# Spatial Agent-Based Model

In the agent-based simulation model, there are *R* regions and *M* raw resources that are (for the moment) ubiquitously available in all regions. In the present setup, each region hosts only one firm agent. Each firm agent has (1) a transformation repository, and (2) an artifact portfolio. Each agent starts with its own unique primitive transformation, whereby this transformation processes a uniform random combination of two raw resources. Each period of the simulation consists of two stages. In the first stage, all agents conduct transformation search. In the second stage, all agents seek to construct artifacts.

## Search Heuristics

Each agent has two search heuristics: (1) to construct an artifact, and (2) to ‘unlock’ more advanced transformations.

The *artifact search heuristic* starts from the most advanced transformation(s) in the agent’s transformation repository. A transformation that is inspected is feasible if each of the inputs required for that transformation are available. Operationally, the artifact construction heuristic recursively builds a tree of transformations, whereby less advanced transformations produce the input needed for more advanced transformations. Whenever a certain input is not available, e.g. it is not produced or it cannot be acquired (because the region of production is out of reach, for instance), the particular transformation is dismissed. If none of the transformations in the repository of a certain level of advancement is feasible, the agent continues with trying to construct artifacts using transformations that are one step less advanced, and so on. Once the agent has found the first artifact that is feasible, it will try to construct artifacts of similar level of advancedness and then stop. As such, an agent ends up with a portfolio of feasible products of the highest possible advancedness. An agent can acquire artifacts from agents in regions not further away than *m* regions away (i.e. at distance *m* regions at most). Consequently, an agent can use all the transformations owned by firms in those regions in trying to construct artifacts.

The *transformation search heuristic* selects, with probability p, ‘splitting search’ to investigate whether a single transformation splits into two, and with probability 1-p, ‘merging search’ to investigate whether two transformations can be combined into a new one. In ‘merging search’, the agent picks the first transformation (uniform randomly) from its own transformation repository and then, with probability q, from the transformation repository from a (uniform randomly) selected firm within distance *n > 0* and, with probability 1 - q, again from its own repository. In this work, we hence assume that agents know the underlying merging-splitting probability *p* and the progressive-conservative probability q. Whenever an agent conducts splitting search on a transformation that actually also splits in the blueprint, it will discover the two new transformations in the blueprint. Whenever an agent conducts merging search on two transformations that are actually also merged in the blueprint, it will discover that one new transformation. Note that, with probability *(1* -*p) q,* two agents combine transformations to try to ‘unlock’ a merged transformation in the blueprint. If they collaboratively ‘unlock’ one, both agents add the discovered transformation to their repository.

We assume that an agent does not seek to develop futuristic transformations, i.e. transformations that are more advanced than its most advanced artifact. We also assume that agents have a memory of which transformations they have tried to split and merge. So, in splitting transformation search, the agent will uniform randomly draw from not yet inspected, “non-futuristic” transformations. If it has tried to split all the non-futuristic transformations in its repository, it will conduct merging research regardless of the merging-splitting probability *p*. In merging search, the agent will randomly draw two unique, non-futuristic transformations that have not yet been inspected together.

## Cellular World of Regions

Both the input artifact and transformation search are spatially confined: artifacts can only be acquired of firms at most *m* regions away, and collaboration for transformation discovery can only be done with agents at most *n* regions away. We model the geographical world as a two-dimensional space composed of hexagonal cells, where each cell is either ‘sea’ or ‘land’. The land cells are the regions. In the present setup, each agent is located in a single land cell and can transport artifacts only over land cells and can only collaborate in research to unlock transformations with agents that can be reached over land cells. The land cells can now be spatially configured in different ways, e.g. a string of cells each with only one or two neighbors, a cluster of cells, or a circle of cells each with two neighbors, see Fig. 5.

Fig. 5 **Examples of the various configurations of cells, notably a circle, a string and a cluster, each consisting of six cells**