def estimate_param(w, reputations):
# get number of bidders
n = reputations.size
# estimate lower and upper extremities
lower_extremities = np.array([(1-w)*r for r in reputations])
upper_extremities = np.array([(1-w)*r + w for r in reputations])
# estimate upper bound on bids
b_upper = upper_bound_bids(lower_extremities, upper_extremities)
# approximate
param = 1e-6
while True:
if param > 1e-4:
return None
try:
bids, costs = solve(w, reputations, param=param)
except Exception:
param += 1e-6
continue
# verify sufficiency
cdfs = []
for l,u in zip(lower_extremities, upper_extremities):
cdfs.append(stats.uniform(loc=l, scale=u-l))
step = len(bids) // 35
sampled_bids, best_responses = best_responses(costs, bids, b_upper, cdfs, step=step)
# calculate average error
errors = []
m = sampled_bids.shape[1]
for i in range(n):
error = 0
for b,br in zip(sampled_bids[i], best_responses[i]):
error += abs(b-br)
errors.append(error / m)
# Check if average is low for each bidder
if all([e < 1e-2 for e in errors]):
break
# Update param
param += 1e-6
return param
def solve(w, reputations):
# infer number of bidders
n = reputations.size
# compute an array of lower and upper extremities
lowers = np.empty(n, dtype=np.float)
uppers = np.empty(n, dtype=np.float)
for i in np.arange(n):
r = reputations[i]
lowers[i] = (1-w) * r
uppers[i] = (1-w) * r + w
# estimate the upper bound on bids
b_upper = upper_bound_bids(lowers, uppers)
# solve the system using EFSM method
bids, costs = efsm.solve(w, reputations)
# truncate solution derived by EFSM where k=n
min_i = np.argmin(np.absolute(np.copy(costs[-1]) - lowers[-1]))
initial = costs.T[min_i,:]
b_lower = bids[min_i]
length = bids.size - min_i
bids = bids[:min_i]
costs = costs[:,:min_i]
# solve the system for k = n using PPM method
coeffs = ppm.fit(initial, uppers, b_lower, b_upper)
bids_ = np.linspace(b_lower, b_upper, length)
def cost_func(lower, cs, b):
sums = sum([c*(b - b_lower)**i for c,i in zip(cs, range(1, len(cs)+1))])
return lower + sums
cost_funcs = [partial(cost_func, l, cs) for l,cs in zip(initial, coeffs)]
costs_ = np.array([[f(b) for b in bids_] for f in cost_funcs])
# combine results from both methods
bids = np.append(bids, bids_)
costs = np.hstack((costs, costs_))
return bids, costs
