English

Twin relationships in Parsimonious Games: some results

Optimization and Control 2014-04-10 v1 Computer Science and Game Theory

Abstract

In a vintage paper concerning Parsimonious games, a subset of constant sum homogeneous weighted majority games, Isbell introduced a twin relationship based on transposition properties of the incidence matrices upon minimal winning coalitions of such games. A careful investigation of such properties allowed the discovery of some results on twin games presented in this paper. In detail we show that a) twin games have the same minimal winning quota and b) each Parsimonious game admits a unique balanced lottery on minimal winning coalitions, whose probabilities are given by the individual weights of its twin game.

Keywords

Cite

@article{arxiv.1404.2305,
  title  = {Twin relationships in Parsimonious Games: some results},
  author = {Flavio Pressacco and Giacomo Plazzotta and Laura Ziani},
  journal= {arXiv preprint arXiv:1404.2305},
  year   = {2014}
}