def DeviationPreservingReduction(game, players={}):
if not players:
return TwinsReduction(game)
DPR_game = Game(game.roles, players, game.strategies)
for reduced_profile in DPR_game.allProfiles():
try:
role_payoffs = {}
for role in game.roles:
role_payoffs[role] = []
for s in reduced_profile[role]:
full_profile = {}
for r in game.roles:
if r == role:
opp_prof = reduced_profile.asDict()[r]
opp_prof[s] -= 1
full_profile[r] = FullGameProfile(opp_prof, \
game.players[r] - 1)
full_profile[r][s] += 1
else:
full_profile[r] = FullGameProfile(reduced_profile[\
r], game.players[r])
role_payoffs[r].append(payoff_data(s, reduced_profile[r\
][s], game.getPayoff(Profile(full_profile), r, s)))
DPR_game.addProfile(role_payoffs)
except KeyError:
continue
return DPR_game
def Subgame(game, strategies={}):
"""
Creates a game with a subset each role's strategies.
default settings result in a subgame with no strategies
"""
if not strategies:
strategies = {r:[] for r in game.roles}
sg = Game(game.roles, game.players, strategies)
if sg.size <= len(game):
for p in sg.allProfiles():
if p in game:
sg.addProfile({r:[payoff_data(s, p[r][s], \
game.getPayoff(p,r,s)) for s in p[r]] for r in p})
else:
for p in game:
if all([all([s in sg.strategies[r] for s in p[r]]) for r in p]):
sg.addProfile({r:[payoff_data(s, p[r][s], \
game.getPayoff(p,r,s)) for s in p[r]] for r in p})
return sg
def HierarchicalReduction(game, players={} ):
if not players:
players = {r : game.players[r] / 2 for r in game.roles}
HR_game = Game(game.roles, players, game.strategies)
for reduced_profile in HR_game.allProfiles():
try:
full_profile = Profile({r:FullGameProfile(reduced_profile[r], \
game.players[r]) for r in game.roles})
HR_game.addProfile({r:[payoff_data(s, reduced_profile[r][s], \
game.getPayoff(full_profile, r, s)) for s in \
full_profile[r]] for r in full_profile})
except KeyError:
continue
return HR_game
