Related papers: Relations Between a Topological Game and the $G_{\…
Within the context of games on networks S. Goyal (Goya (2007), pg. 39) posed the following problem. Under any arbitrary but fixed topology, does there exist at least one pure Nash equilibrium that exhibits a positive relation between the…
The main goal of this paper is to investigate relations between topologies obtained by: $\theta$-open sets, $\omega$-open sets, $\theta_\omega$-open sets, local function, and local closure function with ideal of the countable sets. As the…
Eigen mode selection ought to be a practical issue in some real game systems, as it is a practical issue in the dynamics behaviour of a building, bridge, or molecular, because of the mathematical similarity in theory. However, its reality…
We consider the Erd\H{o}s-P\'osa property for immersions and topological minors in tournaments. We prove that for every simple digraph $H$, $k\in \mathbb{N}$, and tournament $T$, the following statements hold: (i) If in $T$ one cannot find…
This paper analyzes key properties of networks generated by geometric preferential attachment. We establish that the expected number of triangles is proportional to that of the standard preferential attachment model, with a proportionality…
In this paper, we continue to adapt the theories of spectra and schemes developed by Grothendieck in algebraic geometry to the category of groups. Let $G$ be a group, and $(H,f_G^H)$ and object of the comma category $C(G)$. In [5], we have…
We consider different choice procedures such as scoring rules, rules, using majority relation, value function and tournament matrix, which are used in social and multi-criteria choice problems. We focus on the study of the properties that…
In 2017, Tkachuk isolated the closed discrete selection property while working on problems related to function spaces [15]. In this paper we will study the closed discrete selection property and the related games and strategies on $C_k(X)$.…
This paper presents simulation-based relations for probabilistic game structures. The first relation is called probabilistic alternating simulation, and the second called probabilistic alternating forward simulation, following the naming…
We define a notion of morphisms between open games, exploiting a surprising connection between lenses in computer science and compositional game theory. This extends the more intuitively obvious definition of globular morphisms as mappings…
We consider a simple game, the $k$-regular graph game, in which players take turns adding edges to an initially empty graph subject to the constraint that the degrees of vertices cannot exceed $k$. We show a sharp topological threshold for…
We introduce the concept of a class of graphs, or more generally, relational structures, being locally tree-decomposable. There are numerous examples of locally tree-decomposable classes, among them the class of planar graphs and all…
The chapter provides an introduction to the basic concepts of Algebraic Topology with an emphasis on motivation from applications in the physical sciences. It finishes with a brief review of computational work in algebraic topology,…
A social choice procedure is modeled as a repeated Nash game between the social agents, who are communicating with each other through a social communication network modeled by an undirected graph. The agents' criteria for this game are…
A game-theoretic model of social preference and enlightened self-interest is formulated. Existence of symmetry and duality in the game matrices with altruistic social preference is revealed. The model is able to quantitatively describe the…
We introduce nonlinear attractive effects into a spatial Prisoner's Dilemma game where the players located on a square lattice can either cooperate with their nearest neighbors or defect. In every generation, each player updates its…
We associate a boundary $\mathcal B_{\pi,u}$ to each covariant representation $(\pi,u,H)$ of $C^*$-dynamical system $(G,A,\alpha)$ and study the action of $G$ on $\mathcal B_{\pi,u}$ and its amenability properties. We relate rigidity…
The object of this study are countably infinite games with perfect information that allow players to choose among arbitrarily many moves in a turn; in particular, we focus on the generalisations of the finite board games of Hex and…
Dialogue games are two-player logic games between a Proponent who puts forward a logical formula A as valid or true and an Opponent who disputes this. An advantage of the dialogical approach is that it is a uniform framework from which…
We introduce some notions of conditional mean dimension for a factor map between two topological dynamical systems and discuss their properties. With the help of these notions, we obtain an inequality to estimate the mean dimension of an…