async def add_restriction(rest):
"""Adds a restriction to be evaluated"""
if not exp_restrictions.add(rest):
return # already explored
if agame.is_pure_restriction(rest):
# Short circuit for pure restriction
return await add_deviations(rest, rest.astype(float),
init_role_dev)
data = await agame.get_restricted_game(rest)
reqa = await loop.run_in_executor(
executor,
functools.partial(nash.mixed_equilibria,
data,
regret_thresh=regret_thresh,
dist_thresh=dist_thresh,
style=style,
processes=1))
if reqa.size:
eqa = restrict.translate(
data.trim_mixture_support(reqa, thresh=support_thresh), rest)
await asyncio.gather(
*[add_deviations(rest, eqm, init_role_dev) for eqm in eqa])
else:
logging.warning(
"couldn't find equilibria in %s with restriction %s. This is "
'likely due to high variance in payoffs which means '
'quiesce should be re-run with more samples per profile. '
'This could also be fixed by performing a more expensive '
'equilibria search to always return one.', agame,
agame.restriction_to_repr(rest))
def _rprofs(self, rest):
"""Get the restricted profiles for a restriction"""
return restrict.translate(
self._red.expand_profiles(
rsgame.empty_copy(self).restrict(rest),
self._rgame.restrict(rest).all_profiles()),
rest)
async def run(args):
"""Brute force entry point"""
sched = await schedspec.parse_scheduler(args.scheduler)
red, red_players = utils.parse_reduction(sched, args)
rest = (
np.ones(sched.num_strats, bool)
if args.restrict is None
else sched.restriction_from_json(json.load(args.restrict))
)
async with sched:
data = await schedgame.schedgame(sched, red, red_players).get_deviation_game(
rest
)
# now find equilibria
eqa = sched.trim_mixture_support(
restrict.translate(
nash.mixed_nash(
data.restrict(rest),
regret_thresh=args.regret_thresh,
dist_thresh=args.dist_thresh,
at_least_one=args.one,
min_reg=args.min_reg,
),
rest,
),
thresh=args.supp_thresh,
)
reg_info = []
for eqm in eqa:
gains = regret.mixture_deviation_gains(data, eqm)
bri = np.argmax(gains)
reg_info.append((gains[bri],) + sched.role_strat_names[bri])
logging.error(
"brute sampling finished finding %d equilibria:\n%s",
eqa.shape[0],
"\n".join(
"{:d}) {} with regret {:g} to {} {}".format(
i, sched.mixture_to_repr(eqm), reg, role, strat
)
for i, (eqm, (reg, role, strat)) in enumerate(zip(eqa, reg_info), 1)
),
)
json.dump(
[
{
"equilibrium": sched.mixture_to_json(eqm),
"regret": reg,
"best_response": {"role": role, "strat": strat},
}
for eqm, (reg, role, strat) in zip(eqa, reg_info)
],
args.output,
)
args.output.write("\n")
def test_rbfgame_restriction(base): # pylint: disable=too-many-locals
"""Test rbf game restriction"""
game = gamegen.gen_num_profiles(base, 13)
reggame = learning.rbfgame_train(game)
rest = game.random_restriction()
rreg = reggame.restrict(rest)
subpays = rreg.payoffs()
fullpays = reggame.get_payoffs(restrict.translate(rreg.profiles(),
rest))[:, rest]
assert np.allclose(subpays, fullpays)
mix = rreg.random_mixture()
sub_dev_profs = rreg.random_role_deviation_profiles(20, mix)
sub_pays = rreg.get_dev_payoffs(sub_dev_profs)
pays = reggame.get_dev_payoffs(restrict.translate(sub_dev_profs,
rest))[:, rest]
assert np.allclose(sub_pays, pays)
for mix in rreg.random_mixtures(20):
dev_pay = rreg.deviation_payoffs(mix)
