The domination game, played on a graph G, was introduced in [3]. Vertices are chosen, one at a time, by two players Dominator and Staller. Each chosen vertex must enlarge the set of vertices of G dominated to that point in the game. Both players use an optimal strategy–Dominator plays so as to end the game as quickly as possible, Staller plays in such a way that the game lasts as many steps as ...

Muscle glycogen is the predominant energy source for soccer match play, though its importance for soccer training (where lower loads are observed) is not well known. In an attempt to better inform carbohydrate (CHO) guidelines, we quantified training load in English Premier League soccer players (n = 12) during a one-, two- and three-game week schedule (weekly training frequency was four, four ...

In this paper we examine Ehrenfeucht-Fräıssé (EF) games on fields and vector spaces. We find the exact length of the EF game on two algebraically closed fields of finite transcendence degree over Q or Z/pZ. We also determine an upper bound on the length of any EF game on models (F1 ,F1) and (F m 2 ,F2 of vector spaces where m = n and a lower bound for the special case F1 = F2.

– The generalization of the problem of adaptive competition, known as the minority game, to the case of K possible choices for each player is addressed, and mapped onto a system of interacting perceptrons with input and output units of the type of K-states Potts-spins. An optimal solution of the minority game as well as the dynamical evolution of the adaptive strategies of the players are solve...

We analyze a network coloring game on hypergraphs which can also describe a voter model. Each node represents a voter and is colored according to its preferred candidate (or undecided). Each hyperedge is a subset of voters that can interact and influence one another. In each round of the game, one hyperedge is chosen randomly, and the voters in the hyperedge can change their colors according to...

The game of lottery is both popular and simple. Focusing on the essentials, and leaving aside additional features of secondary importance, which vary across different lottery implementations, the rules of the game are as follows: each player submits to the lottery organizers a ticket consisting of M integers selected by the player, without repetitions, selection order being unimportant from the...

The DEVS framework of discrete event modeling is known to be compatible with the object-oriented (OO) world view. This paper proposes a methodology for the OO development of war game models within the framework. The methodology develops war game models at two layers: a discrete event system (DES) layer and an object model (OM) layer. Within the methodology the DES layer represents abstract beha...

We study the core of a non-atomic game v which is uniformly continuous with respect to the DNA-topology and continuous at the grand coalition. Such a game has a unique DNA-continuous extension v on the space B1 of ideal sets. We show that if the extension v is concave then the core of the game v is non-empty i ̈ v is homogeneous of degree one along the diagonal of B1. We use this result to obtai...

A cooperative game with transferable utility is said to be homogeneous of degree one if for any integer m, the value of cloning m times all players at any given coalition, leads to m times the value of the original coalition. We show that this property coupled with sub-additivity, guarantee the non-emptyness of the core of the game and of all its subgames, namely the game is totally balanced. E...

We consider the following guessing game: fix positive integers k, m, and n. Player A (“Ann”) chooses a (uniformly) random integer α from the set {1,2,3, . . . ,n}, but does not reveal α to Player B (“Gus”). Gus then presents Ann with a k-option multiple choice question about which number she chose, to which Ann responds truthfully. After m such questions have been asked, Gus must attempt to gue...