In search of efficient network structures: The needle in the haystack

The modelling of networks formation has recently became the object of an increasing interest in economics. One of the important issues raised in this literature is the one of networks efficiency. Nevertheless, for non trivial payoff functions, searching for efficient network structures turns out to be a very difficult analytical problem as well as a huge computational task, even for a relatively small number of agents. In this paper, we explore the possibility of using genetic algorithms (GA) techniques for identifying efficient network structures, because the GA have proved their power as a tool for solving complex optimization problems. The robustness of this method in predicting optimal network structures is tested on two simple stylized models introduced by Jackson and Wolinski (1996), for which the efficient networks are known over the whole state space of parameters values. We also show that this approach can provide new exploratory results for the linear-spatialized connections model of Johnson and Gilles (2000), in which the efficient allocation of bilateral connections is driven by contradictory forces that push either for a centralized structure around a coordinating agent, or for only locally and evenly distributed connections.