def rbfgame_json(json):
"""Read an rbf game from json"""
utils.check(json['type'].split('.', 1)[0] == 'rbf', 'incorrect type')
base = rsgame.empty_json(json)
offsets = base.payoff_from_json(json['offsets'])
coefs = base.payoff_from_json(json['coefs'])
lengths = np.empty((base.num_strats, ) * 2)
for role, strats in json['lengths'].items():
for strat, pay in strats.items():
ind = base.role_strat_index(role, strat)
base.payoff_from_json(pay, lengths[ind])
profiles = [None] * base.num_strats
for role, strats in json['profiles'].items():
for strat, profs in strats.items():
ind = base.role_strat_index(role, strat)
profiles[ind] = np.stack(
[base.profile_from_json(p, verify=False) for p in profs])
alphas = [None] * base.num_strats
for role, strats in json['alphas'].items():
for strat, alph in strats.items():
ind = base.role_strat_index(role, strat)
alphas[ind] = np.array(alph)
sizes = np.fromiter( # pragma: no branch
(a.size for a in alphas), int, base.num_strats)
return _RbfGpGame(base.role_names, base.strat_names, base.num_role_players,
offsets, coefs, lengths, sizes, np.concatenate(profiles),
np.concatenate(alphas))
async def sample_payoffs(self, profile):
gu.check(self._is_open, "not open")
self._check_fetcher()
hprof = gu.hash_array(profile)
data = self._profiles.setdefault(
hprof, ([0], [0], [0], [None], asyncio.Queue()))
scheduled, _, claimed, prof_id, pays = data
claimed[0] += 1
if scheduled[0] < claimed[0]:
scheduled[0] += self._simult_obs
async with self._sched_lock:
for _ in range(self._simult_obs):
await self._scheduled.acquire()
pid = prof_id[0]
if pid is not None:
await self._sched.remove_profile(pid)
assignment = self._game.profile_to_repr(profile)
prof_id[0] = (await
self._sched.add_profile(assignment,
scheduled[0]))["id"]
if pid is None:
self._prof_ids[prof_id[0]] = data
pay = await pays.get()
self._check_fetcher()
return pay
def parse_index_spec(game, spec):
"""Parse restriction index specification"""
rest = np.zeros(game.num_strats, bool)
rest[list(map(int, spec.split(',')))] = True
utils.check(game.is_restriction(rest),
'"{}" does not define a valid restriction', spec)
return rest
def dump(game, filelike):
"""Dump game to gambit file"""
utils.check(game.is_complete(), 'gambit games must be complete')
game = matgame.matgame_copy(game)
filelike.write('NFG 1 R "gameanalysis game"\n{ ')
for role in game.role_names:
filelike.write('"')
filelike.write(role.replace('"', '\\"'))
filelike.write('" ')
filelike.write('}\n{\n')
for strats in game.strat_names:
filelike.write(' { ')
for strat in strats:
filelike.write('"')
filelike.write(strat.replace('"', '\\"'))
filelike.write('" ')
filelike.write('}\n')
filelike.write('}\n\n{\n')
perm = tuple(range(game.num_roles - 1, -1, -1)) + (game.num_roles, )
pays = np.transpose(game.payoff_matrix(), perm)
for outcome in pays.reshape((-1, game.num_roles)):
filelike.write(' { "" ')
filelike.write(', '.join(map(str, outcome)))
filelike.write(' }\n')
filelike.write('}\n1')
for i in range(2, game.num_profiles + 1):
filelike.write(' ')
filelike.write(str(i))
async def aopen(self): # pylint: disable=too-many-locals
"""Open the eosched"""
gu.check(not self._is_open, "already open")
try:
game = await self._api.get_game(self._game_id)
obs = await game.get_observations()
gu.check(
rsgame.empty_copy(self._game) == rsgame.empty_json(obs),
"egtaonline game didn't match specified game",
)
conf = dict(obs.get("configuration", ()) or ())
profiles = obs.get("profiles", ()) or ()
# Parse profiles
num_profs = len(profiles)
num_pays = 0
for jprof in profiles:
pid = jprof["id"]
prof, spays = self._game.profsamplepay_from_json(jprof)
spays.setflags(write=False)
hprof = gu.hash_array(prof)
pays = asyncio.Queue()
num_spays = len(spays)
num_pays += num_spays
for pay in spays:
pays.put_nowait(pay)
data = ([num_spays], [num_spays], [0], [pid], pays)
self._profiles[hprof] = data
self._prof_ids[pid] = data
logging.info(
"found %d existing profiles with %d payoffs in game %d",
num_profs,
num_pays,
self._game_id,
)
# Create and start scheduler
self._sched = await obs.create_generic_scheduler(
"egta_" + eu.random_string(20),
True,
self._obs_memory,
self._obs_time,
self._simult_obs,
1,
conf,
)
logging.warning(
"created scheduler %d for running simulations of game %d: "
"https://%s/generic_schedulers/%d",
self._sched["id"],
self._game_id,
self._api.domain,
self._sched["id"],
)
self._fetcher = asyncio.ensure_future(self._fetch())
self._is_open = True
except Exception as ex:
await self.aclose()
raise ex
return self
def open(self):
"""Open the zip scheduler"""
utils.check(not self._is_open, "can't be open")
try:
self._num = 0
self._sim_dir = tempfile.TemporaryDirectory()
self._prof_dir = tempfile.TemporaryDirectory()
with zipfile.ZipFile(self.zipf) as zfil:
zfil.extractall(self._sim_dir.name)
sim_files = [
d for d in os.listdir(self._sim_dir.name)
if d not in {"__MACOSX"}
]
utils.check(
len(sim_files) == 1,
"improper zip format, only one file should exist in root",
)
self._sim_root = os.path.join(self._sim_dir.name, sim_files[0])
os.chmod(os.path.join(self._sim_root, "script", "batch"), 0o700)
with open(os.path.join(self._sim_root, "defaults.json")) as fil:
self._base["configuration"] = json.load(fil).get(
"configuration", {})
self._base["configuration"].update(self.conf)
self._is_open = True
except Exception as ex:
self.close()
raise ex
def neighbor_json(json):
"""Read neighbor game from json"""
utils.check(
json['type'].split('.', 1)[0] == 'neighbor', 'incorrect type')
return _NeighborDeviationGame(
gamereader.loadj(json['model']),
num_neighbors=json.get('neighbors', json.get('devs', None)))
def rock_paper_scissors(win=1, loss=-1):
"""Return an instance of rock paper scissors"""
if isinstance(win, abc.Iterable):
win = list(win)
else:
win = [win] * 3
if isinstance(loss, abc.Iterable):
loss = list(loss)
else:
loss = [loss] * 3
utils.check(
all(l < 0 for l in loss) and all(w > 0 for w in win) and len(loss) == 3
and len(win) == 3,
'win must be greater than 0 and loss must be less than zero')
profiles = [[2, 0, 0],
[1, 1, 0],
[1, 0, 1],
[0, 2, 0],
[0, 1, 1],
[0, 0, 2]]
payoffs = [[0., 0., 0.],
[loss[0], win[0], 0.],
[win[1], 0., loss[1]],
[0., 0., 0.],
[0., loss[2], win[2]],
[0., 0., 0.]]
