# Can two arms-racing species be stabilized?

I am trying to build an evolution simulator in which there is group A and group B, each group has 9 members each generation. Each generation, each member of group A will enter a competition (in the form of combat) with a random member of group B, and fitness will be calculated based on how quickly and with how little losses will one member's army destroy the other. The best few members of each group then becomes the parents of the next generation.

(Note that an "individual" of each group is in fact a genetically determine neural network that controls a swarm of robots, think of it as a swarm of ants sharing the same DNA and thus can be effective consider one individual)

Will this end up with both group A and B having phenotype/strategy that do not change very much over many generations, or will it result in strategies that gradually changes throughout generation, with each successful, significant change out-smarting the opponent's old strategy until the opponent develop a counter strategy?

• "Each generation, each member of group A will enter a competition (in the form of combat) with a random member of group B, and fitness will be calculated based on how quickly and with how little losses will one member's army destroy the other." It is not clear what you mean here. You mentioned 9 individuals per group; then what comprises each individual's army? – sterid May 15 '17 at 3:12
• Question updated, to explain in short, an army is made of a swarm of identical robots controlled by said individual. – user289661 May 15 '17 at 13:34
• Consider adjusting your scenario: you are locking time-to-reproduce and you are only considering violence as a winning strategy. Small furry mammals are the best fit for their environments generally by being precocious breeders with massive litters. If you add these two axes, you may avoid the arms race. Consider also that eventually you will have more than two groups, but this will complicate the processing. – Yorik Jun 14 '17 at 15:05

To rephrase Cort Ammon. It depends on how you setup the system.

Imagine each combat strategy as a point on a landscape. Good strategies are on higher ground, poorer strategies are on lower ground.

A and B each have their own combat strategy and thus start at different points on this landscape. Mutations allow a species (say A) to explore the strategies around its starting point. Selection will cause the curtail that exploration.

If A find itself on a slop of a hill, selection (ie your combat and mating system) will cause the A population to drift upwards on this slop. However if A find itself on the peak of a small hill, it has no where else to go.

So how the scenario will play out will depend on the initial start conditions of population A and B. The mutation rate/genetic variability of the population (ie how many strategies population can explore around its initial strategy).

Additional factors is the genetic system that you have. If individuals of your species can only have one strategy (haploid), the species will be bound to its local hill. However if an individual can have more than one combat strategy at a time, (ie a diploid or gene duplication in RL), then the individual can have a combat strategy that work (local peak) and have a second strategy that is free to evolve... free to explore the landscape... going down valleys of bad strategies... and may eventually find the foot of a mountain... which a peak fitness higher than even the local peak it started.

Unfortunately, the answer to this varies greatly based on your individual implementations of the simulation.

Let's assume As are dominant at a given iteration. We can enumerate the genomes of B which can defeat A. With that, we can see how "close" B is to one of those genomes. If B is far enough from those "winning" genomes, it can be difficult for B to eventually overcome A.

Note I say difficult, rather than impossible. Eventually due to random chance B will eventually find the counter to what A is doing if we assume B gets to do this in a vacuum.

Remember that, while your individuals are "competing," its actually the populations that evolve. If your rules permit enough introspection of how B's operating, A may groom B into weakness. A may intentionally let a few of B's least fit individuals win a fight, for the expressed purpose of abusing your rules for the next-generation to make sure B remains unfit. Any B's which start looking interesting will get obliterated as fast as possible.

We actually do this with pest control. One known method of pest control is to leave one small corner of a field unprotected and spray the rest. Any insects which develop a resistance are likely to mate with the many insects that grew up on the sprayed corner, increasing the likelihood of those resistant genes getting diluted or even lost. This increases how long a farmer can use a given pesticide before having to increase its usage or switch to a new pesticide.

On the other hand, there are games where arms-racing species never stabilize. If you build a system based on the Chinese 5 Elements, the system is designed to encourage two entities to spin eternally on the cycle, never fully stabilizing unless you reach an overacting state (which is considered highly undesirable for both parties).

So it really depends what your particular rules do. Your rules could permit stability, or they could not.