full_pay = reggame.deviation_payoffs(restrict.translate(mix,
rest))[rest]
assert np.allclose(dev_pay, full_pay)
assert rreg.min_strat_payoffs().shape == (rreg.num_strats, )
assert rreg.max_strat_payoffs().shape == (rreg.num_strats, )
jgame = json.dumps(rreg.to_json())
copy = learning.rbfgame_json(json.loads(jgame))
assert hash(copy) == hash(rreg)
assert copy == rreg
rrest = rreg.random_restriction()
rrreg = rreg.restrict(rrest)
assert rrreg.min_strat_payoffs().shape == (rrreg.num_strats, )
assert rrreg.max_strat_payoffs().shape == (rrreg.num_strats, )
jgame = json.dumps(rrreg.to_json())
copy = learning.rbfgame_json(json.loads(jgame))
assert hash(copy) == hash(rrreg)
assert copy == rrreg
def dev_profs(red_players, full_players, mask, rst):
"""Deviation profiles for a particular role"""
rgame = rsgame.empty(red_players, support)
sub_profs = restrict.translate(rgame.all_profiles(), rest)
game = rsgame.empty(full_players, full_game.num_role_strats)
non_devs = hierarchical.expand_profiles(game, sub_profs)
ndevs = np.sum(~mask)
devs = np.zeros((ndevs, full_game.num_strats), int)
devs[:, rst:rst + mask.size][:, ~mask] = np.eye(ndevs, dtype=int)
profs = non_devs[:, None] + devs
profs.shape = (-1, full_game.num_strats)
return profs
def dev_profs(red_players, full_players, mask, rst):
"""Deviation profiles for a particular role"""
rgame = rsgame.empty(red_players, support)
sub_profs = restrict.translate(rgame.all_profiles(), rest)
game = rsgame.empty(full_players, full_game.num_role_strats)
non_devs = hierarchical.expand_profiles(game, sub_profs)
ndevs = np.sum(~mask)
devs = np.zeros((ndevs, full_game.num_strats), int)
devs[:, rst:rst + mask.size][:, ~mask] = np.eye(ndevs, dtype=int)
profs = non_devs[:, None] + devs
profs.shape = (-1, full_game.num_strats)
return profs
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 get_dev_payoffs(self, dev_profs):
"""Compute the payoff for deviating
This implementation is more efficient than the default since we don't
need to compute the payoff for non deviators."""
prof_view = np.rollaxis(restrict.translate(dev_profs.reshape(
(-1, self.num_roles, self.num_strats)), self._rest), 1, 0)
payoffs = np.empty(dev_profs.shape[:-2] + (self.num_strats,))
pay_view = payoffs.reshape((-1, self.num_strats)).T
for pays, profs, reg in zip(
pay_view, utils.repeat(prof_view, self.num_role_strats),
self._regressors):
np.copyto(pays, reg.predict(profs))
return payoffs * self._scale + self._offset
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
async def test_basic_asyncgame():
"""Test that wrapped async games work"""
game = gamegen.game([4, 3], [3, 4])
agame = asyncgame.wrap(game)
rest = agame.random_restriction()
rgame = await agame.get_restricted_game(rest)
assert rgame.is_complete()
assert rsgame.empty_copy(rgame) == rsgame.empty_copy(game.restrict(rest))
dgame = await agame.get_deviation_game(rest)
mix = restrict.translate(rgame.random_mixture(), rest)
assert not np.isnan(dgame.deviation_payoffs(mix)).any()
dup = asyncgame.wrap(game)
assert hash(dup) == hash(agame)
assert dup == agame
def get_dev_payoffs(self, dev_profs):
"""Compute the payoff for deviating
This implementation is more efficient than the default since we don't
need to compute the payoff for non deviators."""
