Networks are often modelled using tools from graph theory. For instance, a social network would be viewed as a directed or a not-directed graph. People would be the vertices of the graph and the relationships between them (friendships or acquaintances) the edges. Within the STATPHYSNETFORMGAME (The statistical physics of network formation games) project, scientists adopted a different modelling approach to how networks form. In the case of a social network, people would exercise discretion in forming their relationships rather than at random. The starting point for this game theoretic approach is to assume that individuals get payoffs that depend on the social network that emerges. They might tend to spend more effort or time in relationships that are more enjoyable and avoid ones that are less so. Different networks would lead to different outcomes. The STATPHYSNETFORMGAME team sought to describe how individuals change their opinion if their friends disagree from a game theoretic perspective. Preferences in the real world often depend on cultural differences as well as between urban and rural populations. Influencing each other's opinions was expected to create consensus on a local scale, but opinions remained uncorrelated over long distances. The scientists were successful in developing a new model of the sharp division between regions where two different opinions occur. In a very different setting, the scientists used the basic concepts and relevant tools of game theory to model mobile phone use in a developing country. They mapped the locations of base stations with respect to the population distribution and the number and duration of calls at each base station. The so-called cartogram that was developed allowed them to identify regions where the per capita base station density is significantly high or the network needs to be expanded. In other words, the findings could be used to improve the existing cellular network. Scientists also analysed the routes of cargo ships that arguably form the world's largest transport network. Based on data dating back to 1890, they derived the distribution of vessel calls and the number of ports with which each port was directly linked. The Gini coefficient, a measure of the statistical dispersion of port traffic was calculated and found to decrease over the study period. This result, revealing a tendency towards a polycentric distribution of cargo shipping, provides valuable guidance for future port expansions. By the end of STATPHYSNETFORMGAME, the scientists had started to work on magnetic resonance imaging data of the human brain using the same techniques applied to cargo shipping. The findings are expected to open the way towards a realistic model of brain functions.
Statistical physics, networks, graph theory, STATPHYSNETFORMGAME, game theory, statistical dispersion