def lenient_boltzmannq(state, fitness):
temperature = 50
kappa = 1
#PD
#A = np.array([[ 5, 0],[10, 1]])
#MP
A = np.array([[5, 0], [10, 1]])
#RPS
#A = np.array([[0,-1,1],[1,0,-1],[-1,1,0]])
x = list()
y = list()
x.append(fitness[0])
x.append(1 - fitness[0])
y.append(fitness[1])
y.append(1 - fitness[1])
fitness_exploitation = list()
for i in range(len(fitness)):
term = 0
for j in range(len(fitness)):
term += A[i][j] * y[j] * (
math.pow(sum([y[k]
for k in range(2) if A[i][k] <= A[i][j]]), kappa)
- math.pow(sum([y[k] for k in range(2) if A[i][k] < A[i][j]]),
kappa)) / sum(
[y[k] for k in range(2) if A[i][k] == A[i][j]])
#j=1
#term1 = A[i][1] * y[1] * ( math.pow(sum([y[k] for k in range(2) if A[i][k] <= A[i][1]]),kappa) - math.pow(sum([y[k] for k in range(2) if A[i][k] < A[i][1]]),kappa)) / sum([y[k] for k in range(2) if A[i][k] == A[i][1]])
fitness_exploitation.append(term)
exploitation = (1. / temperature) * dynamics.replicator(
state, fitness_exploitation)
exploration = (np.log(state) - state.dot(np.log(state).transpose()))
return exploitation - state * exploration
def _q_learning_dynamics(composition, payoff, temperature):
r"""An equivalent implementation of `dynamics.boltzmannq`."""
return 1 / temperature * dynamics.replicator(composition, payoff) + \
composition * _sum_j_x_j_ln_x_j_over_x_i(composition)
def replicator(state, fitness):
return egt_dyn.replicator(state, fitness)