This work presents a study on the effects of different memory sizes in the Minority Game (MG) market model [Zhang, 1998]. We analyse the effects on an agent’s performance when this agent is endowed with a different memory size with respect to other agents in the game. Our aim is to identify in which situations a large or small memory might be advantageous in the game. From the obtained results ...

This paper introduces a new Ehrenfeucht-Fraı̈ssé type game that is played on two classes of models rather than just two models. This game extends and generalizes the known Ajtai-Fagin game to the case when there are several alternating (coloring) moves played in different models. The game allows Duplicator to delay her choices of the models till (practically) the very end of the game, making it ...

In a (1 : b) Maker-Breaker game, one of the central questions is to find the maximal value of b that allows Maker to win the game (that is, the critical bias b∗). Erdős conjectured that the critical bias for many Maker-Breaker games played on the edge set of Kn is the same as if both players claim edges randomly. Indeed, in many Maker-Breaker games, “Erdős Paradigm” turned out to be true. There...

a {em roman dominating function} on a graph $g = (v ,e)$ is a function $f : vlongrightarrow {0, 1, 2}$ satisfying the condition that every vertex $v$ for which $f (v) = 0$ is adjacent to at least one vertex $u$ for which $f (u) = 2$. the {em weight} of a roman dominating function is the value $w(f)=sum_{vin v}f(v)$. the roman domination number of a graph $g$, denoted by $gamma_r(g)$, equals the...

We consider a caching game in which a unit amount of infinitely divisible material is distributed among n ≥ 2 locations. A Searcher chooses how to distribute his search effort r about the locations so as to maximize the probability she will find a given minimum amount m̄ = 1−m ≤ r of the material. If the search effort yi invested by the Searcher in a given location i is at least as great as the ...

The classical positional game Box was introduced by Chvátal and Erdős in 1978 in their study of the biased connectivity game on the complete graph. Their analysis was subsequently extended by Hamidoune and Las Vergnas. The board of the Box game consists of elements of n disjoint sets (boxes), which might vary in size. The game is played by two players, Maker and Breaker. Maker claims m board el...

Pursuit-evasion games, such as the game of Revolutionaries and Spies, are a simplified model for network security. In the game we consider in this paper, a team of r revolutionaries tries to hold an unguarded meeting consisting of m revolutionaries. A team of s spies wants to prevent this forever. For given r and m, the minimum number of spies required to win on a graph G is the spy number σ(G,...

We introduce a new setting where a population of agents, each modelled by a finite-state system, are controlled uniformly: the controller applies the same action to every agent. The framework is largely inspired by the control of a biological system, namely a population of yeasts, where the controller may only change the environment common to all cells. We study a synchronisation problem for su...

Music plays in important role in human culture. This is also the case for exercise, games and exergames. In this study we examine the influence of previous game experience and the presence of music and sound on game performance and game experience. Sixteen students (12 males, 4 females; age: M = 24.8 years, SD = 3.4) played two exergames with and without sound and music. Game performance, game ...