return paygame.game_names(['all'], 2, [['paper', 'rock', 'scissors']],
profiles, payoffs)
def dump(game, filelike):
"""Dump game to gambit file"""
utils.check(game.is_complete(), 'gambit games must be complete')
game = matgame.matgame_copy(game)
filelike.write('NFG 1 R "gameanalysis game"\n{ ')
for role in game.role_names:
filelike.write('"')
filelike.write(role.replace('"', '\\"'))
filelike.write('" ')
filelike.write('}\n{\n')
for strats in game.strat_names:
filelike.write(' { ')
for strat in strats:
filelike.write('"')
filelike.write(strat.replace('"', '\\"'))
filelike.write('" ')
filelike.write('}\n')
filelike.write('}\n\n{\n')
perm = tuple(range(game.num_roles - 1, -1, -1)) + (game.num_roles,)
pays = np.transpose(game.payoff_matrix(), perm)
for outcome in pays.reshape((-1, game.num_roles)):
filelike.write(' { "" ')
filelike.write(', '.join(map(str, outcome)))
filelike.write(' }\n')
filelike.write('}\n1')
for i in range(2, game.num_profiles + 1):
filelike.write(' ')
filelike.write(str(i))
def aggfn_json(json): # pylint: disable=too-many-locals
"""Read an Aggfn from json
Json versions of the game will generally have 'type': 'aggfn...' in them,
but as long as the proper fields exist, this will succeed."""
base = rsgame.empty_json(json)
_, version = json.get('type', '.3').split('.', 1)
utils.check(version == '3',
'parsing versions below 3 is currently unsupported')
num_functions = len(json['function_tables'])
function_inputs = np.empty((base.num_strats, num_functions), bool)
action_weights = np.empty((num_functions, base.num_strats))
function_table = np.empty((num_functions, ) +
tuple(base.num_role_players + 1))
offsets = np.empty(base.num_strats)
base.payoff_from_json(json.get('offsets', {}), offsets)
for inps, jinps in zip(function_inputs.T, json['function_inputs']):
base.restriction_from_json(jinps, inps, verify=False)
for weights, jweights in zip(action_weights, json['action_weights']):
base.payoff_from_json(jweights, weights)
function_table.fill(0)
for table, jtable in zip(function_table, json['function_tables']):
for elem in jtable:
copy = elem.copy()
value = copy.pop('value')
table[tuple(int(i) for i in base.role_from_json(copy))] = value
return aggfn_replace(base, action_weights, function_inputs, function_table,
offsets)
def __init__(self, model_game):
super().__init__(model_game.role_names, model_game.strat_names,
model_game.num_role_players)
utils.check(
model_game.is_complete(),
'deviation models must be complete games')
self.model = model_game
def parse_sorted(red, game):
"""Parser reduction input for roles in sorted order"""
players = red.split(',')
utils.check(
len(players) == game.num_roles,
'Must input a reduced count for every role')
return np.fromiter(map(int, players), int, len(players))
def reduce_game(full_game, red_players):
"""Reduce a game using hierarchical reduction
Parameters
----------
full_game : Game
The game to reduce.
red_players : ndarray-like
The reduced number of players for each role. This will be coerced
into the proper shape if necessary.
