human
I am working on the file "Nature-Cooperation.ipynb".
The first task is:
Evolutionary Games
Two player games
\begin{align}
\dot{x_A} = x_A ~ [f_A(\vec{x}) - \phi ]\
\dot{x_B} = x_B ~ [f_B(\vec{x}) - \phi ]
\end{align}
\begin{align}
f_A(\vec{x}) = a~x_A+b~x_B\
f_B(\vec{x}) = c~x_A+d~x_B
\end{align}
Payoff matrix:
\begin{align}
\begin{pmatrix}
    a &  b \
    c &  d \
  \end{pmatrix}
\end{align}
In following demo you can determine values for $a, b, c$ and $d and see how their values change determine the outcome of the game. You can also run the demo with different number of players.
Can you write Python program for it?

What is a Python program to determine values for $a, b, c$ and $d and see how their values change determine the outcome of the game?
assistant
#Here is Python program to determine values for $a, b, c$ and $d and see how their values change determine the outcome of the game.

fig = plt.figure()
plt.close(fig)

def evolutionaryGame(x_,f,labels = None):
  np.random.seed(0)
  clear_output(wait=True)
  t_f = 10 
  dt = 0.1
  x_ = np.asarray(x_)
  x_ = np.atleast_2d(x_).T
  f = np.asarray(f)
  
  def int_(t,x):
    mean = x.T.dot(f.dot(x))
    dev = x*(f.dot(x)-mean)
    return dev

  integ = integrate.ode(int_)
  integ.set_integrator("dopri5").set_initial_value(np.asarray(x_))
  y = np.zeros((int(t_f/dt)+1,x_.shape[0]))
  x = np.zeros((int(t_f/dt)+1,x_.shape[0]))
  xdot = np.zeros((int(t_f/dt)+1,x_.shape[0]))

  i = 0
  while integ.successful() and integ.t<t_f:
    y[i,:] = integ.y[:,0]
    x[i,:] = integ.t
    xdot[i,:] = int_(integ.t,y[i,:])
    integ.integrate(integ.t+dt)
    i=i+1
    
  fig.clf()
  ax = fig.gca()
  with sns.color_palette("PuBuGn_d",n_colors=2):
    for ind_ in range(x.shape[1]):
      
      ax.plot(x[:,ind_], y[:,ind_], label="Type: %d" % (ind_+1) if labels is None else labels[ind_])
  
  ax.set_ylim(-0.1,1.1)
  ax.set_xlabel("time")
  ax.set_ylabel("Quasi specie")
  ax.legend(ncol=min(4,x.shape[1]))
  
  display(fig)

items_strat = [
  widgets.IntText(
    value=2,
    min=2,
    max=5.0,
    description="r",layout=widgets.Layout(width='50%', height='80px'))
  ,widgets.Button(
    description="submit")]

def _EvolutionaryGames(v):
  init = []
  payoff = []
  for ind_,obj in enumerate(objects_strat):
    if ind_ < len(objects_strat)-1:
      init.append(obj[0].value)
    else:
      if sum(init)>1:
        status_labelstrat.value = "Initial rates should sum to <1"
        return
      else:
        status_labelstrat.value = ""
      init.append(1-sum(init))
    rate_ = []
    for j in range(0,len(objects_strat)):
      rate_.append(obj[j+1].value)
    payoff.append(rate_)
  init = np.asarray(init)
  payoff = np.asarray(payoff)
  if len(objects_strat)==3:
    status_labelstrat.value = "Determinant: %.2f" % linalg.det(payoff)
  return evolutionaryGame(init,payoff)

objects_strat = []
status_labelstrat = None
box_vstrat = None

def call_back_mute(v):
  global...