# Source code for axelrod.strategies.dbs

from axelrod.action import Action
from axelrod.player import Player

C, D = Action.C, Action.D

[docs]class DBS(Player):
"""
A strategy that learns the opponent's strategy and uses symbolic noise
detection for detecting whether anomalies in player’s behavior are
deliberate or accidental. From the learned opponent's strategy, a tree
search is used to choose the best move.

Default values for the parameters are the suggested values in the article.
When noise increases you can try to diminish violation_threshold and
rejection_threshold.

Names

- Derived Belief Strategy: [Au2006]_
"""

# These are various properties for the strategy
name = "DBS"
classifier = {
"memory_depth": float("inf"),
"stochastic": False,
"long_run_time": True,
"inspects_source": False,
"manipulates_source": False,
"manipulates_state": False,
}

def __init__(
self,
discount_factor=0.75,
promotion_threshold=3,
violation_threshold=4,
reject_threshold=3,
tree_depth=5,
):
"""
Parameters

discount_factor: float, optional
Used when computing discounted frequencies to learn opponent's
strategy. Must be between 0 and 1. The default is 0.75.
promotion_threshold: int, optional
Number of successive observations needed to promote an opponent
behavior as a deterministic rule. The default is 3.
violation_threshold: int, optional
Number of observations needed to considerate opponent's strategy has
changed. You can lower it when noise increases. The default is 4,
which is good for a noise level of .1.
reject_threshold: int, optional
Number of observations before forgetting opponent's previous
strategy. You can lower it when noise increases. The default is 3,
which is good for a noise level of .1.
tree_depth: int, optional
Depth of the tree for the tree-search algorithm. Higher depth means
more time to compute the move. The default is 5.
"""
super().__init__()

# The opponent's behavior is represented by a 3 dicts: Rd, Rc, and Rp.
# Its behavior is modeled by a set of rules. A rule is the move that
# the opponent will play (C or D or a probability to play C) after a
# given outcome (for instance after (C, D)).
# A rule can be deterministic or probabilistic:
# - Rc is the set of deterministic rules
# - Rp is the set of probabilistic rules
# - Rd is the default rule set which is used for initialization but also
# keeps track of previous policies when change in the opponent behavior
# happens, in order to have a smooth transition.
# - Pi is a set of rules that aggregates all above sets of rules in
# order to fully model the opponent's behavior.

# Default rule set is Rd.
# Default opponent's policy is TitForTat.
self.Rd = create_policy(1, 1, 0, 0)
# Set of current deterministic rules Rc
self.Rc = {}
# Aggregated rule set Pi
self.Pi = self.Rd
# For each rule in Rd we need to count the number of successive
# violations. Those counts are saved in violation_counts.
self.violation_counts = {}
self.reject_threshold = reject_threshold
self.violation_threshold = violation_threshold
self.promotion_threshold = promotion_threshold
self.tree_depth = tree_depth
# v is a violation count used to know when to clean the default rule
# set Rd
self.v = 0
# A discount factor for computing the probabilistic rules
self.alpha = discount_factor

# The probabilistic rule set Rp is not saved as an attribute, but each
# rule is computed only when needed. The rules are computed as
# discounted frequencies of opponent's past moves. To compute the
# discounted frequencies, we need to keep up to date an history of what
# has been played following each outcome (or condition):
# We save it as a dict history_by_cond; keys are conditions
# (ex (C, C)) and values are a tuple of 2 lists (G, F)
# for a condition j and an iteration i in the match:
# G[i] = 1 if cond j was True at turn i-1 and C has been played
# by the opponent; else G[i] = 0
# F[i] = 1 if cond j was True at turn i-1; else F[i] = 0
# This representation makes the computing of discounted frequencies
# easy and efficient.
# The initial hypothesized policy is TitForTat.
self.history_by_cond = {
(C, C): ([1], [1]),
(C, D): ([1], [1]),
(D, C): ([0], [1]),
(D, D): ([0], [1]),
}

[docs]    def should_promote(self, r_plus, promotion_threshold=3):
"""
This function determines if the move r_plus is a deterministic
behavior of the opponent, and then returns True, or if r_plus
is due to a random behavior (or noise) which would require a
probabilistic rule, in which case it returns False.

To do so it looks into the game history: if the k last times
when the opponent was in the same situation than in r_plus it
played the same thing then then r_plus is considered as a
deterministic rule (where K is the user-defined promotion_threshold).

