Modelling competition for space: Emergent inefficiency and inequality due to spatial self-organization among a group of crowd-avoiding agents

Competition for a limited resource is the hallmark of many complex systems, and often, that resource turns out to be the physical space itself. In this work, we study a novel model designed to elucidate the dynamics and emergence in complex adaptive systems in which agents compete for some spatially spread resource. Specifically, in the model, the dynamics result from the agents trying to position themselves in the quest to avoid physical crowding experienced locally. We characterize in detail the dependence of the emergent behavior of the model on the population density of the system and the individual-level agent traits such as the extent of space an agent considers as her neighborhood, the limit of occupation density one tolerates within that neighborhood, and the information accessibility of the agents about neighborhood occupancy. We show that the efficiency with which the agents utilize the physical space shows transitions at two values of densities. The first of these transitions demarcates efficient and inefficient phases of the system, and the second one signifies the density at which the inefficiency is maximum. We show that the variation of inefficiency with respect to the information accessible to the agents shows opposing behavior above and below this second transition density. We also look into the inequality of resource sharing in the model and show that although inefficiency can be a non-monotonic function of information depending upon the parameters of the model, inequality, in general, decreases with information. Our study sheds light on the role of competition, spatial constraints, and agent traits within complex adaptive systems, offering insights into their emergent behaviors.