async def test_sparse_trace():
"""Test that tracing sparsely samples profiles"""
base = rsgame.empty(4, 3)
game1 = paygame.game_replace(base, base.all_profiles(),
(base.all_profiles() > 0) * [1, 0, 0])
game2 = paygame.game_replace(base, base.all_profiles(),
(base.all_profiles() > 0) * [-0.5, 1.5, 0])
save1 = savesched.savesched(gamesched.gamesched(game1))
save2 = savesched.savesched(gamesched.gamesched(game2))
sgame1 = schedgame.schedgame(save1)
sgame2 = schedgame.schedgame(save2)
await asyncio.gather(innerloop.inner_loop(sgame1),
innerloop.inner_loop(sgame2))
# Assert that innerloop doesn't scheduler all profiles
assert save1.get_game().num_profiles == 11
assert save2.get_game().num_profiles == 11
((st1, *_, en1), _), ((st2, *_, en2), _) = ( # pylint: disable=too-many-star-expressions
await trace.trace_all_equilibria(sgame1, sgame2))
# Assert that trace found the expected equilibria
assert np.isclose(st1, 0)
assert np.isclose(en1, 1 / 3, atol=1e-3)
assert np.isclose(st2, 1 / 3, atol=1e-3)
assert np.isclose(en2, 1)
# Assert that trace didn't need many extra profiles
assert save1.get_game().num_profiles == 12
assert save2.get_game().num_profiles == 12
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 full_game(role_names, role_players, strat_names):
"""Return a full game"""
base = rsgame.empty_names(
role_names, role_players, strat_names)
return paygame.game_replace(
base, base.all_profiles(),
np.zeros((base.num_all_profiles, base.num_strats)))
def get_game(self):
profs = []
pays = []
for hprof, fpay in self._profiles.items():
if fpay.done():
profs.append(hprof.array)
pays.append(fpay.result())
return self._wrap(paygame.game_replace(
self, np.stack(profs), np.stack(pays)))
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 test_random_game_addition(strats):
"""Test random addition"""
mpayoffs = rand.random(tuple(strats) + (len(strats),))
matg = matgame.matgame(mpayoffs)
payoffs = rand.random(matg.payoffs().shape)
payoffs[matg.profiles() == 0] = 0
game = paygame.game_replace(matg, matg.profiles(), payoffs)
assert paygame.game_copy(matg + game) == game + matg
empty = rsgame.empty_copy(matg)
assert matg + empty == empty
def test_random_game_addition(strats):
"""Test random addition"""
mpayoffs = rand.random(tuple(strats) + (len(strats), ))
matg = matgame.matgame(mpayoffs)
payoffs = rand.random(matg.payoffs().shape)
payoffs[matg.profiles() == 0] = 0
game = paygame.game_replace(matg, matg.profiles(), payoffs)
assert paygame.game_copy(matg + game) == game + matg
empty = rsgame.empty_copy(matg)
assert matg + empty == empty
def deviation_payoffs(self, mixture, *, jacobian=False, **_):
# TODO This is not smooth because there are discontinuities when the
# maximum probability profile jumps at the boundary. If we wanted to
# make it smooth, one option would be to compute the smoother
# interpolation between this and lower probability profiles. All we
# need to ensure smoothness is that the weight at profile
# discontinuities is 0.
profiles = self.nearby_profiles(
self.max_prob_prof(mixture), self.num_neighbors)
payoffs = self.get_payoffs(profiles)
game = paygame.game_replace(self, profiles, payoffs)
return game.deviation_payoffs(mixture, ignore_incomplete=True,
jacobian=jacobian)
def deviation_payoffs(self, mixture, *, jacobian=False, **_):
# TODO This is not smooth because there are discontinuities when the
# maximum probability profile jumps at the boundary. If we wanted to
# make it smooth, one option would be to compute the smoother
# interpolation between this and lower probability profiles. All we
# need to ensure smoothness is that the weight at profile
# discontinuities is 0.
profiles = self.nearby_profiles(self.max_prob_prof(mixture),
self.num_neighbors)
payoffs = self.get_payoffs(profiles)
game = paygame.game_replace(self, profiles, payoffs)
return game.deviation_payoffs(mixture,
ignore_incomplete=True,
jacobian=jacobian)
async def _get_game(self, profs):
"""Get a game from the profiles to sample"""
futures = []
for prof in profs:
hprof = utils.hash_array(prof)
future = self._profiles.get(hprof, None)
if future is None:
future = asyncio.ensure_future(
self._sched.sample_payoffs(prof))
self._profiles[hprof] = future
futures.append(future)
lpays = await asyncio.gather(*futures)
pays = np.stack(lpays)
return paygame.game_replace(self, profs, pays)
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 gen_num_profiles(base, num, distribution=default_distribution):
"""Generate profiles given game structure
Parameters
----------
base : RsGame
Game to generate payoffs for.
count : int
The number of profiles to generate.
distribution : (shape) -> ndarray, optional
Distribution function to draw payoffs from.
"""
utils.check(
0 <= num <= base.num_all_profiles,
'num must be in [0, {:d}] but was {:d}', base.num_all_profiles, num)
profiles = sample_profiles(base, num)
payoffs = np.zeros(profiles.shape)
mask = profiles > 0
payoffs[mask] = distribution(mask.sum())
return paygame.game_replace(base, profiles, payoffs)
def test_payoff_vals():
"""Test payoff values"""
profiles = [[2, 0, 1, 0, 0],
[2, 0, 0, 1, 0],
[2, 0, 0, 0, 1],
[1, 1, 1, 0, 0],
[1, 1, 0, 1, 0],
[1, 1, 0, 0, 1],
[0, 2, 1, 0, 0],
[0, 2, 0, 1, 0],
[0, 2, 0, 0, 1]]
payoffs = [[4, 0, 8, 0, 0],
[-1, 0, 0, 10, 0],
[1, 0, 0, 0, 5],
[1, 6, 6, 0, 0],
[0, 3, 0, 5, 0],
[-2, 3, 0, 0, 9],
[0, 6, 11, 0, 0],
[0, 3, 0, 6, 0],
[0, 3, 0, 0, 10]]
copy = paygame.game_replace(_GAME, profiles, payoffs)
assert paygame.game_copy(_GAME) == copy
def keep_num_profiles(base, num):
"""Keep random profiles from an existing game
Parameters
----------
base : RsGame
Game to keep profiles from.
num : int
The number of profiles to keep from the game.
"""
utils.check(
0 <= num <= base.num_profiles, 'num must be in [0, {:d}] but was {:d}',
base.num_profiles, num)
if num == 0:
profiles = np.empty((0, base.num_strats), int)
payoffs = np.empty((0, base.num_strats))
elif base.is_complete():
profiles = sample_profiles(base, num)
payoffs = base.get_payoffs(profiles)
else:
inds = rand.choice(base.num_profiles, num, replace=False)
profiles = base.profiles()[inds]
payoffs = base.payoffs()[inds]
return paygame.game_replace(base, profiles, payoffs)
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 full_game(role_names, role_players, strat_names):
"""Return a full game"""
base = rsgame.empty_names(role_names, role_players, strat_names)
return paygame.game_replace(
base, base.all_profiles(),
np.zeros((base.num_all_profiles, base.num_strats)))
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])
