Game theory – simulating the evolution of aggression
Source of work and inspiration from youtube by Primer. (It’s a great channel and I loved it for quite some time.)
The source introduced an experiment of evolution, simulated it on a computer, explained the non-intuitive results with game theory, and calculated the nash equilibrium, similar to how we did it in class.
The evolution focused on the action of aggression within a species. Every creature can go out and find food. Two creatures might find the same food. They can either be nice, share the food and both survive, or be aggressive and fight for the food. (See source for a more detailed description of the game)
When the population starts with only non-aggression and introduces aggression halfway, it is natural to find the number of aggression increases and non-aggression decrease – you get more food if you are aggressive. The biggest surprise for me in the simulation is that, if starting the entire population with only aggression and introducing non-aggressive behavior later on, the non-aggression count also increases.
The following graph is the simulation run on a computer. Left adding aggression at day 10, and right adding non-aggression at day 10.
This can be explained by the nash equilibrium that we learned in class. The exact calculation will be found at 10:04 of the source, but it’s trivial to see that the two equilibriums are (aggression, non-aggression) and (non-aggression, aggression). Since anyone would just be aggressive to get more food in (non-aggression, non-aggression) case, and two fighting does not benefit anyone in (aggression, aggression) case. In conclusion, it turns out that in this problem, the equilibrium is at 50/50, so when there’s more aggression, it’s better to play non-aggression, and when there’s more non-aggression, it’s better to play aggression!