fmtl (fairness-mediated team learning)

Simulation code for the paper "Evolutionary instability of selfish learning in repeated games" by Alex McAvoy, Julian Kates-Harbeck, Krishnendu Chatterjee, and Christian Hilbe. The details of these simulations may be found in the Methods section of the paper, available at http://arxiv.org/abs/2105.06199.

Instructions

To simulate, set parameters in simulate.m as desired and run

>> simulate

from the MATLAB command line. By default, the parameters are

% learning rules for X and Y. must be either 'FMTL' or 'SELFISH'
learning_rule_X = 'FMTL';
learning_rule_Y = 'SELFISH';

% payoffs [R, S, T, P] for the one-shot game
game_parameters = [1, -1, 2, 0]; %donation game with b = 2 and c = 1

% discounting factor for the repeated game
discounting_factor = 0.999;

% locality parameter for mutating strategies
s = 0.1;

% width parameter determining the balance between fairness and effciency
% when a learner uses FMTL
sig = 0.1;

% number of steps without an update for either learner before termination
convergence_threshold = 1e4;

% threshold needed before x>y is meaningful. in other words, x>y is true if
% and only if x>y+error_threshold.
error_threshold = 1e-12;

% total number of sample runs to be considered
max_samples = 1e5;

Games

The following values of [R, S, T, P] are example values for game_parameters.

Prisoner's Dilemma

[1, -1, 2, 0] (variant with 2P<S+T<2R)

[3, -1, 9, 0] (variant with S+T>2R)

[4, 0, 5, 3] (variant with S+T<2P)

Snowdrift Game

[3, 0, 4, -1] (variant with S+T<2R)

[3, 0, 9, -1] (variant with S+T>2R)

Stag Hunt Game

[5, 1, 4, 2] (variant with S+T>2P)

[4, 0, 3, 2] (variant with S+T<2P)

Hero Game

[1, 3, 2, 0]

Contact information

Please direct questions to Alex McAvoy (alexmcavoy@gmail.com) or Christian Hilbe (hilbe@evolbio.mpg.de).