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

Cooperative interval game is a cooperative game in which every coalition gets assigned some closed real interval. This models uncertainty about how much the members of a coalition get for cooperating together. In this paper we study…

Positional games are a branch of combinatorics, researching a variety of two-player games, ranging from popular recreational games such as Tic-Tac-Toe and Hex, to purely abstract games played on graphs and hypergraphs. It is closely…

In this paper we will be examining impartial scoring play games. We first give the basic definitions for what impartial scoring play games are and look at their general structure under the disjunctive sum. We will then examine the game of…

A generalized model of games is proposed, in which cooperative games and non-cooperative games are special cases. Some games that are neither cooperative nor non-cooperative can be expressed and analyzed. The model is based on relationships…

In his celebrated book "On Number and Games" (Academic Press, New-York, 1976), J.H. Conway introduced twelve versions of compound games. We analyze these twelve versions for the Node-Kayles game on paths. For usual disjunctive compound,…

Cooperative games are an important class of problems in game theory, where the goal is to distribute a value among a set of players who are allowed to cooperate by forming coalitions. An outcome of the game is given by an allocation vector…

Conventional noncooperative game theory hypothesizes that the joint strategy of a set of players in a game must satisfy an "equilibrium concept". All other joint strategies are considered impossible; the only issue is what equilibrium…

We give a self contained introduction to a few quantum game protocols, starting with the quantum version of the two-player two-choice game of Prisoners dilemma, followed by a n-player generalization trough the quantum minority games, and…

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…

In this talk we introduce several topics in combinatorial number theory which are related to groups; the topics include combinatorial aspects of covers of groups by cosets, and also restricted sumsets and zero-sum problems on abelian…

We propose an interpretation of the infinite sum of combinatorial games. In such an interpretation, plays involve infinite runs, but without loops. The notion of a run is quite natural, but different possibilities arises for the notion of…

We define generalized quantum games by introducing the coherent payoff operators and propose a simple scheme to illustrate it. The scheme is implemented with a single spin qubit system and two entangled qubit system. The Nash Equilibrium…

Game theory has been one of the most successful quantitative concepts to describe social interactions, their strategical aspects, and outcomes. Among the payoff matrix quantifying the result of a social interaction, the interaction…

Causality and game theory are two influential fields that contribute significantly to decision-making in various domains. Causality defines and models causal relationships in complex policy problems, while game theory provides insights into…

Combinatorial games are widely used in finite model theory, constraint satisfaction, modal logic and concurrency theory to characterize logical equivalences between structures. In particular, Ehrenfeucht-Fraisse games, pebble games, and…

Genetic programming is the practice of evolving formulas using crossover and mutation of genes representing functional operations. Motivated by genetic evolution we develop and solve two combinatorial games, and we demonstrate some…

For any given sequence of integers there exists a quantum field theory whose Feynman rules produce that sequence. An example is illustrated for the Stirling numbers. The method employed here offers a new direction in combinatorics and graph…

We provide game-theoretic proofs of some well-known existence theorems of Friedberg numberings for the class of all partial computable functions, including (1) the existence of two incomparable Friedberg numberings; (2) the existence of a…

Game comonads offer a categorical view of a number of model-comparison games central to model theory, such as pebble and Ehrenfeucht-Fra\"iss\'e games. Remarkably, the categories of coalgebras for these comonads capture preservation of…

By treating combinatorial games as dynamical systems, we are able to address a longstanding open question in combinatorial game theory, namely, how the introduction of a "pass" move into a game affects its behavior. We consider two well…