Morality Metrics

Tyler Singer-Clark’s June 2014 paper, “Morality Metrics On Iterated Prisoner’s Dilemma Players” [Singer-Clark2014]), describes several interesting metrics which may be used to analyse IPD tournaments all of which are available within the ResultSet class. (Tyler’s paper is available here: http://www.scottaaronson.com/morality.pdf).

Each metric depends upon the cooperation rate of the players, defined by Tyler Singer-Clark as:

\[CR(b) = \frac{C(b)}{TT}\]

where C(b) is the total number of turns where a player chose to cooperate and TT is the total number of turns played.

A matrix of cooperation rates is available within a tournament’s ResultSet:

>>> import axelrod as axl
>>> players = [axl.Cooperator(), axl.Defector(),
...            axl.TitForTat(), axl.Grudger()]
>>> tournament = axl.Tournament(players)
>>> results = tournament.play()
>>> [[round(float(ele), 3) for ele in row] for row in results.normalised_cooperation]
[[1.0, 1.0, 1.0, 1.0], [0.0, 0.0, 0.0, 0.0], [1.0, 0.005, 1.0, 1.0], [1.0, 0.005, 1.0, 1.0]]

There is also a ‘good partner’ matrix showing how often a player cooperated at least as much as its opponent:

>>> results.good_partner_matrix
[[0, 10, 10, 10], [0, 0, 0, 0], [10, 10, 0, 10], [10, 10, 10, 0]]

Each of the metrics described in Tyler’s paper is available as follows (here they are rounded to 2 digits):

>>> [round(ele, 2) for ele in results.cooperating_rating]
[1.0, 0.0, 0.67, 0.67]
>>> [round(ele, 2) for ele in results.good_partner_rating]
[1.0, 0.0, 1.0, 1.0]
>>> [round(ele, 2) for ele in results.eigenjesus_rating]
[0.58, 0.0, 0.58, 0.58]
>>> [round(ele, 2) for ele in results.eigenmoses_rating]
[0.37, -0.37, 0.6, 0.6]