14.10. Exercises¶
The code for this chapter is in the notebook chap14.ipynb in the repository for this book. Open the notebook, read the code, and run the cells. You can use this notebook to work on the following exercises.
Exercise 1: The simulations in this chapter depend on conditions and parameters that were chosen arbitrarily. As an exercise, you are encouraged to explore other conditions to see what effect they have on the results. Here are some suggestions:
Vary the initial conditions: instead of starting with all defectors, see what happens if you start with all cooperators, all TFT, or random agents.
In
Tournament.melee, we shuffle the agents at the beginning of each time step, so each agent plays against two randomly-chosen agents. What happens if you don’t shuffle? In that case, each agent plays against the same neighbors repeatedly. That might make it easier for a minority strategy to invade a majority, by taking advantage of locality.Since each agent only plays against two other agents, the outcome of each round is highly variable: an agent that would do well against most other agents might get unlucky during any given round, or the other way around. What happens if you increase the number of opponents each agent plays against during each round? Or what if an agent’s fitness at the end of each step is the average of its current score and its fitness at the end of the previous round?
The function used in
prob_survivalvaries from 0.7 to 0.9, so the least fit agent, with p=0.7, lives for 3.33 time steps on average, and the most fit agent lives for 10 time steps. What happens if you make the degree of differential survival more or less “aggressive”?We set
num_rounds= 6 so that each element of the genome has roughly the same impact on the outcome of a match. But that is substantially shorter than what Alexrod used in his tournaments. What happens if you increasenum_rounds? Note: if you explore the effect of this parameter, you might want to modifyNicenessto measure the niceness of the last 4 elements of the genome, which will be under more selective pressure asnum_roundsincreases.The given implementation has differential survival but not differential reproduction. What happens if you add differential reproduction?
Exercise 2: In the simulations, the population never converges to a state where a majority share the same, presumably optimal, genotype. There are two possible explanations for this outcome: one is that there is no optimal strategy, because whenever the population is dominated by a majority genotype, that condition creates an opportunity for a minority to invade; the other possibility is that the mutation rate is high enough to maintain a diversity of genotypes.
To distinguish between these explanations, try lowering the mutation rate to see what happens. Alternatively, start with a random population and run without mutation until only one genotype survives. Or run with mutation until the system reaches something like a steady state; then turn off mutation and run until there is only one surviving genotype. What are the characteristics of the genotypes that prevail in these conditions?
Exercise 3: The agents in the experiment are “reactive” in the sense that their choice during each round depends only on what the opponent did during previous rounds. Explore strategies that also take into account the agent’s past choices. These strategies can distinguish an opponent who retaliates from an opponent who defects without provocation.