An analytic approach to competition dynamics

Abstract

Complex adaptive agents develop strategies in the presence of competition. In modern human societies, there is an inherent sense of locality when describing inter-agent dynamics because of its network structure. One then wonders whether the traditional advertising schemes which are globally publicized and target random individuals are as effective in attracting a larger portion of the population as those that take advantage of local neighbourhoods, like "word of mouth" marketing schemes. Here, we demonstrate using a differential equation model that schemes targeting local cliques within the network are more successful at gaining a larger share of the population than those that target users randomly at a global scale (e.g. television commercials, print ads, etc.). This suggests that success in the competition is not only dependent on the number of individuals in the population but also on how they are connected in the network. We further show that the model is general in nature by considering examples of competition dynamics, particularly those of business competition and language death.