Simulated results from an agent-based model examining inequality and innovation in social networks

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 behavior 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, population size has a positive effect on innovation, but 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; and that the highest performing agents tend to occupy more central network positions. Moreover, we show that every network factor which facilitates innovation leads to a proportional increase in inequality of performance, creating "genius effects" among otherwise "dumb" agents in both idealized and real-world networks.

Methods
The data presented here were generated from an agent-based model of cultural innovation.

Each model is comprised of agents assembled as nodes on a network. The principle model dynamic is elaborated through pairs of agents (dyads) combining sets of items beginning from an initial inventory of six that each agent starts with. Each ideal network is unweighted, but several of the real-world networks (chimpanzee, baboon, and Agta hunter-gatherer) are weighted networks.

Items in each agent's inventory are initialized in an array containing two values: the name of the item and the item's score. In order to craft new items, three specific items must be combined between two agents. With the initial set of six items, there are two valid combinations which can be made: a combination of items a1, a2, and a3 or a combination of items b1, b2, and b3. These will form items 1a and 1b, respectively, which can be combined with items from the initial set in order to make further items. Agents select each item based on a probability calculated by dividing each specific item's score by the sum of the scores of all the items in the inventories. Because each novel item discovered is on another "tier" above the set of items used to create it and has a higher score, this creates path dependency in the model (agents are unlikely to go back and use older items in their inventory over new ones). There are four such "tiers" of items which can be discovered and combined and a fifth tier, which is formed by combining each of the two items on the two separate fourth tiers with one another. The specific scores and item combinations are seen in Fig. 1.

Each ideal network has a number of state variables which are manipulated. Random networks are initialized as Erdős–Rényi networks with the number of agents and critical edge probability as initial variables, ring networks are initialized with the number of agents as initial variables, and connected cavemen are initialized with the number of cliques and clique size as initial variables. Common to these network structures are the probability of diffusion (or the probability that each individual neighbor of an individual agent which discovers an item receives a new innovation when the focal agent discovers one) and the probability of link alteration, or the probability that each agent has one of its links removed and a new one added at the end of each step in the model.