Simulator of cultural rivalry

This repository is a mirror of my university project.

Introduction

The problem is inspired by the r/k selection theory. The main idea is to have two population where one has a higher growth rate and the other is a stronger competitor. This model is applied to agent interaction.

This environment models the process of cultural assimilation with asymmetric strategies. Agents here:

• are mortal. Each has an age attribute, measured in ticks of the simulation.
• move randomly in all directions.
• can breed. Fertility depends on the strategy.
• exchange messages. Every tick agent sends messages to all agents in close range. The message contains the culture value of the sender.
• have a culture attribute. It defines the agent's strategy and belonging to one of the populations. Acquires value from -100 for RED up to 100 for BLUE

RED - Have more children per individual (greater fertility factor).
BLUE - Have the ability to assimilate more efficiently (greater assimilation factor).

The application has two modes of operation:

• Gui mode - mode allows the user to follow simulation dynamics.
• Analysis mode - build the heatmap of the parameter space of the simulation.

Gui mode is the default when running the app via executable jar. Analysis can be started only with IDE. Mode switch with command-line flags TBA.

Example of simulation dynamics

RANDOM disposition for 15000 agents.

Rules of the simulation

Number of agents

There are a fixed number of agents per simulation run. During the run, their number remains constant according to these rules:

• every tick age increased by 1.
• agents die when their age gets bigger than TOTAL_STEPS_OF_LIFE.
• when the agent dies, a new agent with random culture and random age will spawn in a random location.
• when a new agent is born, a randomly selected agent will be wiped out from the board.

Such rules effectively mean that we see only a slice of the actual population, nevertheless, this slice is uniformly distributed, so it keeps a relative amount of agents on the board.

Movement of agents

• Agent picks a random direction and a random number of steps it will perform
• Repeat when the counter of chosen direction goes to zero.

The simulation board comes as a toroidal wrap space, so if an agent crosses the upper border, it will appear at the bottom (same for left and right). All distances between agents are calculated accordingly.

Reproduction of agents

The lifetime of the agents is separated into three equal sub-periods. During the mid-period agents can breed. Reproduction is driven by a normal distribution with the mean equal to the according fertility.

Message exchange

With each tick, an agent sends messages with its (sender's) culture level to all agents within communicationRadius. Since communicationRadius is the constant for the simulation run and is equal for all participants, message exchange between two agents is always mutual. An agent who receives the message slightly adjusts its (receiver's) culture level.

Messaging is the key part of the simulation. Two different approaches were tested:

• Receiving and sending agents adjust their culture to the average of both communicating parts. This strategy leads to the situation when all agents on the board gravitate towards the culture = 0, or it wipes out any population difference.
  This approach was rejected because it weakly corresponds to reality.

• Receiving agent adds some fraction of the sender's culture to its own. This creates an environment where in isolated areas, agents of the same population mutually push each other to more extreme values of the culture. This approach is applied in the simulation.

Analysis

Setup

The analysis explores the 2d parameter space:

• Assimilation factor - roughly speaking, it is the multiplier of how much BLUEs are more efficient at in inclining REDs on their side. Strictly speaking, it is the additional message multiplier for all agents whose culture is greater than 0.
• Fertility factor - the multiplier of how much faster do REDs reproduce than BLUEs. Here BLUE fertility is fixed at 1.5 and remains constant, so RED fertility is calculated as 1.5 * Fertility factor.

All parameters are set according to defaults unless otherwise explicitly specified. For clarifying: 1000 agent, 1500 ticks of the simulation (or five lifetimes of the agent, since one can live 300 ticks max)

Results

It is necessary to say that with an infinite amount of ticks to run, one of the population will inevitably take an irresistible advantage over the other. It is just a question of time. However, it does not mean the 'losing side' will become completely extinct since agents can appear with random culture. It means that the number of agents on the 'losing side' will be so small that they will never be able to recover above a few percent.

Analyse was performed for three different staring dispositions: HALF, CELLS, and RANDOM. For each disposition were built two(!) 60 by 60 heatmaps, and for each cell of the heatmap (do not mess with CELLS disposition) the simulation was run 10 times. The analysis is parallelized. On the Intel i7-8700 CPU, the full analysis took about 3 hours.

Two different types of heatmaps are necessary because of possible interpretation ambiguity.

• Left heatmap shows the normal average. Cell compute procedure:
  • take parameters according to the cell
  • run the simulation
  • compute the average culture level across all agents on the board
  • repeat 10 times
  • compute the average value across all simulation runs per cell. It will represent the result

The ambiguity lies in the interpretation of the white color. It can be interpreted as "both populations have an equal amount of agents after the simulation run" or "both populations finished 'winners' an equal number of times". Because of that second heatmap is needed.

