def find_nash(la, mu, n, print_matrix=False):
model = DispatcherAndHospitalsModel(la, mu, n, N_lim, t_c)
matrix = model.game_matrix(disp_strategies_number=2)
if print_matrix:
print(matrix)
game = GameWith3Players(matrix)
equs = game.find_pne_for_dispatcher_and_hospitals()
if is_inconsistent(equs, matrix):
return ['Inconsistent']
return equs
def find_solution(self, l, mu, n, disp_strategy_index):
hospital = DispatcherAndHospitalsModel(l, mu, n, N_lim, t_c)
G = hospital.game_matrix()[disp_strategy_index]
A = self.extract_player_utility(G, 1)
B = self.extract_player_utility(G, 2)
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 disp_regulation(n):
points = 10
matches = np.array([0] * 3)
for la in np.linspace(0.05, 5, points):
for mu in np.linspace(0.05, 5, points):
model = DispatcherAndHospitalsModel(la, mu, n, N_lim, t_c)
game_matrix = model.game_matrix()
global_matrix = model.global_average_time_matrix()
nash_equs = [find_nash(game_matrix, i) for i in range(3)]
global_equs = [find_global(global_matrix, i) for i in range(3)]
matches += intersection(nash_equs, global_equs)
return matches / ([points**2] * 3)
def find_nash(la, mu, n, print_matrix=False):
model = DispatcherAndHospitalsModel(la, mu, n, 3, 10)
matrix = model.game_matrix()
if print_matrix:
print(matrix)
text = "NFG 1 R \"Ambulance Dispatching Game\" { \"Dispatcher\" \"Hospital1\" \"Hospital2\" }\n\n"
text += "{ { \"N2\" \"N1\" }\n"
text += "{ \"A\" \"R\" }\n"
text += "{ \"A\" \"R\" }\n"
text += "}\n\"\"\n\n"
text += "{\n"
for k in range(2):
for j in range(2):
for i in range(2):
text += "{ \"\" %f, %f, %f }\n" % (matrix[i][j][k][0], matrix[i][j][k][2], matrix[i][j][k][2])
text += "}\n"
text += "1 2 3 4 5 6 7 8"
game = Game(text)
sol = game.findEquilibria('pne')
return extract_strategies_from_solutions(sol)
for dominated_strategy_payoff in dominated_strategies_payoff:
if dominate_strategy_payoff[
player_idx] < dominated_strategy_payoff[player_idx]:
return False
return True
def find_pne_for_dispatcher_and_hospitals(self):
equs = self.find_pure_nash_equ()
return sorted(
set([self.convert_strategy_idx_to_name(equ) for equ in equs]))
def convert_strategy_idx_to_name(self, str_indices):
disp_strategy = 'N2'
if str_indices[0] == 1:
disp_strategy = 'N1'
elif str_indices[0] == 2:
return 'BE'
hosp1_strategy = 'A' if str_indices[1] == 0 else 'R'
hosp2_strategy = 'A' if str_indices[2] == 0 else 'R'
return '{}-{}{}'.format(disp_strategy, hosp1_strategy, hosp2_strategy)
if __name__ == '__main__':
model = DispatcherAndHospitalsModel(2, 2, [2, 2], 5, 10)
matrix = model.game_matrix(2)
print(matrix)
game = GameWith3Players(matrix)
print(game.find_pne_for_dispatcher_and_hospitals())