Related papers: An Introduction to Conway's Games and Numbers

This short note is a conceptual prologue to the series of articles devoted to the analysis of interrelations between the representation theory (especially, its inverse problems) and the control and games theory.

Coloring games are combinatorial games where the players alternate painting uncolored vertices of a graph one of $k > 0$ colors. Each different ruleset specifies that game's coloring constraints. This paper investigates six impartial…

Absolute combinatorial game theory was recently developed as a unifying tool for constructive/local game comparison (Larsson et al. 2018). The theory concerns {\em parental universes} of combinatorial games; standard closure properties are…

The class of Guaranteed Scoring Games (GS) are two-player combinatorial games with the property that Normal-play games (Conway et. al.) are ordered embedded into GS. They include, as subclasses, the scoring games considered by Milnor…

This thesis presents some geometric insights into three different types of two player prediction games -- namely general learning task, prediction with expert advice, and online convex optimization. These games differ in the nature of the…

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…

Game semantics is a rich and successful class of denotational models for programming languages. Most game models feature a rather intuitive setup, yet surprisingly difficult proofs of such basic results as associativity of composition of…

Justification theory is a unifying semantic framework. While it has its roots in non-monotonic logics, it can be applied to various areas in computer science, especially in explainable reasoning; its most central concept is a justification:…

A class of discrete Bidding Combinatorial Games that generalize alternating normal play was introduced by Kant, Larsson, Rai, and Upasany (2022). The major questions concerning optimal outcomes were resolved. By generalizing standard game…

We introduce and investigate a range of general notions of a game. Our principal notion is based on a set of agents modifying a relational structure in a discrete evolution sequence. We also introduce and study a variety of ways to model…

In cooperative game theory, the social configurations of players are modeled by balanced collections. The Bondareva-Shapley theorem, perhaps the most fundamental theorem in cooperative game theory, characterizes the existence of solutions…

Game theory is an established branch of mathematics that offers a rich set of mathematical tools for multi-person strategic decision making that can be used to model the interactions of decision makers in security problems who compete for…

Quantum games have proposed a new point of view for the solution of the classical problems and dilemmas in game theory. Certain quantization relationships can be proposed with the objective that a game can be generalized into a quantum…

This article presents an overview of computability logic -- the game-semantically constructed logic of interactive computational tasks and resources. There is only one non-overview, technical section in it, devoted to a proof of the…

Main papers on quantum games are written by physicists for physicists, and the inevitable exploitation of physics jargon may create difficulties for mathematicians or economists. Our goal here is to make clear the physical content and to…

We illustrate how one can use basic combinatorial theory and computer programming technique (Python) to analyze the combinatorial game: Mahjong. The results confirm some folklore concerning the game, and expose some unexpected results.…

In this paper, we propose a Quantum variation of combinatorial games, generalizing the Quantum Tic-Tac-Toe proposed by Allan Goff. A combinatorial game is a two-player game with no chance and no hidden information, such as Go or Chess. In…

We study games with finitely many participants, each having finitely many choices. We consider the following categories of participants: (I) populations: sets of nonatomic agents, (II) atomic splittable players, (III) atomic non splittable…

Game theory-based approaches have recently gained traction in a wide range of applications, importantly in power and energy systems. With the onset of cooperation as a new perspective for solving power system problems, as well as the nature…

We introduce the concept of Conversion/Preference Games, or CP games for short. CP games generalize the standard notion of strategic games. First we exemplify the use of CP games. Second we formally introduce and define the CP-games…