"""
red_game = rsgame.empty_names(full_game.role_names, red_players,
full_game.strat_names)
utils.check(np.all(red_game.num_role_players > 0),
'all reduced players must be greater than zero')
utils.check(
np.all(full_game.num_role_players >= red_game.num_role_players),
'all full counts must not be less than reduced counts')
if full_game.is_empty():
return red_game
elif full_game.num_profiles < red_game.num_all_profiles:
profiles = full_game.profiles()
payoffs = full_game.payoffs()
else:
profiles = expand_profiles(full_game, red_game.all_profiles())
payoffs = full_game.get_payoffs(profiles)
valid = ~np.all(np.isnan(payoffs) | (profiles == 0), 1)
profiles = profiles[valid]
payoffs = payoffs[valid]
red_profiles, mask = _common.reduce_profiles(
full_game, red_game.num_role_players[None], profiles)
return paygame.game_replace(red_game, red_profiles, payoffs[mask])
def rbfgame_json(json):
"""Read an rbf game from json"""
utils.check(json['type'].split('.', 1)[0] == 'rbf', 'incorrect type')
base = rsgame.empty_json(json)
offsets = base.payoff_from_json(json['offsets'])
coefs = base.payoff_from_json(json['coefs'])
lengths = np.empty((base.num_strats,) * 2)
for role, strats in json['lengths'].items():
for strat, pay in strats.items():
ind = base.role_strat_index(role, strat)
base.payoff_from_json(pay, lengths[ind])
profiles = [None] * base.num_strats
for role, strats in json['profiles'].items():
for strat, profs in strats.items():
ind = base.role_strat_index(role, strat)
profiles[ind] = np.stack([
base.profile_from_json(p, verify=False) for p in profs])
alphas = [None] * base.num_strats
for role, strats in json['alphas'].items():
for strat, alph in strats.items():
ind = base.role_strat_index(role, strat)
alphas[ind] = np.array(alph)
sizes = np.fromiter( # pragma: no branch
(a.size for a in alphas), int, base.num_strats)
return _RbfGpGame(
base.role_names, base.strat_names, base.num_role_players, offsets,
coefs, lengths, sizes, np.concatenate(profiles),
np.concatenate(alphas))
def mix(agame0, agame1, prob):
"""Mix two async games"""
utils.check(
rsgame.empty_copy(agame0) == rsgame.empty_copy(agame1),
"games must have identically structure",
)
return _MixedAsyncGame(agame0, agame1, prob)
def __init__(self, model, num_samples=100):
super().__init__(model)
utils.check(num_samples > 0, 'num samples must be greater than 0')
# TODO It might be interesting to play with a sample schedule, i.e.
# change the number of samples based off of the query number to
# deviation payoffs (i.e. reduce variance as we get close to
# convergence)
self.num_samples = num_samples
def __init__(self, model, num_samples=100):
super().__init__(model)
utils.check(num_samples > 0, 'num samples must be greater than 0')
# TODO It might be interesting to play with a sample schedule, i.e.
# change the number of samples based off of the query number to
# deviation payoffs (i.e. reduce variance as we get close to
# convergence)
self.num_samples = num_samples
def trace_interpolate(game0, game1, peqs, eqa, targets, **kwargs): # pylint: disable=too-many-locals
"""Get an equilibrium at a specific time
Parameters
----------
game0 : RsGame
The game to get data from when the mixture probability is 0.
game1 : RsGame
The game to get data from when the mixture probability is 1.
peqs : [float]
A parallel list of probabilities for each equilibria in a continuous
trace.
eqa : [eqm]
A parallel list of equilibria for each probability representing
continuous equilibria for prob mixture games.
targets : [float]
The probabilities to compute an equilibria at.
kwargs : options
The same options as `trace_equilibrium`.
"""
peqs = np.asarray(peqs, float)
eqa = np.asarray(eqa, float)
targets = np.asarray(targets, float)
# Make everything sorted
if np.all(np.diff(peqs) <= 0):
peqs = peqs[::-1]
eqa = eqa[::-1]
order = np.argsort(targets)
targets = targets[order]
utils.check(np.all(np.diff(peqs) >= 0),
'trace probabilities must be sorted')
utils.check(peqs[0] <= targets[0] and targets[-1] <= peqs[-1],
'targets must be internal to trace')
result = np.empty((targets.size, game0.num_strats))
scan = zip(utils.subsequences(peqs), utils.subsequences(eqa))
(pi1, pi2), (eqm1, eqm2) = next(scan)
for target, i in zip(targets, order):
while target > pi2:
(pi1, pi2), (eqm1, eqm2) = next(scan)
(*_, pt1), (*_, eqt1) = trace_equilibrium( # pylint: disable=too-many-star-expressions
game0, game1, pi1, eqm1, target, **kwargs)
(*_, pt2), (*_, eqt2) = trace_equilibrium( # pylint: disable=too-many-star-expressions
game0, game1, pi2, eqm2, target, **kwargs)
if np.isclose(pt1, target) and np.isclose(pt2, target):
mixgame = rsgame.mix(game0, game1, target)
_, _, result[i] = min(
(regret.mixture_regret(mixgame, eqt1), 0, eqt1),
(regret.mixture_regret(mixgame, eqt2), 1, eqt2))
elif np.isclose(pt1, target):
result[i] = eqt1
elif np.isclose(pt2, target):
result[i] = eqt2
else: # pragma: no cover
raise ValueError('ode solving failed to reach prob')
return result
def translate(profiles, rest):
"""Translate a strategy object to the full game"""
utils.check(profiles.shape[-1] == rest.sum(),
'profiles must be valid for the restriction')
if rest.all():
return profiles
new_profs = np.zeros(profiles.shape[:-1] + (rest.size, ), profiles.dtype)
new_profs[..., rest] = profiles
return new_profs
def reduce_game(full_game, red_players): # pylint: disable=too-many-locals
"""Reduce a game using deviation preserving reduction
Parameters
----------
full_game : Game
The game to reduce.
red_players : ndarray-like
The reduced number of players for each role. This will be coerced
into the proper shape if necessary.
