Main task: Implementation of a specified EWA algorithm (for example reinforcement learning or
belief based learning) to simulate learning in iterated 2x2 games with Python and a statistical
evaluation of the results.
Definition: A simulation double sequence S(i,j) (1 ≤ i ≤ n); (1 ≤ j ≤ m) consists of n*m simulations with one
given game G in strategic normal form.
Solution Outline: You need to implement S(i, j)(1 ≤ i ≤ n); (1 ≤ i ≤ m).
For a fixed i* the simulation S(i*, j)(1 ≤ i ≤ m) looks like:
1. In the first period all parameter values need to be initialized.
2. For n simulations and m periods a given game G is played.
In each period j (1 ≤ j ≤ m)
-the players chose their strategy according to the EWA learning algorithm
-play the game
-update their strategic behavior (for example propensities) according to the EWA learning
-an output for each round is written into a csv file.
An example layout for the csv-file could look like this:
csv file viewed in Excel:
A Simulation S(i*, j)(1 ≤ i ≤ m) can be seen as one observation. That means all parameters (like initial
propensities) are the same in the first period S(i, 1)for all 1 ≤ i ≤ n. The statistic should be done at
least for one Simulation double sequences S(i, j)(1 ≤ i ≤ n) (1 ≤ i ≤ m).
The statistical analysis can be done with EXCEL, R, SPSS or any other statistical tool. The analysis
should give information about the distributions of relative frequencies of the chosen strategies.
The statistical analysis should contain at least a graphic representation of the distributions, mean,
standard deviation. Also time series of fix S(i*, j*) are welcome.
Hint 1: It is recommended to use the following data structure for 2x2 games:
Transform the game matrix
into a list [1,2,3,4,5,6,7,8]
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