individually losing games combine to win. The basic formulation and definitions of Parrondo's games are described in Harmer et al.. These games have recently gained…
Nim is a well-known combinatorial game in which two players alternately remove stones from distinct piles. A player who removes the last stone wins under the normal play rule, while a player loses under the mis\`ere play rule. In this…
We study a modified prisoner's dilemma game taking place on two-dimensional disordered square lattices. The players are pure strategists and can either cooperate or defect with their immediate neighbors. In the generations each player…
Decision making in modern large-scale and complex systems such as communication networks, smart electricity grids, and cyber-physical systems motivate novel game-theoretic approaches. This paper investigates big strategic (non-cooperative)…
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…
Game theory formalizes certain interactions between physical particles or between living beings in biology, sociology, and economics, and quantifies the outcomes by payoffs. The prisoner's dilemma (PD) describes situations in which it is…
Intransitivity is a property of connected, oriented graphs representing species interactions that may drive their coexistence even in the presence of competition, the standard example being the three species Rock-Paper-Scissors game. We…
In this paper, we introduce a couple of dynamical systems that are related to the Chaos Game. We begin by discussing different methods of generating the Sierpinski gasket. Then we show how the transition from random to uniform selection…
We study the network replicator equation and characterize its fixed points on arbitrary graph structures for $2 \times 2$ symmetric games. We show a relationship between the asymptotic behavior of the network replicator and the existence of…
A combinatorial simplex algorithm is an instance of the simplex method in which the pivoting depends on combinatorial data only. We show that any algorithm of this kind admits a tropical analogue which can be used to solve mean payoff…
While Artificial Intelligence has successfully outperformed humans in complex combinatorial games (such as chess and checkers), humans have retained their supremacy in social interactions that require intuition and adaptation, such as…
In multi-agent settings, game theory is a natural framework for describing the strategic interactions of agents whose objectives depend upon one another's behavior. Trajectory games capture these complex effects by design. In competitive…
We use the example of playing a 2-player game with entangled quantum objects to investigate the effect of quantum correlation. We find that for simple game scenarios it is classical correlation that is the central feature and that these…
Learning in zero-sum games studies a situation where multiple agents competitively learn their strategy. In such multi-agent learning, we often see that the strategies cycle around their optimum, i.e., Nash equilibrium. When a game…