Related papers: The Four Number Game
The numbers game is a one-player game played on a finite simple graph with certain "amplitudes" assigned to its edges and with an initial assignment of real numbers to its nodes. The moves of the game successively transform the numbers at…
Simple games cover voting systems in which a single alternative, such as a bill or an amendment, is pitted against the status quo. A simple game or a yes-no voting system is a set of rules that specifies exactly which collections of ``yea''…
In a monotonic sequence game, two players alternately choose elements of a sequence from some fixed ordered set. The game ends when the resulting sequence contains either an ascending subsequence of length a or a descending one of length d.…
The relationship between topology and dynamics of complex systems has motivated continuing interest from the scientific community. In the present work, we address this interesting topic from the perspective of simple games, involving two…
A general model for zero-sum stochastic games with asymmetric information is considered. In this model, each player's information at each time can be divided into a common information part and a private information part. Under certain…
Game dynamics theory, as a field of science, the consistency of theory and experiment is essential. In the past 10 years, important progress has been made in the merging of the theory and experiment in this field, in which dynamics cycle is…
In this paper we introduce the inaccessible game, an information-theoretic dynamical system constructed from four axioms. The first three axioms are known and define \emph{information loss} in the system. The fourth is a novel…
The numbers game is a one-player game played on a finite simple graph with certain "amplitudes" assigned to its edges and with an initial assignment of real numbers to its nodes. The moves of the game successively transform the numbers at…
Classify simple games into sixteen "types" in terms of the four conventional axioms: monotonicity, properness, strongness, and nonweakness. Further classify them into sixty-four classes in terms of finiteness (existence of a finite carrier)…
A cellular game is a dynamical system in which cells, placed in some discrete structure, are regarded as playing a game with their immediate neighbors. Individual strategies may be either deterministic or stochastic. Strategy success is…
When are all positions of a game numbers? We show that two properties are necessary and sufficient. These properties are consequences of that, in a number, it is not an advantage to be the first player. One of these properties implies the…
Players are arranged on a regular lattice and coded with a specific strategy for a pre-defined game. Each player sums their payoffs from playing the game with each of their neighbors, and then adopts the strategy of the most successful…
The focus of this essay is a rigorous treatment of infinite games. An infinite game is defined as a play consisting of a fixed number of players whose sequence of moves is repeated, or iterated ad infinitum. Each sequence corresponds to a…
This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…
Dynamical Systems theory generally deals with fixed point iterations of continuous functions. Computation by Turing machine although is a fixed point iteration but is not continuous. This specific category of fixed point iterations can only…
Nonzero sum games typically have multiple Nash equilibriums (or no equilibrium), and unlike the zero sum case, they may have different values at different equilibriums. Instead of focusing on the existence of individual equilibriums, we…
In this paper we investigate a differential game in which countably many dynamical objects pursue a single one. All the players perform simple motions. The duration of the game is fixed. The controls of a group of pursuers are subject to…
Dynamic games arise when multiple agents with differing objectives choose control inputs to a dynamic system. Dynamic games model a wide variety of applications in economics, defense, and energy systems. However, compared to single-agent…
The satisfactory development of Quaternionic Analysis has indicated new solutions for physical and mathematical problems. It is worth mentioning the fact that quaternions possess four dimensions, and in this way they may be considered as…
We analyze a coin-based game with two players where, before starting the game, each player selects a string of length $n$ comprised of coin tosses. They alternate turns, choosing the outcome of a coin toss according to specific rules. As a…