• Right heatmap shows the absolute average. Cell compute procedure:
  • take parameters according to the cell
  • run the simulation
  • compute the average culture level across all agents on the board
  • take an absolute value from the previous step
  • repeat 10 times
  • compute the average value across all simulation runs per cell. It will represent the result

Thus right heatmap distinguishes the situation when at the end of the simulation both populations are equally represented (dark shade), or only one population 'wins' (light shade). We, however, cannot read from the right heatmap which one of the population 'won' (if any), so we need both heatmaps to clearly interpret the result.

Result heatmaps were post-processed with a Gaussian filter with sigma = 1.

Half mode

Here we can see the strict border between REDs and BLUEs with the noticeable dark region on the right map. If parameters are appropriately set, it is possible to keep the balance for at least five full generations. Otherwise, the REDs have a much larger area of the parameter space.

Cells mode

In this experiment, we can see that on the right map, the borderline is way less dark and that the same region on the left map diverges. It means that on the borderline situation not only collapses more frequently to one of the population, making the whole equilibrium even less stable, but that borderline itself is getting wider in comparison with the HALF disposition.

Another valid observation is that results with BLUEs 'winning' now take up more area of the parameter space.

Random mode

Here we see a continuation of the trend from the previous example. BLUEs now occupy more than a half of the parameter space, borderline diverges more explicitly and became more light on the right map, which means that at the extreme value of the parameter the simulation becomes totally chaotic, with a small or zero chance of predicting the result beforehand.

Conclusion

According to conducted experiments, the relation between the Assimilation factor and Fertility factor is not linear and depends on the starting disposition. More precisely, it depends on the contact boundary length between populations. Longer the contact boundary - the bigger chance for the BLUEs and vice versa. In a RANDOM disposition, contact boundary length is actually the maximum.

Because of that, in the run of the simulation, the following features can be distinguished, which, however, are not determined by the logic of the behavior of agents, but exclusively by their interaction.

• REDs are trying to minimize their contact zone with BLUEs in fact creating round compact areas where they can safely reproduce.
• Each lonely RED agent without a group will be assimilated and become a BLUE one.
• If the RED group was able to survive, it starts actively reproducing itself, consistently raising their relative numbers but staying in a compact area. When the relative number of BLUEs drops below a certain limit, REDs break out of their 'capsule' and occupy the hole board.
• If REDs was unable to cluster themselves into a group (the group was too small, the group did not have an optimally minimal contact zone) they will be assimilated by BLUEs.

One more conclusion is that with the growth of the parameters value, simulation becomes more chaotic and hard to predict. This relation is affected by the disposition as well. A greater contact zone leads to a more unpredictable result.

Possible extensions

Several ideas to extend the environment:

• Add the possibility of creating borders and/or gates on the simulation board. This meant to represent inter-district/interstate borders where crossing them is limited in one direction or both.
• Make a more precise simulation of humans adopting the near culture. Especially the observation that younger individuals are more tolerant of the cultural transition than their older parents. This aspect is currently ignored.

Codebase of the project

Project is posted on the faculty gitlab as cultural-darwinism-simulator

Appendix A - Parameters of the simulation

Name of parameter = default value. Constants are hyper-parameters.

The simulation board itself has the PLAYGROUND_SIZE = 100 parameter. All spatial modifiers (marked with *) are, in fact, fractions of the PLAYGROUND_SIZE.

DISPOSITION is starting the configuration of agents on the board. In all cases, starting the number of REDs and BLUEs are equal.

• RANDOM - age and culture are uniformly distributed
• HALF - the left half of the board is RED, right half is BLUE
• QUARTER - the board is divided into 4 alternating quadrants
• FOUR_LINES - the board is divided by 4 alternating vertical lines
• CELLS - the board is divided into 16 alternating quadrants
• CIRCLE - RED agents are located in the middle of the board and grouped into a circle.

Gui mode

Description	Parameter	Default value
Radius of the agent on the board*	AGENT_RADIUS	1.15
Agent's maximum lifetime	TOTAL_STEPS_OF_LIFE	300
Distance covered by agent in one tick*	distancePerStep	0.08
Radius of agent's communication*	communicationRadius	5
Culture multiplier in message exchange	messageFactor	0.001
Additional culture multiplier for BLUE	assimilationFactor	3
BLUE fertility	k_fertility	1.5
RED fertility	r_fertility	4.5

Analyser mode

Description	Parameter	Default value
Number of agents	NUMBER_OF_AGENTS	1000
Number of ticks per run	NUMBER_OF_STEPS	1500
Result heatmap resolution	GRANULARITY	2
Number of repeated runs per heatmap cell	NUMBER_OF_ROUNDS	4
Starting configuration of agents.	DISPOSITION	RANDOM