Effects of group size on goal-directed agents in distributed environments

A model is presented of a large number of decision-making agents, each of whom maintains a probability distribution for selecting from a set of strategies. The overall effect of these distributions is to cause a fraction of agents over time to select each strategy. An optimal fraction, or goal, exists for each strategy and it is assumed that the agents attempt to move toward the goals, by autonomously adjusting their own distributions. In a successful system, the agents reach equilibrium in their mixed strategies. However, due to the nature of the distributed environment, the agents perform the search process for equilibrium using aged information with respect to other agents probability distributions. A dynamical equation is derived and the analysis shows the group size and information delay that prevent the agents from reaching equilibrium. For large groups, this delay approaches a predictable asymptote implying that intelligent agents should maintain at least this level of communication