"""
red_game = rsgame.empty_names(full_game.role_names, red_players,
full_game.strat_names)
utils.check(
np.all((red_game.num_role_players > 1)
| (full_game.num_role_players == 1)),
'all reduced players must be greater than zero')
utils.check(
np.all(full_game.num_role_players >= red_game.num_role_players),
'all full counts must not be less than reduced counts')
if full_game.is_empty():
return red_game
elif full_game.num_profiles < red_game.num_all_dpr_profiles:
full_profiles = full_game.profiles()
full_payoffs = full_game.payoffs()
else:
full_profiles = expand_profiles(full_game, red_game.all_profiles())
full_payoffs = full_game.get_payoffs(full_profiles)
valid = ~np.all(np.isnan(full_payoffs) | (full_profiles == 0), 1)
full_profiles = full_profiles[valid]
full_payoffs = full_payoffs[valid]
# Reduce
red_profiles, red_inds, full_inds, strat_inds = _reduce_profiles(
red_game, full_profiles, True)
if red_profiles.size == 0: # Empty reduction
return red_game
# Build mapping from payoffs to reduced profiles, and use bincount
# to count the number of payoffs mapped to a specific location, and
# sum the number of payoffs mapped to a specific location
cum_inds = red_inds * full_game.num_strats + strat_inds
payoff_vals = full_payoffs[full_inds, strat_inds]
red_payoffs = np.bincount(cum_inds, payoff_vals,
red_profiles.size).reshape(red_profiles.shape)
red_payoff_counts = np.bincount(
cum_inds, minlength=red_profiles.size).reshape(red_profiles.shape)
mask = red_payoff_counts > 1
red_payoffs[mask] /= red_payoff_counts[mask]
unknown = (red_profiles > 0) & (red_payoff_counts == 0)
red_payoffs[unknown] = np.nan
valid = ~np.all((red_profiles == 0) | np.isnan(red_payoffs), 1)
return paygame.game_replace(red_game, red_profiles[valid],
red_payoffs[valid])
def is_pure_profile(game, prof):
"""Returns true of the profile is pure"""
# For an asymmetric game, this will always return false, but then it
# shouldn't be an issue, because pure strategy regret will be more
# informative.
pure = np.any(np.add.reduceat(prof, game.role_starts) > 1.5)
utils.check(
game.is_profile(np.asarray(prof, int)) if pure else
game.is_mixture(prof), 'profile must be valid')
return pure
def nngame_train( # pylint: disable=too-many-arguments,too-many-locals
game,
epochs=100,
layer_sizes=(32, 32),
dropout=0.2,
verbosity=0,
optimizer='sgd',
loss='mean_squared_error'):
"""Train a neural network regression model
This mostly exists as a proof of concept, individual testing should be done
to make sure it is working sufficiently. This API will likely change to
support more general architectures and training.
"""
utils.check(layer_sizes, 'must have at least one layer')
utils.check(0 <= dropout < 1, 'dropout must be a valid probability')
# This is for delayed importing inf tensor flow
from keras import models, layers
model = models.Sequential()
lay_iter = iter(layer_sizes)
model.add(
layers.Dense(next(lay_iter),
input_shape=[game.num_strats],
activation='relu'))
for units in lay_iter:
model.add(layers.Dense(units, activation='relu'))
if dropout:
model.add(layers.Dropout(dropout))
model.add(layers.Dense(1, activation='sigmoid'))
regs = []
offsets = np.empty(game.num_strats)
scales = np.empty(game.num_strats)
for i, profs, pays in _dev_profpay(game):
# XXX Payoff normalization specific to sigmoid. If we accept alternate
# models, we need a way to compute how to potentially normalize
# payoffs.
min_pay = pays.min()
offsets[i] = min_pay
max_pay = pays.max()
scale = 1 if np.isclose(max_pay, min_pay) else max_pay - min_pay
scales[i] = scale
reg = models.clone_model(model)
reg.compile(optimizer=optimizer, loss=loss)
reg.fit(profs, (pays - min_pay) / scale,
epochs=epochs,
verbose=verbosity)
regs.append(reg)
return _DevRegressionGame(game, tuple(regs), offsets, scales,
game.min_strat_payoffs(),
game.max_strat_payoffs(),
np.ones(game.num_strats, bool))
def min_regret_profile(game):
"""Finds the profile with the confirmed lowest regret
An error will be raised if there are no profiles with a defined regret.
"""
utils.check(not game.is_empty(), 'Game must have a profile')
reg, _, prof = min(
(_nan_to_inf(regret.pure_strategy_regret(game, prof)), i, prof)
for i, prof in enumerate(game.profiles()))
utils.check(not np.isinf(reg), 'No profiles had valid regret')
return prof
def min_regret_profile(game):
"""Finds the profile with the confirmed lowest regret
An error will be raised if there are no profiles with a defined regret.
"""
utils.check(not game.is_empty(), 'Game must have a profile')
reg, _, prof = min(
(_nan_to_inf(regret.pure_strategy_regret(game, prof)), i, prof)
for i, prof in enumerate(game.profiles()))
utils.check(not np.isinf(reg), 'No profiles had valid regret')
return prof
def translate(profiles, rest):
"""Translate a strategy object to the full game"""
utils.check(
profiles.shape[-1] == rest.sum(),
'profiles must be valid for the restriction')
if rest.all():
return profiles
new_profs = np.zeros(
profiles.shape[:-1] + (rest.size,), profiles.dtype)
new_profs[..., rest] = profiles
return new_profs
def _dev_profpay(game):
"""Iterate over deviation profiles and payoffs"""
sgame = paygame.samplegame_copy(game)
profiles = sgame.flat_profiles()
payoffs = sgame.flat_payoffs()
for i, pays in enumerate(payoffs.T):
mask = (profiles[:, i] > 0) & ~np.isnan(pays)
utils.check(mask.any(), "couldn't find deviation data for a strategy")
profs = profiles[mask]
profs[:, i] -= 1
yield i, profs, pays[mask]
def compress_profile(self, profile):
"""Compress profile in array of ints
Normal profiles are an array of number of players playing a strategy.
Since matrix games always have one player per role, this compresses
each roles counts into a single int representing the played strategy
per role.