Parameters

r_plus: tuple of (tuple of actions.Action, actions.Action)
example: ((C, C), D)
r_plus represents one outcome of the history, and the
following move played by the opponent.
promotion_threshold: int, optional
Number of successive observations needed to promote an
opponent behavior as a deterministic rule. Default is 3.
"""
if r_plus[1] == C:
opposite_action = 0
elif r_plus[1] == D:
opposite_action = 1
k = 1
count = 0
# We iterate on the history, while we do not encounter
# counter-examples of r_plus, i.e. while we do not encounter
# r_minus
while k < len(self.history_by_cond[r_plus[0]][0]) and not (
self.history_by_cond[r_plus[0]][0][1:][-k] == opposite_action
and self.history_by_cond[r_plus[0]][1][1:][-k] == 1
):
# We count every occurrence of r_plus in history
if self.history_by_cond[r_plus[0]][1][1:][-k] == 1:
count += 1
k += 1
if count >= promotion_threshold:
return True
return False

[docs]    def should_demote(self, r_minus, violation_threshold=4):
"""
Checks if the number of successive violations of a deterministic
rule (in the opponent's behavior) exceeds the user-defined
violation_threshold.
"""
return self.violation_counts[r_minus[0]] >= violation_threshold

[docs]    def update_history_by_cond(self, opponent_history):
"""
Updates self.history_by_cond between each turns of the game.
"""
two_moves_ago = (self.history[-2], opponent_history[-2])
for outcome, GF in self.history_by_cond.items():
G, F = GF
if outcome == two_moves_ago:
if opponent_history[-1] == C:
G.append(1)
else:
G.append(0)
F.append(1)
else:
G.append(0)
F.append(0)

[docs]    def compute_prob_rule(self, outcome, alpha=1):
"""
Uses the game history to compute the probability of the opponent
playing C, in the outcome situation (example: outcome = (C, C)).
When alpha = 1, the results is approximately equal to the frequency of
the occurrence of outcome C. alpha is a discount factor that gives more
weight to recent events than earlier ones.

Parameters

outcome: tuple of two actions.Action
alpha: int, optional. Discount factor. Default is 1.
"""
G = self.history_by_cond[outcome][0]
F = self.history_by_cond[outcome][1]
discounted_g = 0
discounted_f = 0
alpha_k = 1
for g, f in zip(G[::-1], F[::-1]):
discounted_g += alpha_k * g
discounted_f += alpha_k * f
alpha_k = alpha * alpha_k
p_cond = discounted_g / discounted_f
return p_cond

[docs]    def strategy(self, opponent: Player) -> Action:
"""Actual strategy definition that determines player's action."""
# First move
if not self.history:
return C
if len(opponent.history) >= 2:
# We begin by update history_by_cond (i.e. update Rp)
self.update_history_by_cond(opponent.history)
two_moves_ago = (self.history[-2], opponent.history[-2])
# r_plus is the information of what the opponent just played,
# following the previous outcome two_moves_ago.
r_plus = (two_moves_ago, opponent.history[-1])
# r_minus is the opposite move, following the same outcome.
r_minus = (two_moves_ago, ({C, D} - {opponent.history[-1]}).pop())

# If r_plus and r_minus are not in the current set of deterministic
# rules, we check if r_plus should be added to it (following the
# rule defined in the should_promote function).
if r_plus[0] not in self.Rc.keys():
if self.should_promote(r_plus, self.promotion_threshold):
self.Rc[r_plus[0]] = action_to_int(r_plus[1])
self.violation_counts[r_plus[0]] = 0
self.violation_counts[r_plus[0]] = 0

# If r+ or r- in Rc
if r_plus[0] in self.Rc.keys():
to_check = C if self.Rc[r_plus[0]] == 1 else D
# (if r+ in Rc)
if r_plus[1] == to_check:
# Set the violation count of r+ to 0.
self.violation_counts[r_plus[0]] = 0
# if r- in Rc
elif r_minus[1] == to_check:
# Increment violation count of r-.
self.violation_counts[r_plus[0]] += 1
# As we observe that the behavior of the opponent is
# opposed to a rule modeled in Rc, we check if the number
# of consecutive violations of this rule is superior to
# a threshold. If it is, we clean Rc, but we keep the rules
# of Rc in Rd for smooth transition.
if self.should_demote(r_minus, self.violation_threshold):
self.Rd.update(self.Rc)
self.Rc.clear()
self.violation_counts.clear()
self.v = 0
# r+ in Rc.
r_plus_in_Rc = r_plus[0] in self.Rc.keys() and self.Rc[
r_plus[0]
] == action_to_int(r_plus[1])
# r- in Rd
r_minus_in_Rd = r_minus[0] in self.Rd.keys() and self.Rd[
r_minus[0]
] == action_to_int(r_minus[1])

# Increment number of violations of Rd rules.
if r_minus_in_Rd:
self.v += 1
# If the number of violations is superior to a threshold, clean Rd.
if (self.v > self.reject_threshold) or (
r_plus_in_Rc and r_minus_in_Rd
):
self.Rd.clear()
self.v = 0

# Compute Rp for conditions that are neither in Rc or Rd.
Rp = {}
all_cond = [(C, C), (C, D), (D, C), (D, D)]
for outcome in all_cond:
if (outcome not in self.Rc.keys()) and (
outcome not in self.Rd.keys()
):
# Compute opponent's C answer probability.
Rp[outcome] = self.compute_prob_rule(outcome, self.alpha)

# We aggregate the rules of Rc, Rd, and Rp in a set of rule Pi.
self.Pi = {}
# The algorithm makes sure that a rule cannot be in two different
# sets of rules so we do not need to check for duplicates.
self.Pi.update(self.Rc)
self.Pi.update(self.Rd)
self.Pi.update(Rp)

