API documentation

Representation of games

Game	A game, the fundamental unit of analysis in game theory.
Player	A player in a Game.
Outcome	An outcome in a Game.
Node	A node in a Game.
Infoset	An information set in a Game.
Action	A choice available at an Infoset in a Game.
Strategy	A plan of action for a Player in a Game.

Creating, reading, and writing games

Game.new_tree([players, title])	Create a new Game consisting of a trivial game tree, with one node, which is both root and terminal.
Game.new_table(dim[, title])	Create a new Game with a strategic representation.
Game.from_arrays(*arrays[, title])	Create a new Game with a strategic representation.
Game.from_dict(payoffs[, title])	Create a new Game with a strategic representation.
Game.read_game(filepath)	Construct a game from its serialised representation in a file.
Game.parse_game(text)	Construct a game from its serialised representation in a string
Game.write([format])	Produce a serialization of the game.

Transforming game trees

Game.append_move(nodes, player, actions)	Add a move for player at terminal nodes.
Game.append_infoset(nodes, infoset)	Add a move in information set infoset at terminal nodes.
Game.insert_move(node, player, actions)	Insert a move for player prior to the node node, with actions actions.
Game.insert_infoset(node, infoset)	Insert a move in information set infoset prior to the node node.
Game.copy_tree(src, dest)	Copy the subtree rooted at 'src' to 'dest'.
Game.move_tree(src, dest)	Move the subtree rooted at 'src' to 'dest'.
Game.delete_parent(node)	Delete the parent node of node.
Game.delete_tree(node)	Truncate the game tree at node, deleting the subtree beneath it.

Transforming game information structure

Game.set_player(infoset, player)	Set the player at an information set.
Game.set_infoset(node, infoset)	Place node in the information set infoset.
Game.leave_infoset(node)	Remove this node from its information set.
Game.reveal(infoset, player)	Reveals the move made at infoset to player.
Game.set_chance_probs(infoset, probs)	Set the action probabilities at chance information set infoset.

Transforming game components

Game.add_player([label])	Add a new player to the game.
Game.add_outcome([payoffs, label])	Add a new outcome to the game.
Game.delete_outcome(outcome)	Delete an outcome from the game.
Game.set_outcome(node, outcome)	Set outcome to be the outcome at node.
Game.add_strategy(player[, label])	Add a new strategy to the set of strategies for player.
Game.delete_strategy(strategy)	Delete strategy from the game.

Information about the game

Game.title	Get or set the title of the game.
Game.comment	Get or set the comment of the game.
Game.is_const_sum	Whether the game is constant sum.
Game.is_tree	Return whether a game has a tree-based representation.
Game.is_perfect_recall	Whether the game is perfect recall.
Game.players	The set of players in the game.
Game.outcomes	The set of outcomes in the game.
Game.min_payoff	The minimum payoff in the game.
Game.max_payoff	The maximum payoff in the game.
Game.strategies	The set of strategies in the game.
Game.root	The root node of the game.
Game.actions	The set of actions available in the game.
Game.infosets	The set of information sets in the game.
Game.nodes([subtree])	Return a list of nodes in the game tree.
Game.contingencies	An iterator over the contingencies in the game.

Player.label	Gets or sets the text label of the player.
Player.number	Returns the number of the player in its game.
Player.game	Gets the Game to which the player belongs.
Player.strategies	Returns the set of strategies belonging to the player.
Player.infosets	Returns the set of information sets at which the player has the decision.
Player.actions	Returns the set of actions available to the player at some information set.
Player.is_chance	Returns whether the player is the chance player.
Player.min_payoff	Returns the smallest payoff for the player in any outcome of the game.
Player.max_payoff	Returns the largest payoff for the player in any outcome of the game.
Player.strategies	Returns the set of strategies belonging to the player.

Outcome.label	The text label associated with this outcome.
Outcome.game	Returns the game with which this outcome is associated.

Node.label	The text label associated with the node.
Node.game	Gets the Game to which the node belongs.
Node.outcome	Returns the outcome attached to the node.
Node.children	The set of children of this node.
Node.parent	The parent of this node.
Node.is_subgame_root	Returns whether the node is the root of a proper subgame.
Node.is_terminal	Returns whether this is a terminal node of the game.
Node.prior_action	The action which leads to this node.
Node.prior_sibling	The node which is immediately before this one in its parent's children.
Node.next_sibling	The node which is immediately after this one in its parent's children.
Node.infoset	The information set to which this node belongs.
Node.player	The player who makes the decision at this node.
Node.is_successor_of(node)	Returns whether this node is a successor of node.

