Theories of innovation often balance contrasting views that either smart people create smart things or smartly constructed institutions create smart things. While population models have shown factors including population size, connectivity and agent behaviour as crucial for innovation, few have taken the individual-central approach seriously by examining the role individuals play within their groups. To explore how network structures influence not only population-level innovation but also performance among individuals, we studied an agent-based model of the Potions Task, a paradigm developed to test how structure affects a group's ability to solve a difficult exploration task. We explore how size, connectivity and rates of information sharing in a network influence innovation and how these have an impact on the emergence of inequality in terms of agent contributions. We find, in line with prior work, that population size has a positive effect on innovation, but also find that large and small populations perform similarly per capita; that many small groups outperform fewer large groups; that random changes to structure have few effects on innovation in the task; and that the highest performing agents tend to occupy more central positions in the network. Moreover, we show that every network factor which improves innovation leads to a proportional increase in inequality of performance in the network, creating 'genius effects' among otherwise 'dumb' agents in both idealized and real-world networks.
Keywords: collective intelligence; cultural evolution; inequality; innovation; networks.