Mathematically Modelling Collusion
This is a fascinating application of graph and network theory: modelling corporate inter-connectedness and measuring the influence of large corporations around the world:
A team of complex systems analysts created a map of how 40,000 transnational companies are connected to each other. Using quantitative factors (like amount of shares of company X held by company Y, and the economic relative strength of company X), the team developed a way to measure the influence a company exerts over another.
In addition to looking at individual companies, this measurement for the evaluation of the system as a whole in terms of equity and stability. The team found that a sub-network of 147 tightly knit companies exerted a disproportionate influence over the entire network. The high level of interconnectedness of this group concentrated power in the network, allowing this small group of less than 1% of the companies to effectively control 40% of the network.
An innovative application of mathematics to the fields of economics, politics, and social justice!