Language change: parameter exploration

Following the example set in the lecture, simulate a population of variational learners, obtaining the evolution (=history) of the average value of \(p\). Explore how variation in the following model parameters affects the population’s evolution. Use the Plots package to visualize your findings.

1. N: population size, i.e. the number of agents
2. p: the initial value of \(p\). Set this to the same value for each learner.
3. P1: probability of a string that only \(G_1\) can parse. Set this to the same value for each learner.
4. P2: probability of a string that only \(G_2\) can parse. Set this to the same value for each learner.
5. gamma: learning rate.

For the learning rate parameter, do both of the following:

1. First, set gamma to the same value for each learner.
2. In a second set of simulations, initialize your population so that each learner gets a randomly chosen gamma from the interval between 0 and 1.

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