DOI: 10.5061/dryad.hhmgqnknz
title: Simulated results from an agent-based model examining inequality and innovation in social networks

description: 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.
description: 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.
description: # Innovation-Facilitating Networks Create Inequality
 [https://doi.org/10.5061/dryad.hhmgqnknz](https://doi.org/10.5061/dryad.hhmgqnknz) This is the repository for Moser & Smaldino (2023) "Innovation-Facilitating Networks Create Inequality". The manuscript is publicly available at [https://osf.io/preprints/socarxiv/n3hc6](https://osf.io/preprints/socarxiv/n3hc6). This repository contains all data analyzed in the study. The Python code for generating the data with an agent-based model, the R script for analysis, and CSVs containing real-world edge lists are in a separate GitHub repository, described below. **For assistance, please contact the corresponding author: Cody Moser ([cmoser2@ucmerced.edu](mailto:cmoser2@ucmerced.edu))** Recommended citation: Moser, C., & Smaldino, P.E (In press). Innovation-Facilitating Networks Create Inequality. *Proceedings of the Royal Society B: Biological Sciences.* ## Description of the Data The data are described in terms of what the dataset contains as well as which figures correspond to the respective CSV. **Primary Results** Variables common to these datasets: * *NumAgents* - Number of agents in the network * *ChangeLink* - Parameter setting for the probability of link alteration * *LinkStep* - Step after which link changes begin (should be set to 0 in all datasets) * *ProbDiff* - Parameter setting for the probability of diffusion of new inventions to neighbors * *Initial Path Length* - Initial path length of the network * *Path Length* - Final path length of the network, for cases with link changes * *Initial Clustering* - Initial clustering coefficient of the network * *Clustering* - Final clustering coefficient of the network, for cases with link changes * *Average Score* - The average innovation score of agents in the network * *Gini* - The Gini coefficient of the network * *Step* - The step at which the simulation ends * *Crossover* - Denotes whether the network successfully discovered the final innovation * *Incomplete* - Denotes if the network is an incomplete graph * *Iteration* - Denotes the iteration of the run, e.g. for 500 runs of the model, iterations should range 0-499 *Files* randowm.csv - Random networks with parameter sweeps on population size, edge probability, diffusion, and random link alteration. Ran to a maximum of 1000 steps. **Figures 2, 4A, S1, S7, S9; Tables S1, S2. Unique variable:** *ProbEdge* - Parameter setting for connectivity in generating the Erdos-Renyi random networks. caveman.csv - Caveman networks with parameter sweeps on clique size, clique count, diffusion, and random link alteration. Ran to a maximum of 1000 steps. **Figures 4A, S2, S6, S8; Tables S1, S2. Unique variables:** * *CliqueSize* - Parameter setting for the size of cliques in connected caveman networks; *CliqueNum* - Parameter setting for the number of cliques in connected caveman networks * ring.csv - Ring networks with parameter sweeps on population size, diffusion, and random link alteration. Ran to a maximum of 1000 step. **Figures 4A, S3; Tables S1, S2.** * realworld.csv - Real-world weighted and unweighted networks. Ran to a maximum of 1000 steps. **Figure 4A; Table 1.** **Unique variable:** *Network -* States which real-world network the graph was generated from * ExtendedRuns.csv- Random networks with parameter sweeps on population size and edge probability, holding diffusion and random link alteration constant. Ran to a maximum of 10,000 steps. **Figure 3.** **Unique variable:** *ProbEdge* - Parameter setting for connectivity in generating the Erdos-Renyi random networks * NewGini.csv & ChangeLinkGini.csv - Random networks with parameter sweeps on population size, edge probability, diffusion, and random link alteration. Ran to a maximum of 1000 steps. Gini coefficient in this dataset is computed based on a potion's rank rather than its score. **Figure S4.** **Unique variable:** *ProbEdge* - Parameter setting for connectivity in generating the Erdos-Renyi random networks **Additional Dynamics**: * PostCrossover.csv - Step-wise data from random networks with parameter sweeps on population size and edge probability, holding diffusion and random link alteration constant. Ran to a maximum of 1,000 steps in addition to 100 steps following crossover. **Figures 4, S5.** **Unique variables:** *ProbEdge* - Parameter setting for connectivity in generating the Erdos-Renyi random networks; *CrossStep* - Number of steps after Crossover has been attained. Should range 0-99. * AgentPosition_ModelVars.csv & AgentPosition_AgentVars.csv- End step data from random networks where, in addition to model performance, agent-level data is measured to assess the centrality of agents and their overall contribution to model performance. Ran to a maximum of 1,000 steps. **Figure 5.** **Unique model-level variables:** *prob_edge* - Parameter setting for connectivity in generating the Erdos-Renyi random networks. **Unique agent-level variables:** * SuccessRate.csv- Success rates at a 1,000 step maximum in the task based on the number of agents in ring, random, and caveman networks. **Table S2.** **Unique variables:** *SuccessRate -* Percent of networks which successfully discovered the final innovation within 1,000 steps; *Network* - Type of network **Missing Data Codes:** NA - Not applicable. For instances when the measure was not calculated. [] - Not calculated. For instances when the measure was not calculated *and* the simulation terminated. Generally found in incomplete networks, which terminate on the first step. ## Code/Software The Python code for running the agent-based model for generating the data, the R script for analyzing the data in this repository, and the CSVs containing the edge lists of the real-world networks are stored in the GitHub repository below: [https://github.com/cmoserj/Potions-Model](https://github.com/cmoserj/Potions-Model)