prof_view = np.rollaxis(
restrict.translate(
dev_profs.reshape((-1, self.num_roles, self.num_strats)),
self._rest), 1, 0)
payoffs = np.empty(dev_profs.shape[:-2] + (self.num_strats, ))
pay_view = payoffs.reshape((-1, self.num_strats)).T
for pays, profs, reg in zip(
pay_view, utils.repeat(prof_view, self.num_role_strats),
self._regressors):
np.copyto(pays, reg.predict(profs))
return payoffs * self._scale + self._offset
async def test_mix_asyncgame():
"""Test that that mixture async games work"""
game0 = gamegen.game([4, 3], [3, 4])
game1 = gamegen.game([4, 3], [3, 4])
agame = asyncgame.mix(asyncgame.wrap(game0), asyncgame.wrap(game1), 0.4)
assert agame.get_game() == rsgame.mix(game0, game1, 0.4)
assert str(agame) == "{} - 0.4 - {}".format(repr(game0), repr(game1))
rest = agame.random_restriction()
rgame = await agame.get_restricted_game(rest)
assert rgame.is_complete()
assert rsgame.empty_copy(rgame) == rsgame.empty_copy(game0.restrict(rest))
dgame = await agame.get_deviation_game(rest)
mix = restrict.translate(rgame.random_mixture(), rest)
assert not np.isnan(dgame.deviation_payoffs(mix)).any()
dup = asyncgame.mix(asyncgame.wrap(game0), asyncgame.wrap(game1), 0.4)
assert hash(dup) == hash(agame)
assert dup == agame
def test_missing_data_maximal_restrictions(base, prob):
"""Test missing data"""
game = gamegen.game_replace(base, prob)
rests = restrict.maximal_restrictions(game)
if rests.size:
maximal = np.all(rests <= rests[:, None], -1)
np.fill_diagonal(maximal, False)
assert not maximal.any(), \
'One maximal restriction dominated another'
for rest in rests:
rgame = rsgame.empty_copy(game).restrict(rest)
restprofs = restrict.translate(rgame.all_profiles(), rest)
assert all(p in game for p in restprofs), \
"Maximal restriction didn't have all profiles"
for dev in np.nonzero(~rest)[0]:
devprofs = restrict.additional_strategy_profiles(
game, rest, dev)
assert not all(p in game for p in devprofs), ( # pragma: no branch
'Maximal restriction could be bigger {} {}'.format(
dev, rest))
def test_translate():
"""Test translate"""
prof = np.arange(6) + 1
rest = np.array([1, 0, 0, 1, 1, 0, 1, 1, 0, 1], bool)
expected = [1, 0, 0, 2, 3, 0, 4, 5, 0, 6]
assert np.all(expected == restrict.translate(prof, rest))
def main(args): # pylint: disable=too-many-statements,too-many-branches,too-many-locals
"""Entry point for analysis"""
game = gamereader.load(args.input)
if args.dpr is not None:
red_players = game.role_from_repr(args.dpr, dtype=int)
game = reduction.deviation_preserving.reduce_game(game, red_players)
elif args.hr is not None:
red_players = game.role_from_repr(args.hr, dtype=int)
game = reduction.hierarchical.reduce_game(game, red_players)
if args.dominance:
domsub = dominance.iterated_elimination(game, 'strictdom')
game = game.restrict(domsub)
if args.restrictions:
restrictions = restrict.maximal_restrictions(game)
else:
restrictions = np.ones((1, game.num_strats), bool)
noeq_restrictions = []
candidates = []
for rest in restrictions:
rgame = game.restrict(rest)
reqa = nash.mixed_equilibria(rgame,
style=args.style,
regret_thresh=args.regret_thresh,
dist_thresh=args.dist_thresh,
processes=args.processes)
eqa = restrict.translate(
rgame.trim_mixture_support(reqa, thresh=args.support), rest)
if eqa.size:
candidates.extend(eqa)
else:
noeq_restrictions.append(rest)
equilibria = collect.mcces(args.dist_thresh * np.sqrt(2 * game.num_roles))
unconfirmed = collect.mcces(args.dist_thresh * np.sqrt(2 * game.num_roles))
unexplored = {}
for eqm in candidates:
support = eqm > 0
# FIXME This treats trimming support differently than quiesce does,
# which means quiesce could find an equilibria, and this would fail to
# find it.
gains = regret.mixture_deviation_gains(game, eqm)
role_gains = np.fmax.reduceat(gains, game.role_starts)
gain = np.nanmax(role_gains)
if np.isnan(gains).any() and gain <= args.regret_thresh:
# Not fully explored but might be good
unconfirmed.add(eqm, gain)
elif np.any(role_gains > args.regret_thresh):
# There are deviations, did we explore them?
dev_inds = ([
np.argmax(gs == mg) for gs, mg in zip(
np.split(gains, game.role_starts[1:]), role_gains)
] + game.role_starts)[role_gains > args.regret_thresh]
for dind in dev_inds:
devsupp = support.copy()
devsupp[dind] = True
if not np.all(devsupp <= restrictions, -1).any():
ind = restrict.to_id(game, devsupp)
old_info = unexplored.get(ind, (0, 0, 0, None))
new_info = (gains[dind], dind, old_info[2] + 1, eqm)
unexplored[ind] = max(new_info, old_info)
else:
# Equilibrium!
equilibria.add(eqm, np.max(gains))
# Output Game
args.output.write('Game Analysis\n')
args.output.write('=============\n')
args.output.write(str(game))
args.output.write('\n\n')
if args.dpr is not None:
args.output.write('With deviation preserving reduction: ')
args.output.write(args.dpr.replace(';', ' '))
args.output.write('\n\n')
elif args.hr is not None:
args.output.write('With hierarchical reduction: ')
args.output.write(args.hr.replace(';', ' '))
args.output.write('\n\n')
if args.dominance:
num = np.sum(~domsub)
if num:
args.output.write('Found {:d} dominated strateg{}\n'.format(
num, 'y' if num == 1 else 'ies'))
args.output.write(game.restriction_to_str(~domsub))
args.output.write('\n\n')
else:
args.output.write('Found no dominated strategies\n\n')
if args.restrictions:
num = restrictions.shape[0]
if num:
args.output.write(
'Found {:d} maximal complete restricted game{}\n\n'.format(
num, '' if num == 1 else 's'))
else:
args.output.write('Found no complete restricted games\n\n')
args.output.write('\n')
# Output social welfare
args.output.write('Social Welfare\n')
args.output.write('--------------\n')
welfare, profile = regret.max_pure_social_welfare(game)
if profile is None:
args.output.write('There was no profile with complete payoff data\n\n')
else:
args.output.write('\nMaximum social welfare profile:\n')
args.output.write(game.profile_to_str(profile))
args.output.write('\nWelfare: {:.4f}\n\n'.format(welfare))
if game.num_roles > 1:
for role, welfare, profile in zip(
game.role_names,
*regret.max_pure_social_welfare(game, by_role=True)):
args.output.write(
'Maximum "{}" welfare profile:\n'.format(role))
args.output.write(game.profile_to_str(profile))
args.output.write('\nWelfare: {:.4f}\n\n'.format(welfare))
args.output.write('\n')
# Output Equilibria
args.output.write('Equilibria\n')
args.output.write('----------\n')
if equilibria:
args.output.write('Found {:d} equilibri{}\n\n'.format(
len(equilibria), 'um' if len(equilibria) == 1 else 'a'))
for i, (eqm, reg) in enumerate(equilibria, 1):
args.output.write('Equilibrium {:d}:\n'.format(i))
args.output.write(game.mixture_to_str(eqm))
args.output.write('\nRegret: {:.4f}\n\n'.format(reg))
else:
args.output.write('Found no equilibria\n\n')
args.output.write('\n')
# Output No-equilibria Subgames
args.output.write('No-equilibria Subgames\n')
args.output.write('----------------------\n')
if noeq_restrictions:
args.output.write(
'Found {:d} no-equilibria restricted game{}\n\n'.format(
len(noeq_restrictions),
'' if len(noeq_restrictions) == 1 else 's'))
noeq_restrictions.sort(key=lambda x: x.sum())
for i, subg in enumerate(noeq_restrictions, 1):
args.output.write(
'No-equilibria restricted game {:d}:\n'.format(i))
args.output.write(game.restriction_to_str(subg))
args.output.write('\n\n')
else:
args.output.write('Found no no-equilibria restricted games\n\n')
args.output.write('\n')
# Output Unconfirmed Candidates
args.output.write('Unconfirmed Candidate Equilibria\n')
args.output.write('--------------------------------\n')
if unconfirmed:
args.output.write('Found {:d} unconfirmed candidate{}\n\n'.format(
len(unconfirmed), '' if len(unconfirmed) == 1 else 's'))
ordered = sorted((sum(e > 0 for e in m), r, m) for m, r in unconfirmed)
for i, (_, reg_bound, eqm) in enumerate(ordered, 1):
args.output.write('Unconfirmed candidate {:d}:\n'.format(i))
args.output.write(game.mixture_to_str(eqm))
args.output.write(
'\nRegret at least: {:.4f}\n\n'.format(reg_bound))
else:
args.output.write('Found no unconfirmed candidate equilibria\n\n')