"""
utils.check(self.is_profile(profile).all(), 'must pass vaid profiles')
profile = np.asarray(profile, int)
return np.add.reduceat(np.cumsum(self._prof_offset - profile, -1),
self.role_starts, -1)
def get_payoffs(self, profiles):
utils.check(
self.is_profile(profiles).all(), 'must pass valid profiles')
payoffs = np.zeros(profiles.shape)
for i, (off, scale, reg) in enumerate(zip(
self._offset, self._scale, self._regressors)):
mask = profiles[..., i] > 0
profs = profiles[mask]
profs[:, i] -= 1
if profs.size:
payoffs[mask, i] = reg.predict(restrict.translate(
profs, self._rest)).ravel() * scale + off
return payoffs
def num_deviation_profiles(game, rest):
"""Returns the number of deviation profiles
This is a closed form way to compute `deviation_profiles(game,
rest).shape[0]`.
"""
rest = np.asarray(rest, bool)
utils.check(game.is_restriction(rest), 'restriction must be valid')
num_role_strats = np.add.reduceat(rest, game.role_starts)
num_devs = game.num_role_strats - num_role_strats
dev_players = game.num_role_players - np.eye(game.num_roles, dtype=int)
return np.sum(
utils.game_size(dev_players, num_role_strats).prod(1) * num_devs)
def __init__( # pragma: no branch # noqa
self,
sgame,
noise_dist=lambda: 0,
param_dist=lambda: ()):
super().__init__(sgame.role_names, sgame.strat_names,
sgame.num_role_players)
utils.check(hasattr(sgame, "get_sample_payoffs"),
"sgame not a sample game")
self._noise_dist = noise_dist
self._param_dist = param_dist
self._sgame = sgame
self._paymap = {}
def num_deviation_profiles(game, rest):
"""Returns the number of deviation profiles
This is a closed form way to compute `deviation_profiles(game,
rest).shape[0]`.
"""
rest = np.asarray(rest, bool)
utils.check(game.is_restriction(rest), 'restriction must be valid')
num_role_strats = np.add.reduceat(rest, game.role_starts)
num_devs = game.num_role_strats - num_role_strats
dev_players = game.num_role_players - np.eye(game.num_roles, dtype=int)
return np.sum(utils.game_size(dev_players, num_role_strats).prod(1) *
num_devs)
def get_payoffs(self, profiles):
utils.check(
self.is_profile(profiles).all(), 'must pass valid profiles')
dev_profiles = np.repeat(
profiles[..., None, :] - np.eye(self.num_strats, dtype=int),
self._sizes, -2)
vec = ((dev_profiles - self._profiles) /
self._lengths.repeat(self._sizes, 0))
rbf = np.einsum('...ij,...ij->...i', vec, vec)
payoffs = self._offset + self._coefs * np.add.reduceat(
np.exp(-rbf / 2) * self._alpha, self._size_starts, -1) # pylint: disable=invalid-unary-operand-type
payoffs[profiles == 0] = 0
return payoffs
def get_payoffs(self, profiles):
utils.check(
self.is_profile(profiles).all(), 'must pass valid profiles')
dev_profiles = np.repeat(
profiles[..., None, :] - np.eye(self.num_strats, dtype=int),
self._sizes, -2)
vec = ((dev_profiles - self._profiles) /
self._lengths.repeat(self._sizes, 0))
rbf = np.einsum('...ij,...ij->...i', vec, vec)
payoffs = self._offset + self._coefs * np.add.reduceat(
np.exp(-rbf / 2) * self._alpha, self._size_starts, -1) # pylint: disable=invalid-unary-operand-type
payoffs[profiles == 0] = 0
return payoffs
def uncompress_profile(self, comp_prof):
"""Uncompress a profile"""
comp_prof = np.asarray(comp_prof, int)
utils.check(
np.all(comp_prof >= 0) and
np.all(comp_prof < self.num_role_strats),
'must pass valid compressed profiles')
profile = np.zeros(comp_prof.shape[:-1] + (self.num_strats,), int)
inds = (comp_prof.reshape((-1, self.num_roles)) +
self.role_starts + self.num_strats *
np.arange(int(np.prod(comp_prof.shape[:-1])))[:, None])
profile.flat[inds] = 1
return profile
def _dev_profpay(game):
"""Iterate over deviation profiles and payoffs"""
sgame = paygame.samplegame_copy(game)
profiles = sgame.flat_profiles()
payoffs = sgame.flat_payoffs()
for i, pays in enumerate(payoffs.T):
mask = (profiles[:, i] > 0) & ~np.isnan(pays)
utils.check(
mask.any(), "couldn't find deviation data for a strategy")
profs = profiles[mask]
profs[:, i] -= 1
yield i, profs, pays[mask]
def matgame_copy(copy_game):
"""Copy a matrix game from an existing game
Parameters
----------
copy_game : RsGame
Game to copy payoff data out of. This game must be complete.
"""
utils.check(copy_game.is_complete(), 'can only copy complete games')
if hasattr(copy_game, 'payoff_matrix'):
return matgame_replace(copy_game, copy_game.payoff_matrix())
# Get payoff matrix
num_role_strats = copy_game.num_role_strats.repeat(
copy_game.num_role_players)
shape = tuple(num_role_strats) + (num_role_strats.size,)
payoff_matrix = np.empty(shape, float)
offset = copy_game.role_starts.repeat(copy_game.num_role_players)
for profile, payoffs in zip(copy_game.profiles(), copy_game.payoffs()):
inds = itertools.product(*[
set(itertools.permutations(np.arange(s.size).repeat(s))) for s
in np.split(profile, copy_game.role_starts[1:])])
for nested in inds:
ind = tuple(itertools.chain.from_iterable(nested))
payoff_matrix[ind] = payoffs[ind + offset]
# Get role names
if np.all(copy_game.num_role_players == 1):
roles = copy_game.role_names
strats = copy_game.strat_names
else:
# When we expand names, we need to make sure they stay sorted
if utils.is_sorted(r + 'p' for r in copy_game.role_names):
# We can naively append player numbers
role_names = copy_game.role_names
else:
# We have to prefix to preserve role order
maxlen = max(map(len, copy_game.role_names))
role_names = (
p + '_' * (maxlen - len(r)) + r for r, p
in zip(copy_game.role_names,
utils.prefix_strings('', copy_game.num_roles)))
roles = tuple(itertools.chain.from_iterable(
(r + s for s in utils.prefix_strings('p', p))
for r, p in zip(role_names, copy_game.num_role_players)))
strats = tuple(itertools.chain.from_iterable(
itertools.repeat(s, p) for s, p
in zip(copy_game.strat_names, copy_game.num_role_players)))
return _MatrixGame(roles, strats, payoff_matrix)
def num_deviation_payoffs(game, rest):
"""Returns the number of deviation payoffs
This is a closed form way to compute `np.sum(deviation_profiles(game, rest)
> 0)`."""