Infoset.label	Get or set the text label of the information set.
Infoset.game	The Game to which the information set belongs.
Infoset.is_chance	Whether the information set belongs to the chance player.
Infoset.player	The player who has the move at this information set.
Infoset.actions	The set of actions at the information set.
Infoset.members	The set of nodes which are members of the information set.
Infoset.precedes(node)	Return whether this information set precedes node in the game tree.

Action.label	Get or set the text label of the action.
Action.infoset	Get the information set to which the action belongs.
Action.precedes(node)	Returns whether node precedes this action in the extensive game.
Action.prob	Get the probability a chance action is played.

Strategy.label	Get or set the text label associated with the strategy.
Strategy.game	The game to which the strategy belongs.
Strategy.player	The player to which the strategy belongs.
Strategy.number	The number of the strategy.

Player behavior

Game.mixed_strategy_profile([data, rational])	Create a mixed strategy profile over the game.
Game.random_strategy_profile([denom, gen])	Create a MixedStrategy on the game, with probabilities drawn from the uniform distribution over the set of mixed strategy profiles.
Game.mixed_behavior_profile([data, rational])	Create a mixed behavior profile over the game.
Game.random_behavior_profile([denom, gen])	Create a MixedBehaviorProfile on the game, with probabilities drawn from the uniform distribution over the set of mixed behavior profiles.
Game.support_profile()

Representation of strategic behavior

Probability distributions over strategies

MixedStrategyProfile	Represents a mixed strategy profile over the strategies in a Game.
MixedStrategyProfile.game	The game on which this mixed strategy profile is defined.
MixedStrategyProfile.mixed_strategies()	Iterate over the mixed strategies in the profile.
MixedStrategyProfile.__iter__	Iterate over the probabilities assigned to strategies by the profile.
MixedStrategyProfile.__getitem__	Access a component of the mixed strategy profile specified by index.
MixedStrategyProfile.__setitem__	Sets a probability or a mixed strategy to value.
MixedStrategyProfile.payoff(player)	Returns the expected payoff to a player if all players play according to the profile.
MixedStrategyProfile.strategy_value(strategy)	Returns the expected payoff to playing the strategy, if all other players play according to the profile.
MixedStrategyProfile.strategy_regret(strategy)	Returns the regret to playing strategy, if all other players play according to the profile.
MixedStrategyProfile.player_regret(player)	Returns the regret of player for playing their mixed strategy, if all other players play according to the profile.
MixedStrategyProfile.max_regret()	Returns the maximum regret of any player.
MixedStrategyProfile.strategy_value_deriv(...)	Returns the derivative of the payoff to playing strategy, with respect to the probability that other is played.
MixedStrategyProfile.liap_value()	Returns the Lyapunov value (see [McK91]) of the strategy profile.
MixedStrategyProfile.as_behavior()	Creates a mixed behavior profile which is equivalent to this mixed strategy profile.
MixedStrategyProfile.normalize()	Create a profile with the same strategy proportions as this one, but normalised so probabilities for each player sum to one.
MixedStrategyProfile.copy()	Creates a copy of the mixed strategy profile.
MixedStrategy(profile, player)	A probability distribution over a player's strategies.
MixedStrategy.__iter__()	Iterate over the probabilities assigned to strategies by the mixed strategy.
MixedStrategy.__getitem__(index)	Returns the probability that the strategy referred to by index is played.
MixedStrategy.__setitem__(index, value)	Sets the probability a strategy is played.

