company_employee_model.py

# Simple models of two competing firms bidding on employees                                                                                                                                                                                   
# Each employee is described in terms of k factors                                                                                                                                                                                            
# Company X knows about the x first factors                                                                                                                                                                                                   
# Company Y knows about the y first factors                                                                                                                                                                                                   

import numpy
from matplotlib import pyplot

n = 10000
k, x, y = 10, 5, 3

M = numpy.random.randn(n, k)
Mk = numpy.sum(M[:,:], axis=1) / k # Real value                                                                                                                                                                                               
Mx = numpy.sum(M[:,:x], axis=1) / x # How much is x willing to pay                                                                                                                                                                            
My = numpy.sum(M[:,:y], axis=1) / y # How much is y willing to pay                                                                                                                                                                            

cost = numpy.minimum(Mx, My) # How much was paid for each employee, because of auction                                                                                                                                                        
value = Mk
color = [['#aa2244', '#2244aa'][int(r)] for r in Mx > My] # blue if x won, red if y won                                                                                                                                                       

pyplot.figure(figsize=(10, 10))
pyplot.scatter(cost, value, marker='x', c=color, alpha=0.5)
pyplot.xlabel('Cost of hiring employee')
pyplot.ylabel('Value from employee')
pyplot.grid()
pyplot.xlim(-2, 2)
pyplot.ylim(-2, 2)
pyplot.savefig('there_is_no_trick.png', transparent=True)

print 'total value for x:', numpy.dot(Mx > My, value - cost)
print 'total value for y:', numpy.dot(My > Mx, value - cost)