def test_random_trace_equilibria(base):
"""Test random equilibrium trace"""
game0 = gamegen.poly_aggfn(base.num_role_players, base.num_role_strats, 6)
game1 = gamegen.poly_aggfn(base.num_role_players, base.num_role_strats, 6)
eqa = game0.trim_mixture_support(nash.mixed_nash(
game0, regret_thresh=1e-4))
for eqm in eqa:
if regret.mixture_regret(game0, eqm) > 1e-3:
# trimmed equilibrium had too high of regret...
continue # pragma: no cover
probs, mixes = trace.trace_equilibrium(game0, game1, 0, eqm, 1)
for prob, mix in zip(probs, mixes):
reg = regret.mixture_regret(rsgame.mix(game0, game1, prob), mix)
assert reg <= 1.1e-3
eqa = game1.trim_mixture_support(nash.mixed_nash(
game1, regret_thresh=1e-4))
for eqm in eqa:
if regret.mixture_regret(game1, eqm) > 1e-3:
# trimmed equilibrium had too high of regret...
continue # pragma: no cover
probs, mixes = trace.trace_equilibrium(game0, game1, 1, eqm, 0)
for prob, mix in zip(probs, mixes):
reg = regret.mixture_regret(rsgame.mix(game0, game1, prob), mix)
assert reg <= 1.1e-3
def test_trace_equilibria():
"""Test trace known game equilibrium"""
profs = [[2, 0],
[1, 1],
[0, 2]]
pays1 = [[1, 0],
[1, 0],
[0, 0]]
game0 = paygame.game(2, 2, profs, pays1)
pays2 = [[0, 0],
[0, 1],
[0, 1]]
game1 = paygame.game(2, 2, profs, pays2)
probs, mixes = trace.trace_equilibrium(game0, game1, 0, [1, 0], 1)
assert np.isclose(probs[0], 0)
assert np.isclose(probs[-1], 0.5, atol=1.1e-3)
assert np.allclose(mixes, [1, 0])
probs, mixes = trace.trace_equilibrium(game0, game1, 1, [0, 1], 0)
assert np.isclose(probs[0], 1)
assert np.isclose(probs[-1], 0.5, atol=1.1e-3)
assert np.allclose(mixes, [0, 1])
def _smooth_trace(game0, game1, probs, eqa, trace_args):
"""Smooth the equilibria in a trace in place
Smoothing attempts to trace out from one time to an adjacent time. If the
new point has lower regret, it's taken instead. This onle goes one
direction, so it should be repeated for reversed views.
"""
for (pfrom, pto), (eqmfrom, eqmto) in zip(utils.subsequences(probs),
utils.subsequences(eqa)):
(*_, pres), (*_, eqmres) = trace.trace_equilibrium( # pylint: disable=too-many-star-expressions
game0, game1, pfrom, eqmfrom, pto, **trace_args)
if np.isclose(pres, pto):
mixgame = rsgame.mix(game0, game1, pto)
regto = regret.mixture_regret(mixgame, eqmto)
regres = regret.mixture_regret(mixgame, eqmres)
if regres < regto:
np.copyto(eqmto, eqmres)
def test_random_trace_interpolate(game0, game1): # pylint: disable=too-many-locals
"""Test random trace interpolation"""
prob = np.random.random()
eqa = game0.trim_mixture_support(nash.mixed_nash(
rsgame.mix(game0, game1, prob),
regret_thresh=1e-4))
for eqm in eqa:
if regret.mixture_regret(rsgame.mix(game0, game1, prob), eqm) > 1e-3:
# trimmed equilibrium had too high of regret...
continue # pragma: no cover
for target in [0, 1]:
# Test that interpolate recovers missing equilibria
probs, mixes = trace.trace_equilibrium(
game0, game1, prob, eqm, target)
if probs.size < 3:
# not enough to test leave one out
continue # pragma: no cover
start, interp, end = np.sort(np.random.choice(
probs.size, 3, replace=False))
interp_mix, = trace.trace_interpolate(
game0, game1, [probs[start], probs[end]],
[mixes[start], mixes[end]], [probs[interp]])
assert np.allclose(interp_mix, mixes[interp], rtol=1e-2, atol=2e-2)
# Test interp at first
mix, = trace.trace_interpolate(
game0, game1, probs, mixes, [probs[0]])
assert np.allclose(mix, mixes[0], rtol=1e-2, atol=2e-2)
# Test interp at last
mix, = trace.trace_interpolate(
game0, game1, probs, mixes, [probs[-1]])
assert np.allclose(mix, mixes[-1], rtol=1e-2, atol=2e-2)
# Test random t
p_interp = np.random.uniform(probs[0], probs[-1])
mix, = trace.trace_interpolate(
game0, game1, probs, mixes, [p_interp])
assert regret.mixture_regret(rsgame.mix(
game0, game1, p_interp), mix) <= 1.1e-3