# React to the opponent's last move
return move_gen(
(self.history[-1], opponent.history[-1]),
self.Pi,
depth_search_tree=self.tree_depth,
)

[docs]class Node(object):
"""
Nodes used to build a tree for the tree-search procedure. The tree has
Deterministic and Stochastic nodes, as the opponent's strategy is learned
as a probability distribution.
"""

# abstract method
def get_siblings(self):
raise NotImplementedError("subclasses must override get_siblings()!")

# abstract method
def is_stochastic(self):
raise NotImplementedError("subclasses must override is_stochastic()!")

[docs]class StochasticNode(Node):
"""
Node that have a probability pC to get to each sibling. A StochasticNode can
be written (C, X) or (D, X), with X = C with a probability pC, else X = D.
"""

def __init__(self, own_action, pC, depth):
self.pC = pC
self.depth = depth
self.own_action = own_action

[docs]    def get_siblings(self):
"""
Returns the siblings node of the current StochasticNode. There are two
siblings which are DeterministicNodes, their depth is equal to current
node depth's + 1.
"""
opponent_c_choice = DeterministicNode(
self.own_action, C, self.depth + 1
)
opponent_d_choice = DeterministicNode(
self.own_action, D, self.depth + 1
)
return opponent_c_choice, opponent_d_choice

[docs]    def is_stochastic(self):
"""Returns True if self is a StochasticNode."""
return True

[docs]class DeterministicNode(Node):
"""
Nodes (C, C), (C, D), (D, C), or (D, D) with deterministic choice
for siblings.
"""

def __init__(self, action1, action2, depth):
self.action1 = action1
self.action2 = action2
self.depth = depth

[docs]    def get_siblings(self, policy):
"""
Returns the siblings node of the current DeterministicNode. Builds 2
siblings (C, X) and (D, X) that are StochasticNodes. Those siblings are
of the same depth as the current node. Their probabilities pC are
defined by the policy argument.
"""
c_choice = StochasticNode(
C, policy[(self.action1, self.action2)], self.depth
)
d_choice = StochasticNode(
D, policy[(self.action1, self.action2)], self.depth
)
return c_choice, d_choice

[docs]    def is_stochastic(self):
"""Returns True if self is a StochasticNode."""
return False

def get_value(self):
values = {(C, C): 3, (C, D): 0, (D, C): 5, (D, D): 1}
return values[(self.action1, self.action2)]

[docs]def create_policy(pCC, pCD, pDC, pDD):
"""
Creates a dict that represents a Policy. As defined in the reference, a
Policy is a set of (prev_move, p) where p is the probability to cooperate
after prev_move, where prev_move can be (C, C), (C, D), (D, C) or (D, D).

Parameters

pCC, pCD, pDC, pDD : float
Must be between 0 and 1.
"""
return {(C, C): pCC, (C, D): pCD, (D, C): pDC, (D, D): pDD}

def action_to_int(action):
if action == C:
return 1
return 0

[docs]def minimax_tree_search(begin_node, policy, max_depth):
"""
Tree search function (minimax search procedure) for the tree (built by
recursion) corresponding to the opponent's policy, and solves it.
Returns a tuple of two floats that are the utility of playing C, and the
utility of playing D.
"""
if begin_node.is_stochastic():
# A stochastic node cannot have the same depth than its parent node
# hence there is no need to check that its depth is < max_depth.
siblings = begin_node.get_siblings()
# The stochastic node value is the expected value of siblings.
node_value = begin_node.pC * minimax_tree_search(
siblings[0], policy, max_depth
) + (1 - begin_node.pC) * minimax_tree_search(
siblings[1], policy, max_depth
)
return node_value
else:  # Deterministic node
if begin_node.depth == max_depth:
# This is an end node, we just return its outcome value.
return begin_node.get_value()
elif begin_node.depth == 0:
siblings = begin_node.get_siblings(policy)
# This returns the two max expected values, for choice C or D,
# as a tuple.
return (
minimax_tree_search(siblings[0], policy, max_depth)
+ begin_node.get_value(),
minimax_tree_search(siblings[1], policy, max_depth)
+ begin_node.get_value(),
)
elif begin_node.depth < max_depth:
siblings = begin_node.get_siblings(policy)
# The deterministic node value is the max of both siblings values
# + the score of the outcome of the node.
a = minimax_tree_search(siblings[0], policy, max_depth)
b = minimax_tree_search(siblings[1], policy, max_depth)
node_value = max(a, b) + begin_node.get_value()
return node_value

[docs]def move_gen(outcome, policy, depth_search_tree=5):
"""
Returns the best move considering opponent's policy and last move,
using tree-search procedure.
"""
current_node = DeterministicNode(outcome[0], outcome[1], depth=0)
values_of_choices = minimax_tree_search(
current_node, policy, depth_search_tree
)
# Returns the Action which correspond to the best choice in terms of
# expected value. In case value(C) == value(D), returns C.
actions_tuple = (C, D)
return actions_tuple[values_of_choices.index(max(values_of_choices))]