Probability distributions over behavior

MixedBehaviorProfile	Represents a mixed behavior profile over the actions in a Game.
MixedBehaviorProfile.game	The game on which this mixed behavior profile is defined.
MixedBehaviorProfile.mixed_behaviors()	Iterate over the mixed behaviors in the profile.
MixedBehaviorProfile.mixed_actions()	Iterate over the mixed actions specified by the profile.
MixedBehaviorProfile.__iter__	Iterate over the probabilities assigned to actions by the profile.
MixedBehaviorProfile.__getitem__	Access a component of the mixed behavior specified by index.
MixedBehaviorProfile.__setitem__	Sets a probability, mixed agent strategy, or mixed behavior strategy to value.
MixedBehaviorProfile.payoff(player)	Returns the expected payoff to a player if all players play according to the profile.
MixedBehaviorProfile.action_regret(action)	Returns the regret to playing action, if all other players play according to the profile.
MixedBehaviorProfile.action_value(action)	Returns the expected payoff to the player of playing an action conditional on reaching its information set, if all players play according to the profile.
MixedBehaviorProfile.infoset_value(infoset)	Returns the expected payoff to the player conditional on reaching an information set, if all players play according to the profile.
MixedBehaviorProfile.node_value(player, node)	Returns the expected payoff to player conditional on play reaching node, if all players play according to the profile.
MixedBehaviorProfile.realiz_prob(node)	Returns the probability with which a node is reached.
MixedBehaviorProfile.infoset_prob(infoset)	Returns the probability with which an information set is reached.
MixedBehaviorProfile.belief(node)	Returns the conditional probability that a node is reached, given that its information set is reached.
MixedBehaviorProfile.is_defined_at(infoset)	Returns whether the profile has probabilities defined at the information set.
MixedBehaviorProfile.liap_value()	Returns the Lyapunov value (see [McK91]) of the strategy profile.
MixedBehaviorProfile.as_strategy()	Returns a MixedStrategyProfile which is equivalent to the profile.
MixedBehaviorProfile.normalize()	Create a profile with the same action proportions as this one, but normalised so probabilities for each infoset sum to one.
MixedBehaviorProfile.copy()	Creates a copy of the behavior strategy profile.
MixedBehavior(profile, player)	A set of probability distributions describing a player's behavior.
MixedBehavior.mixed_actions()	Iterate over the mixed actions specified by the mixed behavior.
MixedBehavior.__iter__()	Iterate over the probabilities assigned to actions by the mixed behavior.
MixedBehavior.__getitem__(index)	Access a component of the mixed behavior specified by index.
MixedBehavior.__setitem__(index, value)	Sets a component of the mixed behavior to value.
MixedAction(profile, infoset)	A probability distribution over a player's actions at an information set.
MixedAction.__iter__()	Iterate over the probabilities assigned to actions by the mixed action.
MixedAction.__getitem__(index)	Returns the probability that the action referred to by index is played.
MixedAction.__setitem__(index, value)	Sets the probability an action is played.

Computation on supports

undominated_strategies_solve(profile[, ...])

Return a support profile including only the strategies in profile which are not dominated by another pure strategy.

Computation of Nash equilibria

NashComputationResult(game, method, ...)	Represents the result of a method which computes Nash equilibria in a game.
enumpure_solve(game[, use_strategic])	Compute all pure-strategy Nash equilibria of game.
enummixed_solve(game[, rational, use_lrs])	Compute all mixed-strategy Nash equilibria of a two-player game using the strategic representation.
lp_solve(game[, rational, use_strategic])	Compute Nash equilibria of a two-player constant-sum game using linear programming.
lcp_solve(game[, rational, use_strategic, ...])	Compute Nash equilibria of a two-player game using linear complementarity programming.
liap_solve(start[, maxregret, maxiter])	Compute approximate Nash equilibria of a game using Lyapunov function minimization.
logit_solve(game[, use_strategic, ...])	Compute Nash equilibria of a game using the logit quantal response equilibrium correspondence.
simpdiv_solve(start[, maxregret, refine, leash])	Compute Nash equilibria of a game using simplicial subdivision.
ipa_solve(perturbation)	Compute Nash equilibria of a game using iterated polymatrix approximation.
gnm_solve(perturbation[, end_lambda, steps, ...])	Compute Nash equilibria of a game using a global Newton method.

Computation of quantal response equilibria

fit_empirical(data)	Use maximum likelihood estimation to estimate a quantal response equilibrium using the empirical payoff method.
fit_fixedpoint(data)	Use maximum likelihood estimation to find the logit quantal response equilibrium on the principal branch for a strategic game which best fits empirical frequencies of play.
LogitQREMixedStrategyFitResult(data, method, ...)	The result of fitting a QRE to a given probability distribution over strategies.