args.output.write('\n')
# Output Unexplored Subgames
args.output.write('Unexplored Best-response Subgames\n')
args.output.write('---------------------------------\n')
if unexplored:
min_supp = min(restrict.from_id(game, sid).sum() for sid in unexplored)
args.output.write(
'Found {:d} unexplored best-response restricted game{}\n'.format(
len(unexplored), '' if len(unexplored) == 1 else 's'))
args.output.write(
'Smallest unexplored restricted game has support {:d}\n\n'.format(
min_supp))
ordered = sorted((
restrict.from_id(game, sind).sum(),
-gain,
dev,
restrict.from_id(game, sind),
eqm,
) for sind, (gain, dev, _, eqm) in unexplored.items())
for i, (_, ngain, dev, sub, eqm) in enumerate(ordered, 1):
args.output.write('Unexplored restricted game {:d}:\n'.format(i))
args.output.write(game.restriction_to_str(sub))
args.output.write('\n{:.4f} for deviating to {} from:\n'.format(
-ngain, game.strat_name(dev)))
args.output.write(game.mixture_to_str(eqm))
args.output.write('\n\n')
else:
args.output.write(
'Found no unexplored best-response restricted games\n\n')
args.output.write('\n')
# Output json data
args.output.write('Json Data\n')
args.output.write('=========\n')
json_data = {
'equilibria': [game.mixture_to_json(eqm) for eqm, _ in equilibria]
}
json.dump(json_data, args.output)
args.output.write('\n')
def main(args): # pylint: disable=too-many-statements,too-many-branches,too-many-locals
"""Entry point for analysis"""
game = gamereader.load(args.input)
if args.dpr is not None:
red_players = game.role_from_repr(args.dpr, dtype=int)
game = reduction.deviation_preserving.reduce_game(game, red_players)
elif args.hr is not None:
red_players = game.role_from_repr(args.hr, dtype=int)
game = reduction.hierarchical.reduce_game(game, red_players)
if args.dominance:
domsub = dominance.iterated_elimination(game, 'strictdom')
game = game.restrict(domsub)
if args.restrictions:
restrictions = restrict.maximal_restrictions(game)
else:
restrictions = np.ones((1, game.num_strats), bool)
noeq_restrictions = []
candidates = []
for rest in restrictions:
rgame = game.restrict(rest)
reqa = nash.mixed_equilibria(
rgame, style=args.style, regret_thresh=args.regret_thresh,
dist_thresh=args.dist_thresh, processes=args.processes)
eqa = restrict.translate(rgame.trim_mixture_support(
reqa, thresh=args.support), rest)
if eqa.size:
candidates.extend(eqa)
else:
noeq_restrictions.append(rest)
equilibria = collect.mcces(args.dist_thresh * np.sqrt(2 * game.num_roles))
unconfirmed = collect.mcces(args.dist_thresh * np.sqrt(2 * game.num_roles))
unexplored = {}
for eqm in candidates:
support = eqm > 0
# FIXME This treats trimming support differently than quiesce does,
# which means quiesce could find an equilibria, and this would fail to
# find it.
gains = regret.mixture_deviation_gains(game, eqm)
role_gains = np.fmax.reduceat(gains, game.role_starts)
gain = np.nanmax(role_gains)
if np.isnan(gains).any() and gain <= args.regret_thresh:
# Not fully explored but might be good
unconfirmed.add(eqm, gain)
elif np.any(role_gains > args.regret_thresh):
# There are deviations, did we explore them?
dev_inds = ([np.argmax(gs == mg) for gs, mg
in zip(np.split(gains, game.role_starts[1:]),
role_gains)] +
game.role_starts)[role_gains > args.regret_thresh]
for dind in dev_inds:
devsupp = support.copy()
devsupp[dind] = True
if not np.all(devsupp <= restrictions, -1).any():
ind = restrict.to_id(game, devsupp)
old_info = unexplored.get(ind, (0, 0, 0, None))
new_info = (gains[dind], dind, old_info[2] + 1, eqm)
unexplored[ind] = max(new_info, old_info)
else:
