Percolation-like behavior of some optimal coalition formation models

TL;DR

This paper studies coalition formation using a Potts glass model, revealing percolation-like phase transitions in the size of the largest coalition as a function of bond probability, with implications for social percolation.

Contribution

It introduces a novel application of an infinite-range Potts glass model to analyze coalition formation and identifies percolation-like behavior in the largest cluster size.

Findings

Largest cluster size exhibits percolation-like transition as a function of bond probability

Renormalization and optimization methods used to analyze finite systems

Discussion of implications for social percolation models

Abstract

The ground-state of an infinite-range Potts glass-type model with +/- J bonds and unrestricted number of states is used to investigate coalition formation. As a function of the q probability of +J bonds in the system it is found that the r relative size of the largest cluster (a cluster being the group of elements in the same state) shows a percolation like behavior. By a simple renormalization approach and several optimization methods we investigate the r(q) curves for finite systems sizes. Non-trivial consequences for social percolation problems are discussed.