rest = np.asarray(rest, bool)
utils.check(game.is_restriction(rest), 'restriction must be valid')
num_role_strats = np.add.reduceat(rest, game.role_starts)
num_devs = game.num_role_strats - num_role_strats
dev_players = (game.num_role_players - np.eye(game.num_roles, dtype=int) -
np.eye(game.num_roles, dtype=int)[:, None])
temp = utils.game_size(dev_players, num_role_strats).prod(2)
non_deviators = np.sum(np.sum(temp * num_role_strats, 1) * num_devs)
return non_deviators + num_deviation_profiles(game, rest)
def get_payoffs(self, profiles):
utils.check(
self.is_profile(profiles).all(), 'must pass valid profiles')
payoffs = np.zeros(profiles.shape)
for i, (off, scale, reg) in enumerate(
zip(self._offset, self._scale, self._regressors)):
mask = profiles[..., i] > 0
profs = profiles[mask]
profs[:, i] -= 1
if profs.size:
payoffs[mask,
i] = reg.predict(restrict.translate(
profs, self._rest)).ravel() * scale + off
return payoffs
def num_deviation_payoffs(game, rest):
"""Returns the number of deviation payoffs
This is a closed form way to compute `np.sum(deviation_profiles(game, rest)
> 0)`."""
rest = np.asarray(rest, bool)
utils.check(game.is_restriction(rest), 'restriction must be valid')
num_role_strats = np.add.reduceat(rest, game.role_starts)
num_devs = game.num_role_strats - num_role_strats
dev_players = (game.num_role_players - np.eye(game.num_roles, dtype=int) -
np.eye(game.num_roles, dtype=int)[:, None])
temp = utils.game_size(dev_players, num_role_strats).prod(2)
non_deviators = np.sum(np.sum(temp * num_role_strats, 1) * num_devs)
return non_deviators + num_deviation_profiles(game, rest)
def expand_profiles(full_game, profiles):
"""Return input profiles
Parameters
----------
full_game : Game
Game that all profiles must be valid for.
profiles : ndarray-like
The profiles.
axis : int, optional
The axis the profiles lie on.
"""
profiles = np.asarray(profiles, int)
utils.check(full_game.is_profile(profiles).all(), 'profiles must be valid')
return profiles.reshape((-1, full_game.num_strats))
def reduce_profiles(red_game, profiles):
"""Reduce profiles using twins
Parameters
----------
red_game : Game
Game that reduced profiles will be profiles for. This game must
have the valid twins reduction number of players.
profiles : ndarray-like
The profiles to reduce.
"""
profiles = np.asarray(profiles, int)
utils.check(np.all(red_game.num_role_players <= 2),
'red game must be a twins game')
return dpr.reduce_profiles(red_game, profiles)
def reduce_profiles(red_game, profiles):
"""Return original profiles
Parameters
----------
red_game : Game
Game that all profiles must be valid for.
profiles : ndarray-like
The profiles.
axis : int, optional
The axis the profiles are on.
"""
profiles = np.asarray(profiles, int)
utils.check(red_game.is_profile(profiles).all(), 'profiles must be valid')
return profiles.reshape((-1, red_game.num_strats))
def reduce_game(full_game, red_players=None):
"""Return original game
Parameters
----------
full_game : Game
The game to reduce.
red_players : ndarray-like, optional
If specified, this must match the number of players per role in
full_game.
"""
utils.check(
red_players is None or np.all(
full_game.num_role_players == red_players),
'identity reduction must have same number of players')
return paygame.game_copy(full_game)
def reduce_profiles(red_game, profiles):
"""Reduce profiles using twins
Parameters
----------
red_game : Game
Game that reduced profiles will be profiles for. This game must
have the valid twins reduction number of players.
profiles : ndarray-like
The profiles to reduce.
"""
profiles = np.asarray(profiles, int)
utils.check(
np.all(red_game.num_role_players <= 2),
'red game must be a twins game')
return dpr.reduce_profiles(red_game, profiles)
def expand_profiles(full_game, profiles):
"""Expand profiles using twins reduction
Parameters
----------
full_game : Game
Game that expanded profiles will be valid for.
profiles : ndarray-like
The profiles to expand
"""
red_players = np.minimum(full_game.num_role_players, 2)
profiles = np.asarray(profiles, int)
red_game = rsgame.empty(red_players, full_game.num_role_strats)
utils.check(
red_game.is_profile(profiles).all(), 'profiles must be valid')
return dpr.expand_profiles(full_game, profiles)
def reduce_game(full_game, red_players=None):
"""Reduce a game using twins reduction
Parameters
----------
full_game : Game
The game to reduce.
red_players : ndarray-like, optional
The reduced number of players for each role. This must be None or
the reduced number of players for the twins reductions.
