As indicated, our model is based on the agent-based cellular automata studied in Heim et al. (2018). There, plots of land are discussed that consist of a combination of roads, and a combination of parcels for business houses and for family houses. Parcels/houses are uniquely associated with streets. Agents (owners of parcels) can be classified according to 3 dimensions: their sales strategy (“keep” vs. “sell”), their development strategy (“built up” vs “don’t build up”) and the urgency to implement them (sell/build: “now” vs. “later”), cf. Table 1 in Heim et al. (2018). Some of these agents just want to build houses for their families, others want to reduce building cost or intend to make business with selling parcels (Seller type) or with well-timed and available houses, whereas others, like Accumulators, intend to gather a number of connected parcels to build larger resorts. The simulations are initiated by providing a certain distribution of these agent types that are randomly dispersed over the plot such that all parcels are covered.
In order to study the impact of tribal structures, we forgo the simulation of build-up and focus solely on the formation of connected settlement blocks of their own tribe through swapping of parcels. Each agent is assigned a tribe and has the goal to get a parcel in the neighborhood of other members of his tribe. To measure the degree of this we use the tribe membership of the 24 parcels around the parcel (with suitable adoptions to parcels at or near the boundary of the plot). We implement two different strategies for the agents:
Strategy 1: Swapping of parcels between two agents of different tribes with the intention to move into a neighborhood that is occupied by more members of the same clan i.e. the surrounding 24 parcels as discussed above. This strategy is purely local and does not involve any communication on a global level.
Strategy 2: Each clan decides to have a dedicated center, e.g. in our case with four tribes each chooses separate corners of the quadratic plot. Using swapping of parcels between two agents each agent tries to get closer to their respective tribe center. I.e., that the Euclidean distance between the center of the previous parcel and the center of new parcel towards the corresponding corner is reduced. Whereas the earlier scenario is local in the sense that each agent tries to maximize their neighborhood, this scenario considers the effects of agreements or tribal members that impose a somewhat binding global strategy on each agent.
To understand how much effort is needed to counter the positive intention of the lottery to spatially mix the different tribes, we implemented as examples the following two scenarios.
Scenario 1: We use agent strategy 1 and distribute four clans in a 1:1:1:1 ratio randomly over the plot. Moreover, we assumed, in favor of the spatial mixing, that the fourth tribe (white) does not follow the idea of forming connected settlement blocks of its members and thus hinders the attempts of the remaining tribes.
Scenario 2: We use agent strategy 2 and distribute five clans in a 1:1:1:1:1 ratio. As before the last tribe stays at their given parcel.
For each scenario 100 Monte Carlo runs were performed in order to rule out statistical biases.Footnote 1 Each simulation works as follows. After the initialization phase the simulation runs of each scenario follow a tailored progression process:
For each parcel the percentage of own tribe neighbors is determined
Run randomly over all combinations of pairs of agents and determine whether the situation for both agents is better at the new parcel (i.e. more neighbors of the own tribe in the new neighborhood or closer to the tribe center)
If the situation is better for all involved agents, then the swapping is performed (in particular in scenario 2 there may be just two-agent interactions and parcel swaps where the third agent remains at their parcel)
Repeat these steps until there are no swaps at a phase (then a stationary situation is achieved).
Note that the situation may occur that—especially at tribe area boundaries—it may be mutually better for two agents to continuously swap their parcels. In these instances, the program terminates if only this type of swaps occurs.