# Equilibrium!
equilibria.add(eqm, np.max(gains))
# Output Game
args.output.write('Game Analysis\n')
args.output.write('=============\n')
args.output.write(str(game))
args.output.write('\n\n')
if args.dpr is not None:
args.output.write('With deviation preserving reduction: ')
args.output.write(args.dpr.replace(';', ' '))
args.output.write('\n\n')
elif args.hr is not None:
args.output.write('With hierarchical reduction: ')
args.output.write(args.hr.replace(';', ' '))
args.output.write('\n\n')
if args.dominance:
num = np.sum(~domsub)
if num:
args.output.write('Found {:d} dominated strateg{}\n'.format(
num, 'y' if num == 1 else 'ies'))
args.output.write(game.restriction_to_str(~domsub))
args.output.write('\n\n')
else:
args.output.write('Found no dominated strategies\n\n')
if args.restrictions:
num = restrictions.shape[0]
if num:
args.output.write(
'Found {:d} maximal complete restricted game{}\n\n'.format(
num, '' if num == 1 else 's'))
else:
args.output.write('Found no complete restricted games\n\n')
args.output.write('\n')
# Output social welfare
args.output.write('Social Welfare\n')
args.output.write('--------------\n')
welfare, profile = regret.max_pure_social_welfare(game)
if profile is None:
args.output.write('There was no profile with complete payoff data\n\n')
else:
args.output.write('\nMaximum social welfare profile:\n')
args.output.write(game.profile_to_str(profile))
args.output.write('\nWelfare: {:.4f}\n\n'.format(welfare))
if game.num_roles > 1:
for role, welfare, profile in zip(
game.role_names,
*regret.max_pure_social_welfare(game, by_role=True)):
args.output.write('Maximum "{}" welfare profile:\n'.format(
role))
args.output.write(game.profile_to_str(profile))
args.output.write('\nWelfare: {:.4f}\n\n'.format(welfare))
args.output.write('\n')
# Output Equilibria
args.output.write('Equilibria\n')
args.output.write('----------\n')
if equilibria:
args.output.write('Found {:d} equilibri{}\n\n'.format(
len(equilibria), 'um' if len(equilibria) == 1 else 'a'))
for i, (eqm, reg) in enumerate(equilibria, 1):
args.output.write('Equilibrium {:d}:\n'.format(i))
args.output.write(game.mixture_to_str(eqm))
args.output.write('\nRegret: {:.4f}\n\n'.format(reg))
else:
args.output.write('Found no equilibria\n\n')
args.output.write('\n')
# Output No-equilibria Subgames
args.output.write('No-equilibria Subgames\n')
args.output.write('----------------------\n')
if noeq_restrictions:
args.output.write(
'Found {:d} no-equilibria restricted game{}\n\n'.format(
len(noeq_restrictions),
'' if len(noeq_restrictions) == 1 else 's'))
noeq_restrictions.sort(key=lambda x: x.sum())
for i, subg in enumerate(noeq_restrictions, 1):
args.output.write(
'No-equilibria restricted game {:d}:\n'.format(i))
args.output.write(game.restriction_to_str(subg))
args.output.write('\n\n')
else:
args.output.write('Found no no-equilibria restricted games\n\n')
args.output.write('\n')
# Output Unconfirmed Candidates
args.output.write('Unconfirmed Candidate Equilibria\n')
args.output.write('--------------------------------\n')
if unconfirmed:
args.output.write('Found {:d} unconfirmed candidate{}\n\n'.format(
len(unconfirmed), '' if len(unconfirmed) == 1 else 's'))
ordered = sorted(
(sum(e > 0 for e in m), r, m) for m, r in unconfirmed)
for i, (_, reg_bound, eqm) in enumerate(ordered, 1):
args.output.write('Unconfirmed candidate {:d}:\n'.format(i))
args.output.write(game.mixture_to_str(eqm))
args.output.write('\nRegret at least: {:.4f}\n\n'.format(
reg_bound))
else:
args.output.write('Found no unconfirmed candidate equilibria\n\n')
args.output.write('\n')
# Output Unexplored Subgames
args.output.write('Unexplored Best-response Subgames\n')
args.output.write('---------------------------------\n')
if unexplored:
min_supp = min(restrict.from_id(game, sid).sum() for sid in unexplored)
args.output.write(
'Found {:d} unexplored best-response restricted game{}\n'.format(
len(unexplored), '' if len(unexplored) == 1 else 's'))
args.output.write(
'Smallest unexplored restricted game has support {:d}\n\n'.format(
min_supp))
ordered = sorted((
restrict.from_id(game, sind).sum(),
-gain, dev,
restrict.from_id(game, sind),
eqm,
) for sind, (gain, dev, _, eqm) in unexplored.items())
for i, (_, ngain, dev, sub, eqm) in enumerate(ordered, 1):
args.output.write('Unexplored restricted game {:d}:\n'.format(i))
args.output.write(game.restriction_to_str(sub))
args.output.write('\n{:.4f} for deviating to {} from:\n'.format(
-ngain, game.strat_name(dev)))
args.output.write(game.mixture_to_str(eqm))
args.output.write('\n\n')
else:
args.output.write(
'Found no unexplored best-response restricted games\n\n')
args.output.write('\n')
# Output json data
args.output.write('Json Data\n')
args.output.write('=========\n')
json_data = {
'equilibria': [game.mixture_to_json(eqm) for eqm, _ in equilibria]}
json.dump(json_data, args.output)
args.output.write('\n')