def m1y_nash_optima(self, n, revenue):
rates = []
for la in np.linspace(la_min, la_max, points):
for mu in np.linspace(mu_min, mu_max, points):
model = HospitalWith1YM(la, mu, n, N_lim, t_c, revenue,
cost_transp + cost_op)
rates.append(
self.find_rate(model.game_matrix(), model.global_matrix()))
return np.average(np.nan_to_num(rates))
def m1y_nash_optima(self, n, revenue):
matches = 0
for la in np.linspace(la_min, la_max, points):
for mu in np.linspace(mu_min, mu_max, points):
model = HospitalWith1YM(la, mu, n, N_lim, t_c, revenue,
cost_transp + cost_op)
nash_equs = self.find_nash(model.game_matrix())
global_equs = self.global_solution(model.global_matrix())
if self.strategies_intersects(global_equs, nash_equs):
matches += 1
return matches / points / points
def find_base_rate(self, la, mu, n):
base_model = HospitalsModel(la, mu, n, N_lim, t_c)
equs = self.find_nash(base_model.game_matrix())
lambdas, times = base_model.lambdas_and_times()
rates = []
for eq in equs:
i = 0 if eq[0][0] == 1 else 1
j = 0 if eq[1][0] == 1 else 1
p_mort = HospitalWith1YM(la, mu, n, N_lim, t_c, revenue, cost_op +
cost_transp).p_mortality(times[i][j])
rates.append((1 - p_mort))
return np.average(np.nan_to_num(rates))
def find_solution(self, l, mu, n):
hospital = HospitalWith1YM(l, mu, n, N_lim, t_c, 2,
cost_transp + cost_op)
G = hospital.game_matrix()
A = self.extract_player_utility(G, 0)
B = self.extract_player_utility(G, 1)
game = nash.Game(A, B)
eqs = self.skip_mixed_strategy(game.support_enumeration())
if eqs and self.is_system_consistent(eqs, A, B):
sol = self.extract_solution(eqs)
return sol
else:
return 'Inconsistent'
def find_solution(self, l, mu, n):
hospital = HospitalWith1YM(l, mu, n, N_lim, t_c,
cost_transp + cost_op + 1,
cost_op + cost_transp)
G = hospital.game_matrix()
A = self.extract_player_utility(G, 0)
B = self.extract_player_utility(G, 1)
game = nash.Game(A, B)
eqs = list(game.support_enumeration())
if self.is_system_consistent(A, B, eqs):
sol = self.mixed_or_pure_solution_value(eqs)
return sol
else:
return 255, 255, 255
def line_plot(self, n, ax=None):
print('Computing for n = {}'.format(n))
data = {
'Lambda': [],
'Strategy': [],
'Proportion of cured patients': []
}
mu = (la_min + la_max) / 2
for la in np.linspace(la_min, la_max, 30):
global_matrix = HospitalWith1YM(la, mu, n, N_lim, t_c, 13, 13).global_matrix()
self.append_if_consistent(data, la, 'AA', global_matrix[0][0])
self.append_if_consistent(data, la, 'AR', global_matrix[0][1])
self.append_if_consistent(data, la, 'RA', global_matrix[1][0])
self.append_if_consistent(data, la, 'RR', global_matrix[1][1])
data = pd.DataFrame(data)
ax = sns.lineplot(x='Lambda', y='Proportion of cured patients', hue='Strategy', data=data, ax=ax)
if ax is not None:
ax.set_title('N = ' + str(n))
def global_matrix(self, la, mu, n):
model = HospitalWith1YM(la, mu, n, N_lim, t_c, 13, 13)
return model.global_matrix()