Frequency Biased Imitation

We have made it possible to add frequency biased imitation to any simulation in DyPy. See the white paper (link on the homepage of the wiki) for how this is incorporated into the code. The parameters of interest are,

• bias_function : This is a user defined function of the frequencies of the strategies. Defaults to Nakahashi's function with a=1.
• bias_strength : This is the relative strength of individual versus conformist selection. 0<=bias_strength<=1 and default value is set to 0.0.
• bias_scale: The strength of conformist transmission. This can be thought of as the payoffs associated with a coordination game. bias_scale >= 0 and default value is set to 0.0.

bias_function has to be defined by the user in the get_expected_payoff method of the PayoffMatrix class in the payoff_matrix module. It is a function that determines the extent to which the frequency of a strategy influences the conformist bias.

bias_strength and bias_scale are Game arguments that can be specified while defining the game. For example if we were defining a Prisoners' Dilemma game,

class PrisonersDilemma(SymmetricNPlayerGame):
    DEFAULT_PARAMS = dict(R=3,S=0,T=5,P=1,bias_strength=0.2,bias_scale=2)
    STRATEGY_LABELS = ('Cooperate', 'Defect')
    EQUILIBRIA_LABELS=('Cooperation','Defection')

    def __init__(self,R,S,T,P,bias_strength,bias_scale):
        payoff_matrix = ((R,S),(T,P))
        super(PD, self).__init__(payoff_matrix,1,bias_strength,bias_scale) 

Since they are Game arguments, they can also be varied using the methods in the VariedGame class.