changereligion.py: to ai

ai/changereligion.py

@@ -0,0 +1,148 @@
+#!/usr/bin/python3
+
+"""
+Copyright (c) 2016
+
+This file is part of free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This file is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public 
+License along with this file.  If not, see <http://www.gnu.org/licenses/>.
+"""
+
+import random
+import numpy as np
+
+import matplotlib.pyplot as plt
+plt.style.use('ggplot') # makes graphs pretty
+
+# initialisation 
+N = 100     # population size
+A = 65      # initial number of believers A
+B = N-A     # initial number of believers B
+
+
+MAX_TIME = 100
+t = 0               # initial time
+Ta = 1.0            # initial attractiveness of option A
+Tb = 2.0            # initial attractiveness of option B
+alpha = 0.1         # strength of the transmission process
+believersA = []    
+believersB = []
+
+believersA.append(A)
+believersB.append(B)
+
+
+def payoff(believers, Tx,Ty):
+    """ payoff is the interest of 'conversion' of believers from one option (religion) to another.
+        It depends on the current proportion between believers in the population.
+        And its attractiveness to believers (defined in the 'attractiveness' function).
+    """
+    proportionBelievers = (believers / N) 
+    attraction = (Tx) / (Ty + Tx)
+    return proportionBelievers * attraction
+
+def attractiveness(Ta, Tb):
+    """ attractiveness is a dynamically changing feature of each cultural option. 
+    The function is composed of the current value for each option (Ta, Tb)
+    and a small stochastic change defined by the function K
+    
+
+    ####### different options for modelling attractiveness  ########
+    # OPTION 1 - fixed attractiveness
+    """
+    Ka = 0.1
+    Kb = 0
+
+
+    Ta = Ta+Ka
+    Tb = Tb+Kb
+
+    return Ta, Tb
+
+
+def attractiveness2(Ta, Tb):   
+    """
+    # OPTION 2 - gaussian noise with strong tail (lognormal distribution)
+    """
+    Ka, Kb = np.random.normal(0, 1, 2)
+    diff = Ka-Kb
+    Ta += diff
+    Tb -= diff
+    return Ta, Tb
+
+
+def attractiveness3(Ta, Tb):
+    """
+    # OPTION 3 - anti-conformist behavior 
+    # sort of lotka-volterra where diff of attractiveness is negatively correlated with diff of populations
+    # we use gamma to add some stochasticity
+    """
+    Ka = 0
+    Kb = 0
+
+    diffPop = np.random.gamma(believersA[t], 1) - np.random.gamma(believersB[t], 1)
+    # if diffPop is negative it means that we have more believers of A than B
+    # so we have to promote Kb
+    if diffPop<0:
+        Ka = -diffPop
+
+    # else we should promote Ka        
+    else:
+        Kb = diffPop
+    # add 1 to avoid dividing by 0 if both are 0        
+    Ta += Ka
+    Tb += Kb
+
+    return Ta, Tb
+
+while t < MAX_TIME: 
+    """ Main loop. Repeat until stop condition is met.
+    1. define the current attractiveness of each option 
+    2. define proportion of population swithching from B to A and vice versa
+    3. calculate current numbers of practicioners of each option
+    4. output the numbers to two lists for plotting    
+    
+    """
+
+    # define the current attractiveness of each option
+    Ta, Tb = attractiveness2(Ta, Tb)
+
+    # calculate the change between believers A and B in the current time step       
+    variationBA = payoff(A, Ta, Tb)      
+    variationAB = payoff(B, Tb, Ta)     
+    difference = variationBA - variationAB
+
+    # B -> A
+    if difference> 0:
+        variation = difference*B
+    # A -> B        
+    else:
+        variation = difference*A
+
+    # control the pace of variation with alpha
+    variation = alpha*variation        
+    # update the population    
+    A = A + variation
+    B = B - variation
+
+    # save the values to a list for plotting    
+    believersA.append(A)
+    believersB.append(B)
+
+    # time = time + 1        
+    t+=1 
+
+# plot the results   
+plt.plot(believersA)
+plt.plot(believersB) 
+
+plt.show()