"""
exp_red_players = np.minimum(full_game.num_role_players, 2)
utils.check(
red_players is None or np.all(exp_red_players == red_players),
"twins reduction didn't get expected reduced players")
return dpr.reduce_game(full_game, exp_red_players)
def reduce_profiles(red_game, profiles):
"""Reduce profiles hierarchically
Parameters
----------
red_game : Game
Game that reduced profiles will be profiles for.
profiles : ndarray-like
The profiles to reduce.
"""
profiles = np.asarray(profiles, int)
utils.check(
profiles.shape[-1] == red_game.num_strats,
'profiles must be appropriate shape')
return _common.reduce_profiles(
red_game, red_game.num_role_players[None],
profiles.reshape((-1, red_game.num_strats)))[0]
def _reduce_profiles(red_game, profiles, return_contributions): # pylint: disable=too-many-locals
"""Reduce profiles using dpr
Parameters
----------
red_game : Game
Game that reduced profiles will be profiles for.
profiles : ndarray-like
The profiles to reduce.
return_contributions : bool, optional
If true return ancillary information about where the payoffs come
from.
"""
profiles = np.asarray(profiles, int)
utils.check(
profiles.shape[-1] == red_game.num_strats,
'profiles not a valid shape')
if not profiles.size:
return np.empty((0, red_game.num_strats), int)
profiles = profiles.reshape((-1, red_game.num_strats))
all_full_players = np.add.reduceat(profiles, red_game.role_starts, 1)
full_players = all_full_players[0]
utils.check(
np.all(all_full_players == full_players), 'profiles must be valid')
num_profs = profiles.shape[0]
dev_profs = profiles.repeat(np.sum(profiles > 0, 1), 0)
_, strat_inds = profiles.nonzero()
dev_profs[np.arange(dev_profs.shape[0]), strat_inds] -= 1
dev_red_players = _devs(red_game, num_profs)
mask = (profiles > 0).ravel()
red_profs, reduced = _common.reduce_profiles(
red_game, dev_red_players[mask], dev_profs)
rstrat_inds = strat_inds[reduced]
red_profs[np.arange(red_profs.shape[0]), rstrat_inds] += 1
red_profs, red_inds = np.unique(
utils.axis_to_elem(red_profs), return_inverse=True)
red_profs = utils.axis_from_elem(red_profs)
if not return_contributions:
return red_profs
full_inds = np.arange(num_profs).repeat(
red_game.num_strats)[mask][reduced]
return red_profs, red_inds, full_inds, rstrat_inds
def expand_profiles(full_game, profiles):
"""Expand profiles hierarchically
Parameters
----------
full_game : Game
Game that expanded profiles will be valid for.
profiles : ndarray-like
The profiles to expand
"""
profiles = np.asarray(profiles, int)
utils.check(
profiles.shape[-1] == full_game.num_strats,
'profiles must be appropriate shape')
return _common.expand_profiles(
full_game, full_game.num_role_players[None],
profiles.reshape((-1, full_game.num_strats)))
def additional_strategy_profiles(game, rest, role_strat_ind):
"""Returns all profiles added by strategy at index"""
# This uses the observation that the added profiles are all of the profiles
# of the new restricted game with one less player in role, and then where
# that last player always plays strat
rest = np.asarray(rest, bool)
utils.check(game.is_restriction(rest), 'restriction must be valid')
new_players = game.num_role_players.copy()
new_players[game.role_indices[role_strat_ind]] -= 1
base = rsgame.empty(new_players, game.num_role_strats)
new_mask = rest.copy()
new_mask[role_strat_ind] = True
profs = base.restrict(new_mask).all_profiles()
expand_profs = np.zeros((profs.shape[0], game.num_strats), int)
expand_profs[:, new_mask] = profs
expand_profs[:, role_strat_ind] += 1
return expand_profs
def expand_profiles(full_game, profiles):
"""Return input profiles
Parameters
----------
full_game : Game
Game that all profiles must be valid for.
profiles : ndarray-like
The profiles.
axis : int, optional
The axis the profiles lie on.
"""
profiles = np.asarray(profiles, int)
utils.check(
full_game.is_profile(profiles).all(),
'profiles must be valid')
return profiles.reshape((-1, full_game.num_strats))
def reduce_profiles(red_game, profiles):
"""Return original profiles
Parameters
----------
red_game : Game
Game that all profiles must be valid for.
profiles : ndarray-like
The profiles.
axis : int, optional
The axis the profiles are on.
"""
profiles = np.asarray(profiles, int)
utils.check(
red_game.is_profile(profiles).all(),
'profiles must be valid')
return profiles.reshape((-1, red_game.num_strats))
def nngame_train( # pylint: disable=too-many-arguments,too-many-locals
game, epochs=100, layer_sizes=(32, 32), dropout=0.2, verbosity=0,
optimizer='sgd', loss='mean_squared_error'):
"""Train a neural network regression model
This mostly exists as a proof of concept, individual testing should be done
to make sure it is working sufficiently. This API will likely change to
support more general architectures and training.
"""
utils.check(layer_sizes, 'must have at least one layer')
utils.check(0 <= dropout < 1, 'dropout must be a valid probability')
# This is for delayed importing inf tensor flow
from keras import models, layers
model = models.Sequential()
lay_iter = iter(layer_sizes)
model.add(layers.Dense(
next(lay_iter), input_shape=[game.num_strats], activation='relu'))
for units in lay_iter:
model.add(layers.Dense(units, activation='relu'))
if dropout:
model.add(layers.Dropout(dropout))
model.add(layers.Dense(1, activation='sigmoid'))
regs = []
offsets = np.empty(game.num_strats)
scales = np.empty(game.num_strats)
for i, profs, pays in _dev_profpay(game):
# XXX Payoff normalization specific to sigmoid. If we accept alternate
# models, we need a way to compute how to potentially normalize
# payoffs.
min_pay = pays.min()
offsets[i] = min_pay
max_pay = pays.max()
scale = 1 if np.isclose(max_pay, min_pay) else max_pay - min_pay
scales[i] = scale
reg = models.clone_model(model)
reg.compile(optimizer=optimizer, loss=loss)
reg.fit(profs, (pays - min_pay) / scale, epochs=epochs,
verbose=verbosity)
regs.append(reg)
return _DevRegressionGame(
game, tuple(regs), offsets, scales, game.min_strat_payoffs(),
game.max_strat_payoffs(), np.ones(game.num_strats, bool))
def travellers_dilemma(players=2, max_value=100):
"""Return an instance of travellers dilemma
Strategies range from 2 to max_value, thus there will be max_value - 1
strategies."""
