spm.py

import math

def poisson(lmbd, k):
    
    return math.exp(-lmbd + k * math.log(lmbd) - math.lgamma(k+1))
    
def poisson_cumulative(lmbd, s):

    return sum([poisson(lmbd, k) for k in range(s+1)])
    
def mean_cost(lmbd, cr, u):

    return sum([cr * (u-v) * poisson(lmbd, v) for v in range(u+1)]) + 1.0 - poisson_cumulative(lmbd, u)
    
def get_gnuplot_data_game1(lmbd=5, cr=0.1, range=100):

    for u in range(range)
        j_1 = sum([cr * (u-v) * poisson(lmbd, v) for v in range(u+1)])
        j_2 = 1.0 - poisson_cumulative(lmbd, u)
        print('{} {} {} {}'.format(u, j_1, j_2, j_1 + j_2))
        
def get_gnuplot_data_game2(lmbd=5, cr=(0.1, 0.05, 0.001), range=100):

    for u in range(range):
        print('{} {}'.format(
            ' '.join([mean_cost(lmbd, c, u) for c in cr])
        ))