This paper introduces a class of coalitional games, called pillage games, as a model of Hobbesian anarchy. Any coalition can pillage, costlessly and with certainty, any less powerful coalition. Power is endogenous, so a pillage game does not have a characteristic function, but pillage provides a domination concept that defines a stable set, which represents an endogenous balance of power. Every...

In this study, we introduce and examine the Egalitarian property for some power indices on the class of simple games. This property means that after intersecting a game with a symmetric or anonymous game the difference between the values of two comparable players does not increase. We prove that the Shapley–Shubik index, the absolute Banzhaf index, and the Johnston score satisfy this property. ...

Cooperative behavior is often assumed to depend on individuals' characteristics, such as altruism and reasoning ability. Evidence is mixed about what the precise impact of these characteristics is, as the subjects of study are generally randomly paired, generating a heterogeneous mix of the two characteristics. In this study we ex-ante create four different groups of subjects by factoring their...

A dominating set D for a graph G is a subset of V (G) such that any vertex not in D has at least one neighbor in D. The domination number γ(G) is the size of a minimum dominating set in G. Vizing’s conjecture from 1968 states that for the Cartesian product of graphs G and H, γ(G)γ(H) ≤ γ(G H), and Clark and Suen (2000) proved that γ(G)γ(H) ≤ 2γ(G H). In this paper, we modify the approach of Cla...

No: 025-1796 POMS 23rd Annual Conference, Chicago, IL April 20 to April 23, 2011

Risk is a well-known turn based board game where the primary objective is nothing less than the world domination. Gameplay is based on battles between armies located in adjacent territories on the map of Earth. The combat’s outcome is decided by rolling dice, and therefore a probabilistic approach can be taken. Although several results are derived, the conclusions suggest that the gameplay is h...

a roman dominating function (rdf) on a graph g = (v,e) is defined to be a function satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. a set s v is a restrained dominating set if every vertex not in s is adjacent to a vertex in s and to a vertex in . we define a restrained roman dominating function on a graph g = (v,e) to be ...