utils.check(players > 1, 'players must be more than one')
utils.check(max_value > 2, 'max value must be more than 2')
base = rsgame.empty(players, max_value - 1)
profiles = base.all_profiles()
payoffs = np.zeros(profiles.shape)
mins = np.argmax(profiles, -1)
mask = profiles > 0
payoffs[mask] = mins.repeat(mask.sum(-1))
rows = np.arange(profiles.shape[0])
ties = profiles[rows, mins] > 1
lowest_pays = mins + 4
lowest_pays[ties] -= 2
payoffs[rows, mins] = lowest_pays
return paygame.game_replace(base, profiles, payoffs)
def expand_profiles(sarr, full_players, profiles): # pylint: disable=too-many-locals
"""Hierarchically expands several role symmetric array profiles
In the event that `full_players` isn't divisible by `reduced_players`,
we first assign by rounding error and break ties in favor of
more-played strategies. The final tie-breaker is index / alphabetical
order."""
reduced_players = np.add.reduceat(profiles, sarr.role_starts, 1)
utils.check(
np.all(full_players >= reduced_players),
'full_players must be at least as large as reduced_players')
utils.check(
np.all((reduced_players > 0) | ((full_players == 0) &
(reduced_players == 0))),
'reduced_players must be greater than zero')
# Maximum prevents divide by zero error; equivalent to + eps
rep_red_players = np.maximum(
reduced_players, 1).repeat(sarr.num_role_strats, -1)
rep_full_players = full_players.repeat(sarr.num_role_strats, -1)
num_profs = profiles.shape[0]
expand_profs = profiles * rep_full_players // rep_red_players
unassigned = full_players - \
np.add.reduceat(expand_profs, sarr.role_starts, 1)
# Order all possible strategies to find which to increment
role_order = np.broadcast_to(sarr.role_indices,
(num_profs, sarr.num_strats))
error = profiles * rep_full_players / rep_red_players - expand_profs
alpha_inds = np.arange(sarr.num_strats)
alpha_ord = np.broadcast_to(alpha_inds, (num_profs, sarr.num_strats))
inds = np.asarray(np.argsort(np.rec.fromarrays(
[role_order, -error, -profiles, alpha_ord]), 1))
# Map them to indices in the expand_profs array, and mask out the first
# that are necessary to meet unassigned
rectified_inds = (inds + np.arange(num_profs)[:, None] *
sarr.num_strats)
ind_mask = (
np.arange(sarr.num_strats) <
np.repeat(sarr.role_starts + unassigned, sarr.num_role_strats, 1))
expand_profs.flat[rectified_inds[ind_mask]] += 1
return expand_profs
def local_effect(num_players, num_strategies, *, edge_prob=0.2):
"""Generate a local effect game
In a local effect game, strategies are connected by a graph, and utilities
are a function of the number of players playing our strategy and the number
of players playing a neighboring strategy, hence local effect.
In this formulation, payoffs for others playing our strategy are negative
quadratics, and payoffs for playing other strategies are positive cubics.
Parameters
----------
num_players : int > 1
The number of players.
num_strategies : int > 1
The number of strategies.
edge_prob : float, optional
The probability that one strategy affects another.
"""
utils.check(num_players > 1, "can't generate a single player game")
utils.check(num_strategies > 1, "can't generate a single strategy game")
local_effect_graph = np.random.rand(
num_strategies, num_strategies) < edge_prob
np.fill_diagonal(local_effect_graph, False)
num_neighbors = local_effect_graph.sum()
num_functions = num_neighbors + num_strategies
action_weights = np.eye(num_functions, num_strategies, dtype=float)
function_inputs = np.eye(num_strategies, num_functions, dtype=bool)
in_act, out_act = local_effect_graph.nonzero()
func_inds = np.arange(num_strategies, num_functions)
function_inputs[in_act, func_inds] = True
action_weights[func_inds, out_act] = 1
function_table = np.empty((num_functions, num_players + 1), float)
function_table[:num_strategies] = -_random_monotone_polynomial(
num_strategies, num_players, 2)
function_table[num_strategies:] = _random_monotone_polynomial(
num_neighbors, num_players, 3)
return aggfn.aggfn(num_players, num_strategies, action_weights,
function_inputs, function_table)
def _read_payoffs(match):
"""Read gambit payoff format"""
role_names = _string_list(match.group('roles'))
num_strats = tuple(map(int, match.group('strats')[1:-1].split()))
num_roles = len(num_strats)
utils.check(
len(role_names) == num_roles,
"player names didn't match number of strategies")
strats = utils.prefix_strings('s', sum(num_strats))
strat_names = [list(itertools.islice(strats, n)) for n in num_strats]
payoffs = list(map(float, match.group('payoffs').split()))
matrix = np.empty(num_strats + (num_roles,))
utils.check(
len(payoffs) == matrix.size,
'incorrect number of payoffs for strategies')
inds = tuple(range(num_roles - 1, -1, -1)) + (num_roles,)
np.transpose(matrix, inds).flat = payoffs
return _normalize(role_names, strat_names, matrix)